Ferrara.ps

%!PS-Adobe-2.0
%%Creator: dvips(k) 5.86 Copyright 1999 Radical Eye Software
%%Title: arXiv:hep-th/9605032 v1   6 May 1996
%%Pages: 82
%%PageOrder: Ascend
%%BoundingBox: 0 0 596 842
%%DocumentPaperSizes: a4
%%EndComments
%DVIPSWebPage: (www.radicaleye.com)
%DVIPSCommandLine: /e-prints/home/teTeX/bin/i686-linux/dvihps -z -R -K1
%+ 9605032.dvi -o
%DVIPSParameters: dpi=300, compressed, comments removed
%DVIPSSource:  TeX output 2003.03.05:1913
%%BeginProcSet: texc.pro
/TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S
N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72
mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0
0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{
landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize
mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[
matrix currentmatrix{A A round sub abs 0.00001 lt{round}if}forall round
exch round exch]setmatrix}N/@landscape{/isls true N}B/@manualfeed{
statusdict/manualfeed true put}B/@copies{/#copies X}B/FMat[1 0 0 -1 0 0]
N/FBB[0 0 0 0]N/nn 0 N/IEn 0 N/ctr 0 N/df-tail{/nn 8 dict N nn begin
/FontType 3 N/FontMatrix fntrx N/FontBBox FBB N string/base X array
/BitMaps X/BuildChar{CharBuilder}N/Encoding IEn N end A{/foo setfont}2
array copy cvx N load 0 nn put/ctr 0 N[}B/sf 0 N/df{/sf 1 N/fntrx FMat N
df-tail}B/dfs{div/sf X/fntrx[sf 0 0 sf neg 0 0]N df-tail}B/E{pop nn A
definefont setfont}B/Cw{Cd A length 5 sub get}B/Ch{Cd A length 4 sub get
}B/Cx{128 Cd A length 3 sub get sub}B/Cy{Cd A length 2 sub get 127 sub}
B/Cdx{Cd A length 1 sub get}B/Ci{Cd A type/stringtype ne{ctr get/ctr ctr
1 add N}if}B/id 0 N/rw 0 N/rc 0 N/gp 0 N/cp 0 N/G 0 N/CharBuilder{save 3
1 roll S A/base get 2 index get S/BitMaps get S get/Cd X pop/ctr 0 N Cdx
0 Cx Cy Ch sub Cx Cw add Cy setcachedevice Cw Ch true[1 0 0 -1 -.1 Cx
sub Cy .1 sub]/id Ci N/rw Cw 7 add 8 idiv string N/rc 0 N/gp 0 N/cp 0 N{
rc 0 ne{rc 1 sub/rc X rw}{G}ifelse}imagemask restore}B/G{{id gp get/gp
gp 1 add N A 18 mod S 18 idiv pl S get exec}loop}B/adv{cp add/cp X}B
/chg{rw cp id gp 4 index getinterval putinterval A gp add/gp X adv}B/nd{
/cp 0 N rw exit}B/lsh{rw cp 2 copy get A 0 eq{pop 1}{A 255 eq{pop 254}{
A A add 255 and S 1 and or}ifelse}ifelse put 1 adv}B/rsh{rw cp 2 copy
get A 0 eq{pop 128}{A 255 eq{pop 127}{A 2 idiv S 128 and or}ifelse}
ifelse put 1 adv}B/clr{rw cp 2 index string putinterval adv}B/set{rw cp
fillstr 0 4 index getinterval putinterval adv}B/fillstr 18 string 0 1 17
{2 copy 255 put pop}for N/pl[{adv 1 chg}{adv 1 chg nd}{1 add chg}{1 add
chg nd}{adv lsh}{adv lsh nd}{adv rsh}{adv rsh nd}{1 add adv}{/rc X nd}{
1 add set}{1 add clr}{adv 2 chg}{adv 2 chg nd}{pop nd}]A{bind pop}
forall N/D{/cc X A type/stringtype ne{]}if nn/base get cc ctr put nn
/BitMaps get S ctr S sf 1 ne{A A length 1 sub A 2 index S get sf div put
}if put/ctr ctr 1 add N}B/I{cc 1 add D}B/bop{userdict/bop-hook known{
bop-hook}if/SI save N @rigin 0 0 moveto/V matrix currentmatrix A 1 get A
mul exch 0 get A mul add .99 lt{/QV}{/RV}ifelse load def pop pop}N/eop{
SI restore userdict/eop-hook known{eop-hook}if showpage}N/@start{
userdict/start-hook known{start-hook}if pop/VResolution X/Resolution X
1000 div/DVImag X/IEn 256 array N 2 string 0 1 255{IEn S A 360 add 36 4
index cvrs cvn put}for pop 65781.76 div/vsize X 65781.76 div/hsize X}N
/p{show}N/RMat[1 0 0 -1 0 0]N/BDot 260 string N/Rx 0 N/Ry 0 N/V{}B/RV/v{
/Ry X/Rx X V}B statusdict begin/product where{pop false[(Display)(NeXT)
(LaserWriter 16/600)]{A length product length le{A length product exch 0
exch getinterval eq{pop true exit}if}{pop}ifelse}forall}{false}ifelse
end{{gsave TR -.1 .1 TR 1 1 scale Rx Ry false RMat{BDot}imagemask
grestore}}{{gsave TR -.1 .1 TR Rx Ry scale 1 1 false RMat{BDot}
imagemask grestore}}ifelse B/QV{gsave newpath transform round exch round
exch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlineto
fill grestore}B/a{moveto}B/delta 0 N/tail{A/delta X 0 rmoveto}B/M{S p
delta add tail}B/b{S p tail}B/c{-4 M}B/d{-3 M}B/e{-2 M}B/f{-1 M}B/g{0 M}
B/h{1 M}B/i{2 M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p -3 w}B/n{
p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{0 S
rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end

%%EndProcSet
%%BeginProcSet: special.pro
TeXDict begin/SDict 200 dict N SDict begin/@SpecialDefaults{/hs 612 N
/vs 792 N/ho 0 N/vo 0 N/hsc 1 N/vsc 1 N/ang 0 N/CLIP 0 N/rwiSeen false N
/rhiSeen false N/letter{}N/note{}N/a4{}N/legal{}N}B/@scaleunit 100 N
/@hscale{@scaleunit div/hsc X}B/@vscale{@scaleunit div/vsc X}B/@hsize{
/hs X/CLIP 1 N}B/@vsize{/vs X/CLIP 1 N}B/@clip{/CLIP 2 N}B/@hoffset{/ho
X}B/@voffset{/vo X}B/@angle{/ang X}B/@rwi{10 div/rwi X/rwiSeen true N}B
/@rhi{10 div/rhi X/rhiSeen true N}B/@llx{/llx X}B/@lly{/lly X}B/@urx{
/urx X}B/@ury{/ury X}B/magscale true def end/@MacSetUp{userdict/md known
{userdict/md get type/dicttype eq{userdict begin md length 10 add md
maxlength ge{/md md dup length 20 add dict copy def}if end md begin
/letter{}N/note{}N/legal{}N/od{txpose 1 0 mtx defaultmatrix dtransform S
atan/pa X newpath clippath mark{transform{itransform moveto}}{transform{
itransform lineto}}{6 -2 roll transform 6 -2 roll transform 6 -2 roll
transform{itransform 6 2 roll itransform 6 2 roll itransform 6 2 roll
curveto}}{{closepath}}pathforall newpath counttomark array astore/gc xdf
pop ct 39 0 put 10 fz 0 fs 2 F/|______Courier fnt invertflag{PaintBlack}
if}N/txpose{pxs pys scale ppr aload pop por{noflips{pop S neg S TR pop 1
-1 scale}if xflip yflip and{pop S neg S TR 180 rotate 1 -1 scale ppr 3
get ppr 1 get neg sub neg ppr 2 get ppr 0 get neg sub neg TR}if xflip
yflip not and{pop S neg S TR pop 180 rotate ppr 3 get ppr 1 get neg sub
neg 0 TR}if yflip xflip not and{ppr 1 get neg ppr 0 get neg TR}if}{
noflips{TR pop pop 270 rotate 1 -1 scale}if xflip yflip and{TR pop pop
90 rotate 1 -1 scale ppr 3 get ppr 1 get neg sub neg ppr 2 get ppr 0 get
neg sub neg TR}if xflip yflip not and{TR pop pop 90 rotate ppr 3 get ppr
1 get neg sub neg 0 TR}if yflip xflip not and{TR pop pop 270 rotate ppr
2 get ppr 0 get neg sub neg 0 S TR}if}ifelse scaleby96{ppr aload pop 4
-1 roll add 2 div 3 1 roll add 2 div 2 copy TR .96 dup scale neg S neg S
TR}if}N/cp{pop pop showpage pm restore}N end}if}if}N/normalscale{
Resolution 72 div VResolution 72 div neg scale magscale{DVImag dup scale
}if 0 setgray}N/psfts{S 65781.76 div N}N/startTexFig{/psf$SavedState
save N userdict maxlength dict begin/magscale true def normalscale
currentpoint TR/psf$ury psfts/psf$urx psfts/psf$lly psfts/psf$llx psfts
/psf$y psfts/psf$x psfts currentpoint/psf$cy X/psf$cx X/psf$sx psf$x
psf$urx psf$llx sub div N/psf$sy psf$y psf$ury psf$lly sub div N psf$sx
psf$sy scale psf$cx psf$sx div psf$llx sub psf$cy psf$sy div psf$ury sub
TR/showpage{}N/erasepage{}N/copypage{}N/p 3 def @MacSetUp}N/doclip{
psf$llx psf$lly psf$urx psf$ury currentpoint 6 2 roll newpath 4 copy 4 2
roll moveto 6 -1 roll S lineto S lineto S lineto closepath clip newpath
moveto}N/endTexFig{end psf$SavedState restore}N/@beginspecial{SDict
begin/SpecialSave save N gsave normalscale currentpoint TR
@SpecialDefaults count/ocount X/dcount countdictstack N}N/@setspecial{
CLIP 1 eq{newpath 0 0 moveto hs 0 rlineto 0 vs rlineto hs neg 0 rlineto
closepath clip}if ho vo TR hsc vsc scale ang rotate rwiSeen{rwi urx llx
sub div rhiSeen{rhi ury lly sub div}{dup}ifelse scale llx neg lly neg TR
}{rhiSeen{rhi ury lly sub div dup scale llx neg lly neg TR}if}ifelse
CLIP 2 eq{newpath llx lly moveto urx lly lineto urx ury lineto llx ury
lineto closepath clip}if/showpage{}N/erasepage{}N/copypage{}N newpath}N
/@endspecial{count ocount sub{pop}repeat countdictstack dcount sub{end}
repeat grestore SpecialSave restore end}N/@defspecial{SDict begin}N
/@fedspecial{end}B/li{lineto}B/rl{rlineto}B/rc{rcurveto}B/np{/SaveX
currentpoint/SaveY X N 1 setlinecap newpath}N/st{stroke SaveX SaveY
moveto}N/fil{fill SaveX SaveY moveto}N/ellipse{/endangle X/startangle X
/yrad X/xrad X/savematrix matrix currentmatrix N TR xrad yrad scale 0 0
1 startangle endangle arc savematrix setmatrix}N end

%%EndProcSet
%%BeginProcSet: hps.pro
/HPSdict 20 dict dup begin /braindeaddistill 50 def /rfch{dup length 1
sub 1 exch getinterval}bind def /splituri{dup(#)search{exch pop}{()exch}
ifelse dup(file:)anchorsearch{pop exch pop 3 -1 roll pop false}{pop 3 -1
roll exch pop true}ifelse}bind def /lookuptarget{exch rfch dup
/TargetAnchors where{pop TargetAnchors dup 3 -1 roll known{exch get true
}{pop pop false}ifelse}{pop pop(target dictionary unknown\012)print
false}ifelse}bind def /savecount 0 def /stackstopped{count counttomark
sub /savecount exch store stopped count savecount sub 1 sub dup 0 gt{{
exch pop}repeat}{pop}ifelse}bind def /tempstring 256 string def
/targetvalidate{1 index dup length 255 gt exch tempstring cvs dup(/)
search{pop pop pop exch pop true exch}{pop}ifelse cvn tempstring cvs
token pop pop length 0 ne or not}bind def /targetdump-hook where{pop}{
/targetdump-hook{dup mark exch gsave initmat setmatrix{{mark /Dest 4 2
roll targetvalidate{aload pop exch pop /Page 3 1 roll /View exch[exch
/FitH exch]/DEST pdfmark}{cleartomark}ifelse}forall}stackstopped pop
grestore}bind def}ifelse /baseurl{mark exch 1 dict dup 3 -1 roll /Base
exch put /URI exch /DOCVIEW{pdfmark}stackstopped pop}bind def
/externalhack systemdict /PDF known def /oldstyle true def /initmat
matrix currentmatrix def /actiondict 2 dict dup /Subtype /URI put def
/weblinkhandler{dup 3 1 roll mark 4 1 roll /Title 4 1 roll splituri 3 -1
roll dup length 0 gt{cvn /Dest exch 4 2 roll}{pop}ifelse{externalhack{
/HTTPFile exch}{actiondict dup 3 -1 roll /URI exch put /Action exch}
ifelse}{externalhack{/HTTPFile exch}{/File exch /Action /GoToR}ifelse}
ifelse counttomark 2 sub -1 roll aload pop /Rect 4 1 roll /Border 3 1
roll /Color exch oldstyle{/LNK}{/Subtype /Link /ANN}ifelse gsave initmat
setmatrix{pdfmark}stackstopped grestore}bind def /externalhandler where{
pop}{/externalhandler{2 copy{weblinkhandler}exec{/externalhack
externalhack not store 2 copy{weblinkhandler}exec{/externalhack
externalhack not store /oldstyle false store 2 copy{weblinkhandler}exec{
(WARNING: external refs disabled\012)print /externalhandler{pop pop}
bind store externalhandler}{pop pop}ifelse}{pop pop /externalhack
externalhack not store}ifelse}{pop pop /externalhandler{weblinkhandler
pop}bind store}ifelse}bind def}ifelse /pdfmnew{dup type /stringtype eq{
externalhandler}{exch dup rfch exch 3 -1 roll lookuptarget{mark 4 1 roll
/Title 4 1 roll aload pop exch pop /Page 3 1 roll /View exch[exch /FitH
exch]5 -1 roll aload pop /Rect 4 1 roll /Border 3 1 roll /Color exch
/LNK gsave initmat setmatrix pdfmark grestore}{pop pop}ifelse}ifelse}
bind def /pdfmold{dup type /stringtype eq{externalhandler}{exch dup rfch
exch 3 -1 roll lookuptarget{mark 4 1 roll /Title 4 1 roll aload pop exch
pop /Page 3 1 roll /View exch[exch /FitH exch]5 -1 roll aload pop pop 0
3 getinterval /Rect 3 1 roll /Border exch /LNK gsave initmat setmatrix
pdfmark grestore}{pop pop}ifelse}ifelse}bind def /pdfm where{pop}{/pdfm
/currentdistillerparams where{pop currentdistillerparams dup
/CoreDistVersion known{/CoreDistVersion get}{0}ifelse dup
braindeaddistill le{(WARNING: switching to old pdfm because version =)
print == /pdfmold}{pop /pdfmnew}ifelse load}{/pdfmark where{pop{dup type
/stringtype eq{externalhandler}{2 copy mark 3 1 roll{pdfmnew}
stackstopped{2 copy mark 3 1 roll{pdfmold}stackstopped{
(WARNING: pdfm disabled\012)print /pdfm{pop pop}store}{
(WARNING: new pdfm failed, switching to old pdfm\012)print /pdfm
/pdfmold load store}ifelse}{/pdfm /pdfmnew load store}ifelse pop pop}
ifelse}}{{pop pop}}ifelse}ifelse bind def}ifelse end def

%%EndProcSet
TeXDict begin 39158280 55380996 1000 300 300 (9605032.dvi)
@start
%DVIPSBitmapFont: Fa cmss10 10 1
/Fa 1 91 df<387FFFF0A2380001E0130314C013071480EB0F005B131E133E133C5B13F8
5B12015B485A12075B120F90C7FC121E123E123C127C1278B512F0A2141D7E9C19>90
D E
%EndDVIPSBitmapFont
%DVIPSBitmapFont: Fb cmsy10 17.28 1
/Fb 1 11 df<EC1FF0ECFFFE903907E00FC090390F0001E00138EB0038498001C0140648
488000031680D806C0EC06C0D80C60EC0C606D1418486CEC30306D1460486CECC0186DEB
01803B60018003000C903800C006EC600C6E5A486D4813066E5A6E5A6E5A92C7FC81EC06
C0EC0C604A7E0060496C130C4A7E4A7E49487E3B3003000180180106EB00C06C48EC6030
4914306C48EC186049140C6C48EC06C06C48EC0380000116006C6C14060170141C6D5C01
0FEB01E0903907E00FC0902600FFFEC7FCEC1FF02F317CA938>10
D E
%EndDVIPSBitmapFont
%DVIPSBitmapFont: Fc cmr17 17.28 3
/Fc 3 94 df<EB7F803801FFF0380701F8380C007E48131F00107F48148048EB07C0A2EC
03E012B012F87EA31278C7FCEC07C0A21580140F15005C141E5C5C14705C495A495A49C7
FC130E130C5B5B5B491320485A48C7FC000614405A12084814C0003FB5FC481480B6FCA2
1B2F7DAE21>50 D<EAFFC0A3EAE000B3B3B3ACEAFFC0A30A4879B512>91
D<EAFFC0A31201B3B3B3AC12FFA30A487FB512>93 D E
%EndDVIPSBitmapFont
%DVIPSBitmapFont: Fd cmmi12 17.28 7
/Fd 7 111 df<1238127C12FEA212FF127D12391201A41202A31204A21208A212101220
124008157A8614>59 D<90270FFFFE01B512C0A2D9003FC73807E000023E5DA44A4A5AA4
4A4AC7FCA44948143EA449485CA449B65AA202C0C7FCA24948495AA449C7485AA4013E4A
5AA4494A5AA4494AC8FCA300015D3B7FFFE00FFFFCB55B3A317DB03A>72
D<ED3FE0913803E03C91380F000F023CEB078002F0EB03C04948EB01E04948EB00F0D90F
80147849C8FC013E157C49153C49153EA2485A4848153F12075B120F5B121FA248C9FCA3
007E167EA4007C16FC12FC17F81601A2EE03F017E01607007C16C0EE0F80A2EE1F006C01
3E133E02415B001E9038808078261F01005BD80F02EB41E0D80782EB4780D803C2014FC7
FCD801E2137CD800F213F090263F03C01380903807FC4090C712609238E00100A25E1606
EDF00EEDF83CEDFFFC5E6F5A5E6F5A6FC7FC30407DB138>81 D<913803F80191381FFF03
91387C07879138E001C7903901C0006E49C7127E0106143E130E49141C13181338A24914
18A401781400A2137C137E6D7E14F06DB4FC6D13E06D13F801017F9038001FFEEC01FF91
38003F80150F150716C01503A3120C481580A3160000385C1506150E003C5C007C141800
7E5C007714E03973C001C039E1F00F8026C07FFEC7FC38800FF028337CB12B>83
D<0007B81280A23B0FF000FC003F018049130F90C7EC0700120E5A0018495AA2481606A2
4A5A5AA34849485BC792C7FCA34A5AA44AC9FCA4143EA45CA45CA4495AA4495AA3EB0FF0
000FB512F0A231317FB029>I<2703C003F0137E3C0C701C1C0383803C0838300E0601C0
00109026400F087F3B303C80071000D93D005BD8603F02E07F013E5C013C4A5BD8C07C01
0F1301017814001200A249011E495AA34D5A48485BA24DC7FC19804848491401171EA2F0
0300484849131C180618046048484848EB0E3000066D48EB03C0391F7E9E3D>109
D<3903C007E03904301838390838601C39103CC00E38303D80EB3F00D8603E130FA2013C
130ED8C07C131E13781200A2495BA35D485AA25D160848481418EC01E0A21630D8078013
C016601640168048C7EAE3000006143C251F7E9E2A>I E
%EndDVIPSBitmapFont
%DVIPSBitmapFont: Fe cmbx6 6 1
/Fe 1 89 df<387FC3F8381F00C0380F8180EA07C33803E700EA01FE6C5A5B137C137E13
DF38018F80380387C0EA0703380E01E0001C13F038FF03FE17117F901A>88
D E
%EndDVIPSBitmapFont
%DVIPSBitmapFont: Ff cmbx8 8 4
/Ff 4 90 df<EB7F813803FFF73807E03F380F000F001E13075A007C1303127800F81300
A700781303127C123C6C13066C130C3807E0383803FFF038007FC018177E961D>67
D<B5FC14E0381F01F06D7E147CA4147814F8EB01E0EBFF80EB03E06D7E6D7EA51560A239
FFE07C40EC1F801B177E961E>82 D<397FF07FC0A23907C01C006D5A6C6C5A3801F86000
005B13FDEB7F806DC7FC7F8080497E1333EB63F0EBC1F83801C0FC3803807CEB007E0006
7F39FFC0FFF0A21C177F961F>88 D<39FFE00FF0A2390FC00380EC07003807E0063803F0
0E6C6C5A14186C6C5AEB7E70EB3F605C131F6D5AA8EB7FF0A21C177F961F>I
E
%EndDVIPSBitmapFont
%DVIPSBitmapFont: Fg cmsl12 12 22
/Fg 22 122 df<3A07FFC1FFF03A007C001F000178131EA5495BA648485BA390B512F890
38E00078A248485BA64848485AA64848485A01807F39FFF83FFE24227DA125>72
D<D807FCEC1FF0D8007CEC3F00015E143E165EA2169EA2018F495AA21502A21504903887
8008D801075C1510A21520EB03C0154000025D1580A2903801E100A214E200044A5A14E4
EB00F8A214F0120C4A485A003E01607F3AFFC0403FFE2C227DA12D>77
D<90380FC080EB30319038C00B00380180071203497E5AA2000E1302A2120F91C7FCA27F
EA07E013FE3803FFC06C7F6C6C7EEB0FF81300147880A31220481338A300601330147014
6000F05B38E80180D8C607C7FCEA81FC19247DA21B>83 D<EA07FCEA0C06EA1E031480EA
0C01000013C0EB0380A2137FEA03E3EA0F03121C38380700127800F01308A2130FA2EB17
10387867A0381F83C015157D9418>97 D<EA0780123F0007C7FCA6120EA6EA1C3FEBC180
381D00C0001E13E0001C1370A2481378A64813F0A214E0130114C0EB038038E80700EAC4
1CEA83F015237BA21B>I<13FF380381C0EA0603120C381C018048C7FC1278127012F0A5
5AA26C138038700100A2EA3806EA1C18EA07E012157C9416>I<141E14FE141CA61438A6
EB7C70EA0383380700F0120C001C13705A007813E0127012F0A438E001C0A4EA7003A238
380F80381C33C03807C3F817237CA21B>I<13FE38038380380701C0380C00E0121C5A12
781270B5FC00F0C7FCA45AA26C134000701380123038380300EA0E0CEA03F013157D9416
>I<EB03C0EB0C30EB3870EB30F0EB7070EBE000A3485AA6EA7FFCEA0380A548C7FCA612
0EA65A121EEAFFE014237EA20F>I<EC0780EB3F08EBE1D13801C0E139038070001207A2
380F00F0A35CEA070100035BD80787C7FCEA04FC48C8FCA3120C380FFF8014E06C7F3818
00784813185AA25AA25C00605B6C5B381C0780D803FCC7FC1921809518>I<136013F012
01A2EA00E01300A8EA01C0120F1201A4EA0380A6EA0700A6120E120FEAFFC00C227FA10E
>105 D<1378EA03F8EA0070A613E0A6EA01C0A6EA0380A6EA0700A6120E120FEAFFE00D
237FA20E>108 D<3A01C1F807E03A0FC60C18303A01D80E60389039E007801CA201C013
000003491338EB800EA54848481370A6000E4913E0000F013C13F03AFFE3FF8FFE27157F
942A>I<3801C3F0380FCC183801D00CEBE00EA213C00003131C1380A538070038A6000E
1370000F137838FFE7FF18157F941B>I<137E38038380380600C04813E0001C13705A00
781378127012F0A44813F0A214E0EAF001007013C0EB038038380700EA1C1CEA07F01515
7D9418>I<EBE1F83807E60C3800E806EBF0079038E00380A2D801C013C0A63903800780
A215005C141E141C38074038EB20E0EB1F8090C8FCA3120EA5121EEAFFC01A1F80941B>
I<EB7C10EA038238070130380E00F05A5A007813E0A25AA4EB01C0A4EA7003130538380B
80EA1C33EA07C3EA0003A3EB0700A55BEB7FE0141F7C941A>I<3801C3C0380FCCE0EA01
D113E1EBE0C0EBC00012035BA548C7FCA6120E120FEAFFF013157F9413>I<EA01F9EA06
07EA0C0312181301A21302EA1C00EA1FC0EA0FF8EA07FCEA007E130EEA4006A31260130C
EAE008EAD830EA87C010157E9413>I<1380A3120113005AA25A5A5AEAFFFCEA0E00A55A
A6EA3810A51320A2EA1C40EA07800E1F7C9E13>I<001C13E0EAFC07EA1C00A4383801C0
A638700380A41307130BEB170038382780380FC7F014157B941B>I<390FFC0FF03901E0
07800000EB030014025CA26D5A13705CA2EB7820EB3840A25C133C011DC7FCA2131E131C
130C1308A25BA25B5B12F05B00F1C8FC12C2127C1C1F80941A>121
D E
%EndDVIPSBitmapFont
%DVIPSBitmapFont: Fh cmmi12 14.4 5
/Fh 5 111 df<127812FCA212FEA2127A1202A41204A31208A212101220124007127B85
10>59 D<90263FFFC0B5FC49018113FE903A03F0000FC04A1480A44948EB1F00A4494813
3EA449C75AA449B55AA2013EC7FCA249495AA449495AA44848495AA44848495AA3000714
1FB53803FFFCA230297DA830>72 D<EC03FC91381C07809138F001C0903901C000F00107
C71278010E80013C141C49141E5B0001815B485A000716805B120F48C8FCA2123EA348ED
1F00A40078153E12F8163C167C167816F800785D4B5A1503007C01F05B3A3C0308078090
2604040FC7FC001E141ED80E085B000F147039078807E0D801C813803A00F41E0020EB1F
F6EB00065E16C0A29138070180150703FFC7FC5D5D6E5A6E5A29367EA92E>81
D<000F017E137E3B1181838183803B21C203C203C09039EC01CC01D841E813C801F001F0
13E001E013E0A23B83C003C003C01203A33B078007800780A3EE0F00390F000F00170416
1EA2001E011EEB1C08163CEE1C1017204849EB0C6000180118EB07802E1A7E9933>109
D<000F137E39118183803921C203C0EBEC01EA41E801F013E013E0A23983C003C01203A3
3907800780A3EC0F00EA0F001504141EA2001EEB1C08143CEC1C10152048EB0C600018EB
07801E1A7E9923>I E
%EndDVIPSBitmapFont
%DVIPSBitmapFont: Fi cmr12 14.4 3
/Fi 3 94 df<EA01FCEA07FF380C0FC0381803E0382001F01260384000F8A200F813FC7E
147CA3007813FCC7FC14F8A2EB01F0A2EB03E014C0EB07801400130E5B5B13305B5B485A
3803000412024813085A5A481318383FFFF84813F0B5FCA216287DA71D>50
D<EAFF80A3EAE000B3B3B2EAFF80A3093C7BAC10>91 D<EAFF80A31203B3B3B212FFA309
3C7FAC10>93 D E
%EndDVIPSBitmapFont
%DVIPSBitmapFont: Fj cmsy10 14.4 2
/Fj 2 85 df<15FF020313E0020F13F09138301FF8ECC00390380180010103130049C7FC
4914F016C0491400A280A2806D7E80EB07FC6DB4FC6D13C09038007FF0EC1FF8EC07FCEC
01FE6E7EED7F8048143F0006141F001C140F5A1278160012F8150E6C5C15186C5C007F5C
01C05B263FF80FC7FC381FFFFC000713F0C690C8FC252B7FA924>83
D<1702170C010FB612F8013F15F090B712C048160027060001C0C7FC000E130348130712
3C007C495A127812E05AC748C8FCA4143EA45CA45CA4495AA4495AA35C1307A25C130F91
C9FCA2131E131813202F2F7EAA21>I E
%EndDVIPSBitmapFont
%DVIPSBitmapFont: Fk cmbx12 14.4 49
/Fk 49 128 df<123C127FEAFF80A213C0A3127F123E1200A2EA0180A3EA0300A2120612
0E5A5A12100A157B8813>44 D<B51280A611067F9016>I<121C127FA2EAFF80A3EA7F00
A2121C09097B8813>I<EB3F803801FFF03807E0FC380FC07E48487E497E481480003E13
0F007E14C0A400FE14E0AF007E14C0A46CEB1F80A26C14006D5A380FC07E6C6C5A3801FF
F038003F801B277DA622>48 D<130E131E137EEA07FE12FFA212F81200B3ABB512FEA317
277BA622>I<EBFF80000713F04813FC381E03FE393800FF80007C133F00FE14C06C131F
15E0140FA2127E003C131FC7FC15C0A2EC3F801500147E5C5C495A495AEB078049C7FC13
1E4913E013705B3901C001C0EA0380EA0600000FB5FC5A5A5AB61280A31B277DA622>I<
EB7F803803FFF04813FC380F81FE381F007FEA3F80EC3F80A3121F1300C7EA7F00A2147E
5C495AEB07F0EBFFC0A2EB01F8EB007E801580EC1FC0A215E0A2123C127EB4FCA215C014
3F481480007CEB7F00383F01FE6CB45A000713F0C613801B277DA622>I<140FA25C5C5C
5C5BA2EB03BFEB073F130E131C133C1338137013E0EA01C0EA038012071300120E5A5A5A
12F0B612F8A3C7EA7F00A890381FFFF8A31D277EA622>I<00181303381F801FEBFFFE5C
5C5C14C091C7FC001CC8FCA7EB7FC0381DFFF8381F80FC381E003F1208C7EA1F8015C0A2
15E0A21218127C12FEA315C05A0078EB3F80A26CEB7F00381F01FE6CB45A000313F0C613
801B277DA622>I<1238123E003FB512F0A34814E015C0158015003870000EA25C485B5C
5CC6485AA2495A130791C7FC5B5B131E133EA2137E137CA213FCA41201A76C5A13701C29
7CA822>55 D<121C127FA2EAFF80A3EA7F00A2121CC7FCA9121C127FA2EAFF80A3EA7F00
A2121C091B7B9A13>58 D<007FB712C0B812E0A26C16C0CBFCAA007FB712C0B812E0A26C
16C02B127C9734>61 D<91387FE003903907FFFC07011FEBFF0F90397FF00F9F9039FF00
01FFD801FC7F4848147F4848143F4848141F485A160F485A1607127FA290C9FC5AA97E7F
1607123FA26C7E160E6C7E6C6C141C6C6C143C6C6C14786CB4EB01F090397FF007C0011F
B512800107EBFE009038007FF028297CA831>67 D<91387FE003903907FFFC07011FEBFF
0F90397FF00F9F9039FF0001FFD801FC7F484880484880484880485A82485A82127FA290
CAFC5AA892B512F87E7F03001300123FA26C7EA26C7E6C7E6C7E6C7E6CB45B90387FF007
011FB5129F0107EBFE0F9039007FF0032D297CA835>71 D<B5D8F00FB5FCA3D803FCC7EA
3FC0AF90B7FCA301FCC7123FB1B5D8F00FB5FCA330297EA835>I<B500F0EBFFFEA3D803
FCC7EA0F00161E5E5E16E0ED03C04B5A4BC7FC151E5D15F04A5A4A5A1407140F4A7EEC7F
F04A7EEBFDE79038FFC3FCEC83FE9038FE01FF497E6F7E826F7E151F6F7E8215076F7E6F
7E8281EE7F80B539F00FFFFEA32F297EA835>75 D<D8FFFE92383FFF80A26D5D0003EFE0
00A2D9BF8014EFA2D99FC0EB01CFA2D98FE0EB038FA3D987F0EB070FA2D983F8130EA2D9
81FC131CA3D980FE1338A2027F1370A291383F80E0A391381FC1C0A291380FE380A29138
07F700A3EC03FEA26E5AA26E5AD8FFFE0203B51280A2157039297DA840>77
D<D8FFFCEC7FFF7F7F00036DEB01C080EBBFE0139F80EB8FF8EB87FCEB83FEEB81FF0180
1380147F15C0EC3FE0EC1FF0EC0FF8EC07FC140315FEEC01FF6E1381ED7FC1ED3FE1ED1F
F1150F16F9ED07FDED03FF8181167FA2163F161F160F1607D8FFFE14031601A230297EA8
35>I<B612F815FF16C03A03FC003FE0ED07F0ED03F816FC150116FEA716FC150316F8ED
07F0ED3FE090B61280EDFE0001FCC8FCB0B512F0A327297EA82E>80
D<ECFFC0010F13FC90383FC0FF9039FE001FC048486D7ED803F0EB03F000078148486D7E
48486D7EA24848147FA2007F1680A290C8123FA24816C0AA6C16806D147FA2003F1600A2
6C6C14FE143E3A0FE07F81FC00079038C1C1F83A03F18063F0D801F9EB67E0D800FFEB3F
C090263FC07FC7FC90380FFFFC01004913C0EC003C811601ED1F8316FF6F1380A2170081
6F5A6F5A6F5A2A357CA833>I<B612E015FE6F7E3A03FC003FE0ED0FF06F7E6F7E150182
A65E4B5A1507ED0FE0ED3FC090B500FEC7FCA29039FC00FF80ED3FC06F7E6F7E6F7EA917
0EA21503923801FC1CB538F000FEEE7FF8EE0FE02F297EA832>I<9038FF80600003EBF0
E0000F13F8381F80FD383F001F003E1307481303A200FC1301A214007EA26C140013C0EA
7FFCEBFFE06C13F86C13FE80000714806C14C0C6FC010F13E0EB007FEC1FF0140F140700
E01303A46C14E0A26C13076C14C0B4EB0F80EBE03F39E3FFFE0000E15B38C01FF01C297C
A825>I<007FB71280A39039807F807FD87C00140F00781507A20070150300F016C0A248
1501A5C791C7FCB3A490B612C0A32A287EA72F>I<B500F0EB7FFFA3D803FEC7EA01C000
01ED0380A26D14076C16006E5B017F140E80013F5CA26E133C011F14386E1378010F1470
8001075CA26D6C485AA2ECFE0301015CECFF076D91C7FC1587EC7F8EA215DEEC3FDC15FC
6E5AA26E5AA36E5AA26E5AA230297FA833>86 D<B500F0EB3FFFA3D803FEC7EA03C06C6C
15806C6DEB07005E6D6C130E6E5B013F143C6D6C13386E5B010F14F06D6C5B6E485A0103
1303D901FF5B0387C7FC6D138FEC7FCE15FC143F6E5A5D140FAE0103B512C0A330297FA8
33>89 D<3803FF80000F13F0381F01FC383F80FE147F801580EA1F00C7FCA4EB3FFF3801
FC3FEA0FE0EA1F80EA3F00127E5AA4145F007E13DF393F839FFC381FFE0F3803FC031E1B
7E9A21>97 D<EAFFE0A3120FACEBE1FE9038EFFF809038FE07E09038F803F09038F001F8
9038E000FCA2157EA2157FA8157EA315FCA29038F001F89038F803F090389C0FE090380F
FF80390E01FC00202A7EA925>I<EB3FF03801FFFC3803F03E380FC07FEA1F80EA3F00A2
48133E007E90C7FCA212FEA7127EA2127F6CEB03801380001FEB0700380FE00E3803F83C
3801FFF838003FC0191B7E9A1E>I<EC7FF0A31407ACEB3F873801FFF73807F03F380FC0
0F381F8007EA3F00A2127EA312FEA8127EA27EA2381F800F380FC01F3907E07FFF3801FF
E738007F87202A7EA925>I<EB3FC03801FFF03803E07C380F803E001F7F130048EB0F80
127E15C0A200FE1307A2B6FCA248C8FCA3127EA2127F6CEB01C07E390F8003803907C007
003803F01E3800FFFCEB3FE01A1B7E9A1F>I<EB07F8EB3FFCEB7E3E3801FC7FEA03F813
F01207143E1400A7B512C0A33807F000B3A3387FFF80A3182A7EA915>I<9038FF80F000
03EBE3F8390FC1FE1C391F007C7C48137E003EEB3E10007EEB3F00A6003E133E003F137E
6C137C380FC1F8380BFFE00018138090C8FC1238A2123C383FFFF814FF6C14C06C14E06C
14F0121F383C0007007CEB01F8481300A4007CEB01F0A2003FEB07E0390FC01F806CB512
0038007FF01E287E9A22>I<EAFFE0A3120FAC147E9038E1FF809038E30FC001E413E0EB
E80701F813F013F0A213E0B039FFFE3FFFA3202A7DA925>I<1207EA0F80EA1FC0EA3FE0
A3EA1FC0EA0F80EA0700C7FCA7EAFFE0A3120FB3A3EAFFFEA30F2B7EAA12>I<EAFFE0A3
120FACEC1FFCA3EC0780EC0F00141E5C5C14E0EBE3C013E7EBEFE0EBFFF08013F3EBE1FC
EBC0FE147FA2EC3F80EC1FC0EC0FE0A2EC07F039FFFC1FFFA3202A7FA923>107
D<EAFFE0A3120FB3B2EAFFFEA30F2A7EA912>I<26FFC07FEB1FC0903AC1FFC07FF0903A
C307E0C1F8D80FC49038F101FC9039C803F20001D801FE7F01D05BA201E05BB03CFFFE3F
FF8FFFE0A3331B7D9A38>I<38FFC07E9038C1FF809038C30FC0D80FC413E0EBC80701D8
13F013D0A213E0B039FFFE3FFFA3201B7D9A25>I<EB3FE03801FFFC3803F07E390FC01F
80391F800FC0393F0007E0A2007EEB03F0A300FE14F8A8007E14F0A26CEB07E0A2391F80
0FC0390FC01F803907F07F003801FFFC38003FE01D1B7E9A22>I<38FFE1FE9038EFFF80
9038FE0FE0390FF803F09038F001F801E013FC140015FEA2157FA8157E15FEA215FC1401
01F013F89038F807F09038FC0FE09038EFFF809038E1FC0001E0C7FCA9EAFFFEA320277E
9A25>I<38FFC1F0EBC7FCEBC63E380FCC7F13D813D0A2EBF03EEBE000B0B5FCA3181B7F
9A1B>114 D<3803FE30380FFFF0EA3E03EA7800127000F01370A27E00FE1300EAFFE06C
B4FC14C06C13E06C13F0000713F8C6FCEB07FC130000E0137C143C7E14387E6C137038FF
01E038E7FFC000C11300161B7E9A1B>I<13E0A41201A31203A21207120F381FFFE0B5FC
A2380FE000AD1470A73807F0E0000313C03801FF8038007F0014267FA51A>I<39FFE07F
F0A3000F1307B2140FA2000713173903F067FF3801FFC738007F87201B7D9A25>I<39FF
FC03FFA3390FF000F0000714E07F0003EB01C0A2EBFC0300011480EBFE070000140013FF
EB7F0EA2149EEB3F9C14FC6D5AA26D5AA36D5AA26D5AA2201B7F9A23>I<39FFFC03FFA3
390FF000F0000714E07F0003EB01C0A2EBFC0300011480EBFE070000140013FFEB7F0EA2
149EEB3F9C14FC6D5AA26D5AA36D5AA26D5AA25CA21307003890C7FCEA7C0FEAFE0E131E
131C5BEA74F0EA3FE0EA0F8020277F9A23>121 D<003FB5FCA2EB00FEEA3C01383803FC
007813F8EB07F0EA700F14E0EB1FC0EA003F1480EB7F005B5B3801FC07120313F8EA07F0
000F130F13E0381FC00E003F131E387F803EEB00FEB5FCA2181B7E9A1E>I<B71280A221
02809122>I<383C01E0387E03F038FF07F8A4387E03F0383C01E015087AAA22>127
D E
%EndDVIPSBitmapFont
%DVIPSBitmapFont: Fl cmsy10 10 5
/Fl 5 78 df<EB03FCEB1FFEEB703EEB801E3801001C1207000E1338000C1330001C1360
481300A212781270A200F0130814381478A2147014F0EAF80114E0EA7C02EA7F0D383FF1
C0EA0FC138000380A2EB0700A2EA180EEA7E08EA7FF0EA1FC017227F9C19>71
D<017E130648B4130CD8061F131C486C133C003814381230D8600E137800C01470EA001E
15F015E0131C1401013C13C048B5FC5A38003803017813801370140713F013E015001201
495A1502D803801306159CD8070013F00004EB07C01F1E809B23>I<90383FFF8048B512
00380700C0EA0C01381C03801230D82007C7FC12005BA2130EA2131EA2131CA2133C1338
A213781370A25B140C48485A495A387FFFE0B51280191C819B17>I<147E49B4FCEB031F
EB060F130C1318EB380CEB78080170C7FCA25BA21201A25BA212035BA21207A290C8FCA2
000E14801403391FE00700EBFC063831FF8C38603FF838C007E0191E7F9C1D>76
D<496C141001031530A21760496C14E01601010514031607A26EEB0DC001091419010814
331673496C13E3ED01C3913870038301201403DA78061380150C903940381807EC3C3815
709038801CE0EC1FC0D801001380EC0F000062130E00FE010414C04890C713F0EE03C000
7892C7FC2C1F7F9C32>I E
%EndDVIPSBitmapFont
%DVIPSBitmapFont: Fm cmmi6 6 9
/Fm 9 108 df<1203EA07E0EA0800120C120412067EEA078012191231EA61C01260EAC1
80A3EA41001262121C0B127E910E>14 D<5AA5EAE10EEA3FF8EA07C0EA0380EA06C0EA04
40EA0820EA1830EA10100F0E7F8C10>63 D<EA0FF0EA0180A2EA0300A41206A45AA45AB4
FC0C117E900E>73 D<EA01FCEA0030A21360A413C0A4EA0180A21281EAC3001286127C0E
117C9011>I<383FFFC0EA30600040134013C01280A200001300485AA448C7FCA41206EA
3FE012117E9012>84 D<38FC03E0383001801400130212185B5BA25BEA1C20EA0C601340
5B000DC7FC120F1206120413117D9012>86 D<1204120C1200A5123012581298A21230A2
12601264A21268123006127E910B>105 D<1320A21300A5EA0380EA04C01208A21200EA
0180A4EA0300A4124612CC12780B1780910D>I<123C120CA25AA31370EA3190EA3230EA
34001238127FEA61801390A2EAC1A0EAC0C00C117E9010>I E
%EndDVIPSBitmapFont
%DVIPSBitmapFont: Fn cmsy6 6 5
/Fn 5 107 df<B512C0A212027D8618>0 D<120CA2EACCC012EDEA7F80EA0C00EA7F80EA
EDC012CCEA0C00A20A0B7D8B10>3 D<1208121CA21238A312301270A21260A212C0A206
0D7E8D09>48 D<380C01E0381C0E60380C300013C0000DC7FC120A121EA2121F1213EA33
801231EA21C03860E020EB7060384038C038C01F0013117E9017>75
D<12C0B3A702197C9209>106 D E
%EndDVIPSBitmapFont
%DVIPSBitmapFont: Fo cmmi7 7 1
/Fo 1 74 df<EA07FCEA00E0EA01C0A4EA0380A4EA0700A4120EA45AEAFF800E147F930F
>73 D E
%EndDVIPSBitmapFont
%DVIPSBitmapFont: Fp cmmi10 10 2
/Fp 2 79 df<5B1302A45BA45BA2137E3801C980380710E0000C13600018137000381330
EA7020A200E01370A2134014E0A2386041C0EB838038308600EA1C9CEA07E00001C7FCA4
1202A414257E9C19>30 D<D801FCEBFF80D8001CEB1C00012E13181510A2132701475B13
431480A2903881C040A3EB80E0D801005B1470A300020139C7FCA3141D48131E140EA212
0C001C1304EAFF80211C7E9B21>78 D E
%EndDVIPSBitmapFont
%DVIPSBitmapFont: Fq cmr7 7 4
/Fq 4 53 df<120C121C12EC120CAFEAFFC00A137D9211>49 D<121FEA60C01360EAF070
13301260EA0070A2136013C012011380EA02005AEA08101210EA2020EA7FE012FF0C137E
9211>I<EA0FC0EA3070EA7038A31200133013E0EA0FC0EA007013381318131C126012F0
1318EAE038EA6070EA1FC00E137F9211>I<136013E0A2EA016012021206120C12081210
1220126012C0EAFFFCEA0060A5EA03FC0E137F9211>I E
%EndDVIPSBitmapFont
%DVIPSBitmapFont: Fr cmr6 6 9
/Fr 9 57 df<120412081210123012201260A2124012C0AA12401260A212201230121012
081204061A7D920C>40 D<128012401220123012101218A21208120CAA12081218A21210
1230122012401280061A7F920C>I<1218127812981218AC12FF08107D8F0F>49
D<121FEA6180EA40C0EA806012C01200A213C0EA0180EA030012065AEA10201220EA7FC0
12FF0B107F8F0F>I<121FEA2180EA60C0A212001380EA0100121FEA00801340136012C0
A2EA8040EA6080EA1F000B107F8F0F>I<EA0180A212031205120D121912111221124112
C1EAFFE0EA0180A4EA0FE00B107F8F0F>I<EA0780EA1840EA30C0126013005A12CFEAF0
80EAE040EAC060A31240EA60C0EA3080EA1F000B107F8F0F>54 D<1240EA7FF013E0EA80
40A2EA0080EA01001202A212061204A2120CA50C117F900F>I<121FEA3180EA60C0A3EA
3180EA3F00120EEA3380EA61C0EAC060A31340EA60C0EA1F000B107F8F0F>I
E
%EndDVIPSBitmapFont
%DVIPSBitmapFont: Fs cmex10 10 36
/Fs 36 116 df<1306130C131813301370136013C012011380120313005A1206120E120C
121CA212181238A312301270A65AB21270A612301238A31218121CA2120C120E12061207
7E1380120113C012001360137013301318130C13060F4A788119>16
D<12C012607E7E121C120C7E12077E1380120113C0120013E013601370A213301338A313
18131CA6130EB2131CA613181338A313301370A2136013E013C012011380120313005A12
065A121C12185A5A5A0F4A7F8119>I<1430146014C0EB0180EB03005B130E130C5B1338
133013705B5B12015B1203A290C7FC5A1206120EA2120C121CA312181238A45AA75AB3A3
1270A77EA41218121CA3120C120EA2120612077E7FA212017F12007F1370133013381318
7F130E7F7FEB0180EB00C014601430146377811F>I<12C012607E7E7E120E7E7E6C7E7F
12007F1370133013381318131CA2130C130E13061307A27F1480A3130114C0A4EB00E0A7
1470B3A314E0A7EB01C0A414801303A314005BA21306130E130C131CA213181338133013
705B5B12015B48C7FC5A120E120C5A5A5A5A14637F811F>I<EAFFE0A3EAE000B3B3B3B3
B3A3EAFFE0A30B63768116>I<EAFFE0A31200B3B3B3B3B3A312FFA30B63808116>I<1470
EB01F0EB03C0EB0780EB0E005B5B5BA213F05BB3AC485AA3485A48C7FC1206120E12385A
12C012707E120E120612076C7E6C7EA36C7EB3AC7F1370A27F7F7FEB0780EB03C0EB01F0
EB007014637B811F>26 D<14181430146014E014C0EB01801303EB07001306130E130C13
1C5BA25BA25BA212015BA2485AA3120790C7FCA25A120EA2121EA3121CA2123CA4123812
78A8127012F0B3A812701278A81238123CA4121CA2121EA3120EA2120F7EA27F1203A36C
7EA27F1200A21370A27FA27F130C130E13061307EB03801301EB00C014E0146014301418
157C768121>32 D<12C012607E123812187E120E7E7E7F12017F6C7EA21370A27FA2133C
131CA27FA3130F7FA214801303A214C0A31301A214E0A4130014F0A814701478B3A81470
14F0A814E01301A414C0A21303A31480A213071400A25B130EA35BA2133C1338A25BA25B
A2485A5B120390C7FC5A120E120C5A123812305A5A157C7F8121>I<EAFFF0A3EAE000B3
B3B3B3B3B3AAEAFFF0A30C7C758118>I<EAFFF0A3EA0070B3B3B3B3B3B3AAEAFFF0A30C
7C808118>I<141C143C14F8EB01E0EB03C0EB0780EB0F00130E131E5BA35BB3B3A25BA3
485AA2485A5B48C7FC120E5A127812E0A21278121C7E7E6C7E7F6C7EA26C7EA31378B3B3
A27FA37F130E130FEB0780EB03C0EB01E0EB00F8143C141C167C7B8121>40
D<12E07E127C121E7E6C7E6C7E12017F6C7EA31378B3B3A27FA37FA27F7FEB0380EB01C0
EB00E01478141CA2147814E0EB01C0EB0380EB07005B131EA25BA35BB3B3A25BA3485A5B
1203485A48C7FC121E127C12F05A167C7B8121>I<140C141814381430146014E014C013
01EB0380A2EB0700A2130EA25BA25BA21378137013F0A25B1201A2485AA4485AA3120F90
C7FCA35AA2121EA3123EA4123CA3127CA81278A212F8B1164B748024>48
D<12C01260127012307E121C120C120E7EA26C7EA26C7EA26C7EA21370A213781338133C
A2131C131EA27FA4EB0780A314C01303A314E0A21301A314F0A41300A314F8A81478A214
7CB1164B7F8024>I<1318137813F0EA01E0EA03C0EA0780EA0F005A121E123E123C127C
A2127812F8B3A50D25707E25>56 D<12F8B3A51278127CA2123C123E121E121F7EEA0780
EA03C0EA01E0EA00F0137813180D25708025>58 D<137CB3A613F8A313F0120113E01203
13C0EA07801300120E5A5A12F012C012F012387E7E7E1380EA03C013E0120113F0120013
F8A3137CB3A60E4D798025>60 D<12F8AE050E708025>62 D<12F8B11278A2127CA8123C
A3123EA4121EA3121FA27EA37F1207A36C7EA46C7EA212007FA2137013781338A27FA27F
A27FA2EB0380A2EB01C0130014E01460143014381418140C164B748224>64
D<147CB11478A214F8A814F0A31301A414E0A31303A214C0A313071480A3EB0F00A4131E
A2131C133CA2133813781370A25BA2485AA2485AA248C7FCA2120E120C121C12185A1270
12605A164B7F8224>I<12F8B3A9051B748024>I<12F8B3A9051B6E8024>I<B912C018E0
6CC81201EE001F6C6CED03F06C6C1500000F17386D16186C6C160C6C6C1604A26C6C1602
6C6C1600137FA26D7E6D7E130F806D7E6D7EA26D7E6D7E147E147F6E7E6E7EA2140F6E5A
14034AC9FC140E5C5C5CA25C495A495A49CAFC130EA24916024916045B49160C00011718
491638484816F848C9EA01F0000E160F48ED01FF003FB812E0A25AB912C0373A7E7F3C>
88 D<ED0380ED0460ED0C70ED18F0A2ED3860ED30001570A2156015E0A314015DA31403
A25DA21407A44AC7FCA55C141EA3143EA4143C147CA45CA6495AA45C1303A45CA313075C
A549C8FCA4130EA2131EA2131CA3133C1338A313301370A21360EA60E0EAF0C012F1EAE1
800063C9FC121E245C7E7F17>90 D<133013FCEA01CE38070380381C00E00030133000C0
130C1607809E17>98 D<141CECFF80903807E3F090383F007ED801F0EB07C0D80F80EB00
F80038C8120E00C0ED01802908809F2A>I<151F913801FFF091381FF1FF903A01FE000F
F0D91FC0EB007FD803F8C8EA03F8003FCAEA1F8000E0EF00E03B08809F3C>I<3807C004
381FE0183830783038601FE038800F801605809D17>I<902607FF80156090B500F8EC03
80280780003F80EB3C000038C70003B512E000C09126003FFCC7FC3B05809E3C>103
D<EAFF80A2EAC000B3B3B3B0EAFF80A2094A778114>I<EAFF80A21201B3B3B3B012FFA2
094A7F8114>I<14E01303EB0F80EB1E005B1370A25BB3A5485AA2485A48C7FC120E123C
12F0A2123C120E7E6C7E6C7EA26C7EB3A51370A2133C7FEB0F80EB03E01300134A7C811C
>110 D<12E012F8123E120F6C7EEA01C0A26C7EB3A51370A27F7F7FEB0780EB01E0A2EB
0780EB0E005B5B5BA25BB3A5485AA2EA078048C7FC123E12F812E0134A7C811C>I<1602
1606A2160CA31618A31630A31660A316C0A3ED0180A3ED0300A31506A35DA35DA35DA35D
A21208001C5C123C127C00DC495A128E120E4AC7FC7EA21406EA0380A25CA2EA01C05CA2
EA00E05CA3EB7060A36D5AA3EB1D80A3011FC8FC7FA2130E1306A2274B7C812A>113
D<16021606A3160CA51618A51630A51660A516C0A5ED0180A5ED0300A51506A65DA55DA5
5DA55DA31208A2001C5CA2123CA2125C4A5A128E120EA34AC7FCA27EA31406A2EA0380A4
5CA2EA01C0A35CA3EA00E0A25CA31370A25CA413385CA5EB1D80A5010FC8FCA5130E1306
A3277D7C812A>115 D E
%EndDVIPSBitmapFont
%DVIPSBitmapFont: Ft cmmi8 8 69
/Ft 69 125 df<EA03C0380C3040EA101800201380EA600C12C0EB0D00130E1280130CEA
C01C132C3860C480381F0300120E7E8D17>11 D<131FEB6180EB80C03801004000021360
14404813C01480EB0100EA087EA213037F00101380A438200300A2EA30065BEA4838EA47
E00040C7FCA25AA4131D7F9614>I<38078040EA1FC03838E080EA6030EAC01038801100
EA0009130AA3130CA31308A35BA41214808D12>I<EA01C0EA07F0EA0438EA0800120CA2
120412067EA2EA0780EA0DC012101220EA606012C0A3EA804013C0EAC08012C1EA630012
3C0D187E9710>I<EA07C0EA1C0012305AA2B4FC12C0A51240EA20C0EA1F000A0E7E8D0E>
I<EA383CEA44C6EA47021246EA8E06120CA3EA180CA4EA3018A21200A21330A313200F14
7F8D12>17 D<12081218A31230A31260A2126112C112C212441278080E7E8D0C>19
D<120E1203A2EA0180A213C01200A21360A31330A213781398EA0118EA020C1204EA080E
EA18061230EAE00312C010177E9615>21 D<EA0402EA0C06A3485AA4485A1480A2133838
785900EA6F8E0060C7FCA25AA35A11147E8D15>I<EA7802EA1806A2130C12301318A213
30EA606013C0EA6180EA660012D812E00F0E7E8D11>I<13401380A213F8EA0378EA0C00
5AA5EA0FE0A2EA18005A5AA25AA37E1270123CEA1F80EA03E0EA00701330EA0420EA03C0
0D1D7F9610>I<380FFFC0123F382108001241485A1202A212061204A2EA0C18A2121813
08120E7F8D14>I<13F0EA0318EA0608EA0C0CA21218A3EA3018A213301320EA68C0EA67
80EA6000A25AA35A0E147E8D12>I<3803FF805A381C3000EA181812301260A3485AA2EA
4060EA6040EA2180001EC7FC110E7F8D14>I<126012F0A2126004047D830A>58
D<126012F0A212701210A21220A21240A2040A7D830A>I<130813181330A31360A313C0
A3EA0180A3EA0300A21206A35AA35AA35AA35AA35AA20D217E9812>61
D<7FA638F08780381FFC00EA07F0EA01C0EA0360EA0220EA0630487EEA0808487E111080
8F12>63 D<EA03F0EA0408EA0804EA1002EA1C0312381200A3EA03E3EA0C13EA100BEA20
07EA600612C0A2130C12801318EAC010EA4020EA20C0EA1F0010177E9613>I<14C0A213
01A21303130514E01308131813101320A213401380A23801FFF0EB007012025AA25A1218
38FE03FE17177F961A>I<3807FFF83800E00E14071403A2EA01C01407A2140E3803803C
EBFFF0A2EB803C3807001C140EA3000E131CA214381470381C01E0B5120018177F961B>
I<EB1F82EBE0443803802C3807001C120C001C13085A123012700060130012E0A35A1420
A214407E00601380EB0100EA3002EA1C1CEA07E017177E9619>I<3807FFF83800E00E14
0315801401D801C013C0A21400A238038001A43907000380A215005C000E130E140C5C14
70381C01C0B5C7FC1A177F961D>I<0007B512803800E003EC0100A3EA01C0A21440A248
485A138113FF1381D80701C7FC1402A26D5A120E140C14081418481370B512F019177F96
1A>I<0007B512803800E003EC0100A3EA01C0A21440A248485A138113FF1381D80701C7
FCA390C8FC120EA45AEAFFC019177F9616>I<EB1F81EBF062380180163807000E120E48
13045A123012700060130012E0A338C007FEEB0070A27E14E012601270EA3001380C06C0
3803F84018177E961B>I<3907FE1FF83900E00380A43901C00700A43803800EA2EBFFFE
EB800E48485AA4000E5BA4485B38FF83FE1D177F961D>I<EA07FEEA00E0A4EA01C0A4EA
0380A4EA0700A4120EA45AEAFFC00F177E960F>I<EB7FE0EB0700A4130EA45BA45BA4EA
607012F0A2485AEA41C0003FC7FC13177E9613>I<3907FE03F83900E001C01500140214
0848485A5C148001C1C7FC485A138FEB938013A3380781C013016D7EA2000E1370A280A2
48133CB46CB4FC1D177F961E>I<EA07FFEA00E0A4485AA4485AA448C7FC1408A2141012
0E143014201460381C01E0B512C015177F9618>I<D807F0EB0FE00000EC1E0013B8152E
154ED80138135C159CEC011C131C0002EB02381404A214080004495A130E142014400008
5C1480EB0F007F39180601C039FE040FF823177F9622>I<3907F007F80000EB00C001B8
1380A2139C39011C0100131E130EA238020702A2EB0382A2380401C4A2EB00E4A2481378
A21438A20018131012FE1D177F961C>I<EB1FC0EB70703801C0183803001C0006130C00
0E130E5A1218123812301270A3141C5A006013381270147014E0383801C038180380380E
0E00EA03F017177F961B>I<3807FFF83800E00E1407A3EA01C0A3140E3803801C1470EB
FFC0EB800048C7FCA4120EA45AB47E18177F9616>I<3807FFF03800E01C14061407A2EA
01C0A3140E48485A1470EBFF80EB80E03807007080A3000E5BA21580A248EB310038FF80
1E19177F961B>82 D<EB3E10EBC1A0380100E0000213601206481340A2000E1300120FEA
07E013FCEA01FEEA003FEB07801303A2EA200138400300A2EA60061304EAD818EA87E014
177E9615>I<381FFFFE38381C0E00201304126012401338128000001300A25BA45BA448
5AA41203EA3FFC17177F9615>I<38FFC0FF381C00181410A3481320A4481340A4481380
A4EB010013025BEA6008EA3830EA0FC018177E9618>I<38FF807F381C00181410143014
20001E1340120E1480EB0100A213025B120F6C5A5BA25B136013405B120390C7FC120218
177E9615>I<3903FE0FE039007807001406EB380C1408EB3C10EB1C20EB1E40EB0E8001
0FC7FC7FA2497E1313EB23C0136113C1380181E0130000027F481370121C38FF03FE1B17
7F961D>88 D<38FF807F381C001C001E1310000E13201440000F1380EA0701EB03001382
EA0384138813D0EA01E05BA4485AA448C7FCEA3FE018177F9614>I<1330134813881201
1308EA0310120212061320EA0C40A21380EA0D00121A121C1218A2123812581288EA0810
EA0C60EA07800D1780960E>96 D<EA0710EA18F0EA30701260136012C0A3EA80C013C4A2
12C1EA46C8EA38700E0E7E8D13>I<127C1218A45AA4EA6780EA68C0EA7040EA606012C0
A4EA80C0A2EA8180EAC1001246123C0B177E960F>I<EA07C0EA0C20EA10701220EA6000
5AA35AA2EAC0101320EA60C0EA3F000C0E7E8D0F>I<133E130CA41318A4EA0730EA18F0
EA30701260136012C0A3EA80C013C4A212C1EA46C8EA38700F177E9612>I<EA07C0EA1C
20EA301012601320EAFFC0EAC000A41310EA4020EA60C0EA1F000C0E7E8D10>I<130E13
131337133613301360A4EA03FCEA00C0A5EA0180A5EA0300A41202126612E65A1278101D
7E9611>I<13E2EA031EEA060E120C130C1218A3EA1018A3EA1838EA08F0EA07301200A2
EA606012E0EAC1C0EA7F000F14808D11>I<121F1206A45AA4EA18F0EA1B18EA1C081218
EA38181230A3EA6030133113611362EAC026133810177E9614>I<120313801300C7FCA6
121C12241246A25A120C5AA31231A21232A2121C09177F960C>I<1318133813101300A6
EA01C0EA0220EA0430A2EA08601200A313C0A4EA0180A4EA630012E312C612780D1D8096
0E>I<121F1206A45AA4EA181C1366138EEA190CEA3200123C123FEA3180EA60C013C4A3
EAC0C813700F177E9612>I<123E120CA41218A41230A41260A412C012C8A312D0127007
177E960B>I<38383C1E3844C6633847028138460301388E0703EA0C06A338180C061520
140C154039301804C0EC07001B0E7F8D1F>I<EA383CEA44C6EA47021246EA8E06120CA3
485A144013181480EA3009EB0E00120E7F8D15>I<EA07C0EA0C20EA1010EA2018126012
C0A3EA8030A2EAC06013C0EA6180EA3E000D0E7E8D11>I<EA1C3CEA2246EA2382130312
461206A3EA0C06A2130C1308EA1A30EA19E0EA1800A25AA312FC1014808D12>I<EA30F0
EA4918EA4E38EA4C30EA9C001218A35AA45AA20D0E7F8D10>114
D<EA07C0EA0C20EA1870A2EA3800121EEA0FC0EA03E0EA0060126012E0EAC0C0EAC180EA
3F000C0E7E8D10>I<1203A21206A4EAFFC0EA0C00A35AA45A1380A2EA31001232121C0A
147F930D>I<EA1C02EA26061246A2EA860C120CA3485A1480A21338380C5900EA078E11
0E7F8D14>I<EA1C04EA26061246A2EA8604120CA3EA1808A213101320EA0C60EA07800F
0E7F8D11>I<381C0204382606061246A238860C04120CA338181808A214101208380C2C
203803C7C0170E7F8D19>I<EA0F1F3811A180EA20C31400EA41801201A348C7FC130212
C3EAE704EAC508EA78F0110E7F8D14>I<EA1C02EA26061246A2EA860C120CA3EA1818A3
1338EA0C70EA07B0EA00301360127013C0EA2180EA1E000F147F8D11>I<EA0704EA0FCC
EA1878EA1010EA00201340EA0180EA02005AEA08081210EA3C30EA43E0EA81C00E0E7F8D
10>I<EA01C0EA0220EA0430A2EA08601200A313C0A4EA0180A4EA630012E312C612780C
14808D0D>124 D E
%EndDVIPSBitmapFont
%DVIPSBitmapFont: Fu cmti12 12 57
/Fu 57 128 df<91380FC0F8913830718E913860F31EECC0F70101EB660C9138800E0013
03A35DEB0700A490B612C090390E003800A45D5BA45D5BA44A5A1370A44A5A13E0A292C7
FC495AA238718E0638F19E0CEB1E1838620C30383C07C0272D82A21E>11
D<EC0FF0EC380CEC600EECC01E1301EC801C01031300A349C7FCA590B512F090380E0070
A215E0A25BA2EC01C0A31338EC0380A315889038700710A4EC03209038E001C091C7FCA2
5BA21201EA718012F100F3C8FC1262123C1F2D82A21B>I<91380FF3809138383F00EC60
7F14C001011337EC800E1303A35DEB0700A35D90B512F890380E0038A25DA35B5DA44948
5AA315C24A5A1370A215881401EC00F04990C7FCA35BA21271EAF18090C9FC1262123C21
2D82A21D>I<1480EB010013025B5B5B13305B5BA2485A48C7FCA21206A2120E120C121C
1218A212381230A21270A21260A212E0A35AAD12401260A21220123012107E113278A414
>40 D<13087F130613021303A27F1480AD1303A31400A25BA21306A2130E130CA2131C13
1813381330A25BA25B485AA248C7FC120612045A5A5A5A5A113280A414>I<120E121EA4
1202A21204A21208A21210122012401280070F7D840F>44 D<EAFFF0A213E00C037C8B11
>I<150815181530A2156015C0A2EC0180A2EC03001406A25CA25C5CA25CA25C495AA249
C7FCA21306A25B5BA25BA25B5BA2485AA248C8FC1206A25AA25A5AA25AA25AA25A1D317F
A419>47 D<EB0F80EB30C0EBE0603801C070EA038013005A5A120E121EA2001C13F0123C
A3387801E0A438F003C0A31480EAE007A214005B130E5BA25BEA60706C5A001FC7FC1422
7AA019>I<13011303A21306131E132EEA03CEEA001CA41338A41370A413E0A4EA01C0A4
EA0380A41207EAFFFC10217AA019>I<EB0FC0EB1060EB6038EB8018141CEA0100380220
1E13101204A33808203CA2EB40381478EB80F0380700E0380001C0EB0300130613181320
13C048C7FC1202481310481330481320481360385F80C0EA63FF0040138038807F00131E
17227CA019>I<EB0FC0EB3070EBC0183801001C120248130CEB401CEA0820A3EB403813
C038070070C71260EB01C0EB070013FC1307EB0380A2EB01C0A31303126012F01480EAE0
0700801300130E5BEA4038EA20F0EA1F8016227BA019>I<1207EA0F80A21300120EC7FC
AB127012F8A25A5A09157A940F>58 D<001FB6FCA2C9FCA8B612F8A2200C7B9125>61
D<1403A25CA25CA25C142FA2EC4F80A21487A2EB01071302A21304A21308131813101320
A290387FFFC0EB40031380EA0100A21202A25AA2120C003CEB07E0B4EB3FFC1E237DA224
>65 D<90B512E090380F0038151C151E011E130E150FA349130E151EA2153C4913781570
EC01E0EC078090B5FC9038F001E0EC00F01578485A1538153CA248481378A315F0485AEC
01E0EC03C0EC0700380F001EB512F020227DA122>I<027F138090390380810090380E00
630138132749131F49130E485A485A48C7FC481404120E121E5A5D4891C7FCA35AA55A15
20A25DA26C5C12704AC7FC6C130200185B001C5B00061330380381C0D800FEC8FC212479
A223>I<90B512F090380F003C150E81011EEB0380A2ED01C0A25B16E0A35BA449EB03C0
A44848EB0780A216005D4848130E5D153C153848485B5DEC03804AC7FC000F131CB512F0
23227DA125>I<90B6FC90380F000F1503A2131EA21502A25BA214011500EB7802A21406
140EEBFFFCEBF00CA33801E008A391C7FC485AA4485AA4120FEAFFF820227DA120>70
D<9039FFF87FFC90390F000780A3011EEB0F00A449131EA4495BA490B512F89038F00078
A348485BA44848485AA44848485AA4000F130739FFF07FF826227DA124>72
D<9039FFF807FC90390F0001E016C01600011E13025D15105D495B5D4AC7FC1404495A14
181438147CEBF0BCEBF23CEBF41E13F83801F01F497EA2813803C007A26E7EA2EA07806E
7EA3000F8039FFF00FFE26227DA125>75 D<EBFFFCEB0F8091C7FCA2131EA45BA45BA45B
A4485AA21520A248481340A21580A23807800115005C140F000F133EB512FE1B227DA11F
>I<D9FF80EB07FC010FEC0F801617A20117EC2F00EB13C0164F168F0123149EED011EA2
15020143495AA21508EB41E00181495A1520A21540D801015C1580ECE100A23A0200F201
E0A214F414F8484A5A14F0A2000C13E0001EEBC007D8FF80EB7FF82E227DA12C>I<01FF
EB0FFC90390F8001E01680ECC0000113EB0100A2EB11E0A201211302EB20F0A390384078
04A3143C01805B143E141EA23901001F10140FA2EC0790000214A0A2EC03E0A2485C1401
A2120C001E6D5AB47E26227DA124>I<90B512C090380F0070153C151C011E130EA2150F
A249131EA3153C4913381570EC01E0EC07809038FFFC00EBF00E80EC0380D801E013C0A4
3903C00780A43907800F001501A2EC0702120F39FFF0038CC812F020237DA124>82
D<903801F02090380E0C4090381802C0EB3001136001E0138013C01201A200031400A291
C7FCA27FEA01F813FF6C13E06D7EEB1FF8EB03FCEB007C143C80A30020131CA314180060
1338143000705B5C38C80180D8C607C7FCEA81FC1B247DA21B>I<001FB512F8391E03C0
3800181418123038200780A200401410A2EB0F001280A200001400131EA45BA45BA45BA4
485AA41203B5FC1D2277A123>I<3BFFE07FF00FF83B1F000F8003C0001E913800018017
001602A2001F5DA26C495BA2022F5BA291384F802002475B14875EEB010701030181C7FC
130201041382A201081384158C011013881590132001A013A013C0D8078013C0A201005B
A2000691C8FC140212042D2376A131>87 D<D8FFF013FF001FC712786C143015407F0007
1480EC0100EBC0020003130614046D5A00015B5C13F05C00005B01F9C7FC13FB137A137C
1378A45BA4485AA4485AEA3FFC202276A124>89 D<EBF8C0EA0185EA0705380E0380A212
1C123C383807001278A3EAF00EA31410EB1C201270133C38305C40138C380F078014157B
9419>97 D<EA03C0EA1F801203A3EA0700A4120EA45A13F8EA1D0CEA1E0EEA3C06EA3807
A2130F1270A4EAE01EA3133C1338A2EA607013E0EA31C0EA1F0010237BA216>I<137EEA
01C138030180EA0703EA0E07121C003CC7FC12381278A35AA45B12701302EA300CEA1830
EA0FC011157B9416>I<143CEB03F8EB0038A31470A414E0A4EB01C013F9EA0185EA0705
380E0380A2121C123C383807001278A3EAF00EA31410EB1C201270133C38305C40138C38
0F078016237BA219>I<13F8EA0384EA0E02121C123C1238EA7804EAF018EAFFE0EAF000
A25AA41302A2EA6004EA7018EA3060EA0F800F157A9416>I<143E144714CFEB018F1486
EB0380A3EB0700A5130EEBFFF0EB0E00A35BA55BA55BA55BA45B1201A2EA718012F100F3
C7FC1262123C182D82A20F>I<EB1F18EB30B813E03801C070A2EA03801207EB00E05AA3
381E01C0A4EB0380120E1307EA060BEB1700EA01E7EA0007A2130EA3EA701CEAF0185BEA
60E0EA3F80151F7E9416>I<13F0EA0FE01200A3485AA4485AA448C7FC131FEB2180EBC0
C0380F00E0A2120EA2381C01C0A438380380A3EB070400701308130E1410130600E01320
386003C016237DA219>I<13C0EA01E013C0A2C7FCA8121E12231243A25AA3120EA25AA3
5AA21340EA7080A3EA71001232121C0B217BA00F>I<14E01301A2EB00C01400A8131E13
23EB43801383A2EA0103A238000700A4130EA45BA45BA45BA3EA70E0EAF0C0EAF1800063
C7FC123C132B82A00F>I<13F0EA07E01200A3485AA4485AA448C7FCEB01E0EB0210EB04
70380E08F01310EB2060EB4000EA1D80001EC7FCEA1FC0EA1C70487EA27F142038703840
A3EB188012E038600F0014237DA216>I<EA01E0EA0FC01201A3EA0380A4EA0700A4120E
A45AA45AA45AA3127112E2A4126412380B237CA20C>I<391C0F80F8392610C10C394760
66063987807807A2EB0070A2000EEBE00EA44848485AA3ED382026380380134015701680
15303A7007003100D83003131E23157B9428>I<38380F80384C30C0384E4060388E8070
EA8F00128EA24813E0A4383801C0A3EB03840070138814081307EB031012E0386001E016
157B941B>I<137EEA01C338038180380701C0120E001C13E0123C12381278A338F003C0
A21480130700701300130E130CEA3018EA1870EA07C013157B9419>I<3801C1F0380262
183804741C3808780CEB700EA2141EEA00E0A43801C03CA3147838038070A2EBC0E0EBC1
C038072380EB1E0090C7FCA2120EA45AA3EAFFC0171F7F9419>I<EBF840380184C0EA07
05380E0380A2121C123C383807001278A3EAF00EA45B1270133CEA305C5BEA0F381200A2
5BA45BA3EA0FFC121F7B9416>I<EA1C1F38262080384741C0EA87831303EB018090C7FC
120EA45AA45AA45A123012157B9415>I<13FCEA018338020080EA0401EA0C03140090C7
FC120F13F0EA07FC6C7EEA003E130F7F1270EAF006A2EAE004EA4008EA2030EA1FC01115
7D9414>I<13C01201A4EA0380A4EA0700EAFFF8EA0700A2120EA45AA45AA31310EA7020
A213401380EA3100121E0D1F7C9E10>I<001E1360002313E0EA4380EB81C01283EA8701
A238070380120EA3381C0700A31408EB0E101218121CEB1E20EA0C263807C3C015157B94
1A>I<381C0180382603C0EA47071303EA8701EA8E00A2000E13805AA338380100A31302
A25B5B1218EA0C30EA07C012157B9416>I<001EEB60E00023EBE0F0384380E1EB81C000
831470D887011330A23907038020120EA3391C070040A31580A2EC0100130F380C0B0238
0613843803E0F81C157B9420>I<3803C1E0380462103808347038103CF0EA2038146014
00C65AA45BA314203861C04012F1148038E2C100EA4462EA383C14157D9416>I<001E13
3000231370EA438014E01283EA8700A2380701C0120EA3381C0380A4EB0700A35BEA0C3E
EA03CEEA000EA25B1260EAF0381330485AEA80C0EA4380003EC7FC141F7B9418>I<3801
E0203803F0603807F8C038041F80380801001302C65A5B5B5B5B5B48C7FC120248138038
080100485AEA3F06EA61FEEA40FCEA807013157D9414>I<B512FC16017C8C19>I<EA3038
EA787C12F81378EA70700E0573A119>127 D E
%EndDVIPSBitmapFont
%DVIPSBitmapFont: Fv cmmi12 12 82
/Fv 82 127 df<133FEBE180390380E0203907006040000E1370481330003CEB3880A248
EB3900A2143A5A143C1438A212701478003013B83938031840D81C1C13803907E007001B
157E941F>11 D<147CEB018390380201801304010813C013101320A213401580EB800315
005C38010006EB07ECEB0830EB0FCC3802000C80A214075AA448130EA35C001813180014
5B5C00125B38210380D820FCC7FC90C8FCA25AA45AA41A2D7FA21C>I<3801E001EA07F8
380FFC02121F38300E04EA600638400308EA8001A200001310EB009014A0A314C0A31480
A31301A3EB0300A41306A31304A218207F9419>I<EB0F80EB3FF013401460EBC000A413
60A21370A27FA27F133E13CEEA038FEA0607120C001C1380123813031270A300E013005B
A21306EA600E130C12305BEA1C30EA07C014247EA316>I<137EEA0380EA0700120E5A5A
12781270EAFFF0EAF000A25AA51270A2EA3806EA1C18EA07E00F157D9414>I<13085BA3
EB0FE0EB1820EB27C0EB40005B48C7FC120212061204120C5A12101230A25AA35AA97E7E
1278123FEA1FE0EA0FF8EA01FCEA003C130EA2130CA212046C5AEA01E0132D7DA215>I<
383C07C038461860384720303887403813801300A2000E1370A44813E0A4383801C0A438
70038012301200A2EB0700A4130EA4130C15207E9418>I<130FEB3180EB60C013E03801
C0E013801203EA0700A25A120E121EA2EA1C01123CA3387FFFC0EA7803A33870078012F0
14005B130EA2485A12605BEA70305BEA30C0EA1180000FC7FC13237EA217>I<12035AA2
120EA45AA35AA35A1308131012E01320EA6040EA6180EA3E000D157E9411>I<EA03806C
7E6C7E7F1370A213781338A2133C131CA2131E130EA2130F7FA21480A2130FEB1BC01331
1361EBC1E0EA01C0EA0380EA0700000E13705A5A007813784813385A48131C16237DA21C
>21 D<EBC0060001130EA248485AA448485AA4000E5BA31580001EEBE100A21301EB0262
EA3B0C3839F03C0038C8FCA25AA45AA45A19207F941D>I<00071306007F130E120F000E
131CA214181438481330147014E014C038380180EB030013065B485A5B13C0EA738000EC
C7FC12F017157E9418>I<13085BA3EB0FE0EB7820EBE7C03801C000485A120748C7FCA3
120EA2120FA2EA077EEA0381EA06FE48C7FC5A5A12201260124012C0A57EA21278123FEA
1FC0EA0FF8EA01FCEA007E130E1306A2EA0404EA030CEA00F0132D7EA215>I<000FB5FC
5A5A3870418000401300EA8081A21200EA01831303A21203A21206A2120EA2000C138012
1CA2EA180118157E941C>I<EB07C0EB1860EB3030EB603813C03801803C1203A2EA0700
A3000E1378A314F04813E0EB01C0121EEB0300EA390EEA38F890C7FCA25AA45AA45A1620
7F9419>I<90387FFF8048B5FC5A390783C000EA0E01486C7E5AA25AA348485AA3495A91
C7FCEA6007130EEA3018EA1870EA07C019157E941C>I<380FFFF84813FC4813F8387020
001240128013601200A25BA412015BA21203A348C7FC7E16157E9415>I<14105CA45CA4
5CA449C7FCEB0FE0EB711C3801C10638030203000E1480001C1301001814C0EA38041270
A339E0080380A2EC070012603870100E00305B5C001C13E038062380D801FEC7FCEA0020
A25BA45BA41A2D7EA21D>30 D<000F1420D811C013407F000014809038F00100EB7002EB
7804EB38085C133CEB1C205CEB1E806DC7FC130E130F7F5B1317EB278013431383380103
C0EA020180EA04005A487F48EB708048EB390048131E1B1F7F941F>I<1408A25CA45CA4
5CA4001EEB80E000231381D8438013F0148039838100701530EA870100071420EA0E02A3
001C14405B1580EC01001402495A000E5B00065B380388E0C6B4C7FC1310A35BA45BA31C
2D7EA220>I<00041470000C14F0000814F84814781538481418A2D840031310A21306A2
1520EAC004010C1360010E13C0131E39E0770380397FE3FF005C383F81FC6CC65A1D1580
941E>I<133F3801FFC0380381E0380400404813005AA31360EA0B98EA0FF80010C7FC5A
5AA35A6C1380124038600100EA300EEA1FFCEA07E013177F9517>I<0008131F48EB3F80
EC7FC048EBE0E0394001806090380300201302485AA25B156090C71240011013C0158000
C0EB0300386020060038131C003F13F8380FFFF06C13C0C648C7FC13C0A31201A25BA212
03A390C8FC1B207E9420>39 D<121E123E126012C0A61260123E121E070C7D960E>44
D<127012F8A3127005057C840E>58 D<127012F812FCA212741204A41208A21210A21220
1240060F7C840E>I<14801301A2EB0300A31306A35BA35BA35BA35BA35BA3485AA448C7
FCA31206A35AA35AA35AA35AA35AA311317DA418>61 D<1308A5131CA400F0EB0780393F
9CFE00380FFFF8000313E0C66CC7FC133E137FEBF78013E33801C1C01380380300600002
1320487F1917819718>63 D<EB0FC0EB3030EB4018497E48487EEBC007120380D8018013
80C7FCA4EB1F87EB70473801C02738038017EA0700000EEB1F00121E121C123C0038131E
1278A25C5A14381478147000705BA2495A6C485AD81807C7FCEA0C1CEA03F019257EA31A
>I<8114018114031407A2140BA2141314331423EC43E0A21481EB0101A21302A2130413
08A201107FEB1FFFEB20005BA25BA248C7FC120281481478120C001E14F83AFF800FFF80
21237EA225>I<90B512F090380F001E81ED0780011E1303A216C0A24914801507A2ED0F
0049131E5D5DEC03E090B55A9038F000F0157881485A151C151EA248485BA35D485A5D4A
5AEC0380000F010FC7FCB512F822227DA125>I<027F138090390380810090380E006301
38132749131F49130E485A485A48C7FC481404120E121E5A5D4891C7FCA35AA55A1520A2
5DA26C5C12704AC7FC6C130200185B001C5B00061330380381C0D800FEC8FC21247DA223
>I<90B512F090380F003C150E81011EEB0380A2ED01C0A25B16E0A35BA449EB03C0A448
48EB0780A216005D4848130E5D153C153848485B5D4A5A0207C7FC000F131CB512F02322
7DA128>I<90B6128090380F00071501A2131EA21600A25BA2140192C7FCEB7802A21406
140EEBFFFCEBF00CA33801E008A21502EC0004485AA25D15184848131015305D15E0000F
1307B65A21227DA124>I<90B6128090380F00071501A2131EA21600A25BA2140192C7FC
EB7802A21406140EEBFFFCEBF00CA33801E008A391C8FC485AA4485AA4120FEAFFFC2122
7DA120>I<027F1340903903C0C08090380E00214913130170130F49EB0700485A485A48
C7FC481402120E121E5A5D4891C7FCA35AA4EC3FFF48EB00F0A34A5A7EA212704A5A7E00
1813076C13096CEB1180380380E0D8007FC8FC22247DA226>I<9039FFF83FFE90390F00
03C0A3011EEB0780A449EB0F00A449131EA490B512FC9038F0003CA348485BA448485BA4
4848485AA4000F130339FFF83FFE27227DA128>I<EBFFF8EB0F00A3131EA45BA45BA45B
A4485AA4485AA4485AA4120FEAFFF815227DA116>I<903803FFE09038001E00A35CA45C
A45CA4495AA4495AA4495AA212381278D8F80FC7FCA2EAF01EEA401C5BEA30E0EA0F801B
237DA11B>I<9039FFF801FF010FC71278166016C0011EEB010015025D5D4913205D5D02
02C7FC495A5C141C147CEBF0BEEBF11E13F2EBF80FEA01F001E07F1407A248486C7EA36E
7EEA0780811400A2000F497E39FFF80FFF28227DA129>I<EBFFFCEB0F8091C7FCA2131E
A45BA45BA45BA4485AA21520A248481340A21580A23807800115005C140F000F133EB512
FE1B227DA121>I<D9FF80EB03FE010FEC07C0160BA2D913C0EB1780A2162716470123EC
4F00168FA2ED010F0143EB021EEB41E01504150801815C1510A21520D80101495AEB00F0
1580ECF10000025D14F2A214F4489038F801E0A21470120C001EEB60033AFFC0403FFE2F
227DA12F>I<9039FF8007FE010FEB00F016C0D90BC0134001131480A2EB11E0A2903921
F001001320A2147801401302147C143CA2496C5AA3140FD801005B15881407A20002EB03
D0A215F01401485C1400A2120C001E1440EAFFC027227DA127>I<147F90380381C09038
0E0060013813385B49131C4848131E4848130E48C7FC48140F120E5A123CA25AA348141E
A3153CA3481478A215F06C14E01401EC03C00070EB0780007814000038130E6C13386C5B
380783C0D800FEC7FC20247DA225>I<90B512E090380F0038151E150E011E1307A44913
0FA3151E5B153C157815E09038F003C09038FFFE0001F0C7FCA2485AA4485AA4485AA412
0FEAFFF820227DA11F>I<147F90380381C090380E0060013813385B49131C4848131E48
48130E48C7FC48140F120E121E5AA25AA348141EA3151C153C5A1578A215F015E06C1301
90381E03C0D87021138039784087000038138E001C13B8000E13F03907C1C0203800FE80
13000101134015C0ECC08014C3ECFF007F5C1478202D7DA227>I<90B512C090380F0078
151C81011E130F811680A249EB0F00A3151E495B5D15E0EC0380D9FFFCC7FCEBF0076E7E
8148486C7EA44848485AA44848485A1680A29138038100120F39FFF801C6C8127821237D
A125>I<903803F81090380E0420903818026090382001E0EB400001C013C05B1201A200
031480A21500A27FEA01F013FE3800FFE06D7EEB1FF8EB01FCEB003C141C80A30020130C
A3140800601318141000705B5C00C85BD8C603C7FCEA81FC1C247DA21E>I<001FB512FE
391E01E00E001814061230382003C0A200401404A2EB07801280A20000140049C7FCA413
1EA45BA45BA45BA41201387FFFC01F227EA11D>I<3A3FFE01FF803A03C0003C00153015
1048485BA448C75AA4001E5CA44849C7FCA4481302A400705B12F05C12705C5C6C5B5C6C
48C8FCEA0606EA01F821237DA121>I<D8FFF0EB3FC0D80F80EB0F0090C7120C1508A25D
6D5B12075D5DA24AC7FC5CEBC0025C12035C5CA25C5C13E000015B13E191C8FC13E2A213
E413F8A26C5A5BA25BA222237DA11C>I<3BFFF03FFC03FF3B1F0003E000786C4A137017
601740A217800207EB0100A2020B130214135E14236F5A02415BA202815B138100070101
5B13825E018413E193C7FC018813E2A2019013E413A015E801C013F86E5A495BA290C75A
120600025C30237DA12E>I<90397FF803FF903907E000F84A13E0010314C09138E00180
0101EB03001506ECF00401005B6E5AEC7820EC7C405D023DC7FC143E141E141FA2142FEC
6F8014C790380187C0140301027F1304EB080101107FEB2000497F49137848C7FC48147C
D80F8013FC3AFFE003FFC028227FA128>I<D8FFF0EB3FE0D81F80EB0F00000F140C1508
00075C6D5B5D00035CEBE00192C7FC000113026D5A00005B5C6D5AEB7860EB7CC05C013D
C8FC133E133CA45BA45BA41201EA1FFF23227EA11C>I<90387FFFFE90387E001E017013
3C4913784913F090388001E000011303010013C0EC07800002EB0F00141EC75A147C1478
5C495A495A495A130F91C7FC131E4913205B49134012015B48481380485A380F0001001E
EB03005C485B48137EB512FE1F227DA121>I<EB0380EB0640EB0C201318A2EB3040A213
60A2EBE08013C03801C100A21382120313841388EA07085B5B5B1206EA0E80000FC7FC12
0EA3121E122E12460086138038060100EA0202EA010CEA00F0132380A214>96
D<EB78603801C4E0EA0302380601C0120E121C123C383803801278A338F00700A31408EB
0E101270131E38302620EA18C6380F03C015157E941A>I<EA03C0EA3F801203A348C7FC
A4120EA45A137CEA1D86EA1E03003C1380123814C0A21270A438E00780A3EB0F00130EEA
601CA2EA3030EA18E0EA0F8012237EA215>I<133FEBE080380380C0EA0701EA0E03121C
003CC7FCA25AA35AA400701340A23830018038380200EA1C1CEA07E012157E9415>I<14
1E14FC141CA31438A41470A414E01378EA01C4EA0302380601C0120E121C123C38380380
1278A338F00700A31408EB0E101270131E38302620EA18C6380F03C017237EA219>I<13
7EEA038138070080120E5A5A38780100EA7006EAFFF800F0C7FCA25AA41480A238700300
EA3004EA1838EA0FC011157D9417>I<141EEC638014C71301ECC30014801303A449C7FC
A4EBFFF8010EC7FCA65BA55BA55BA4136013E0A25BA21271EAF18090C8FC1262123C192D
7EA218>I<EB0F86EB384EEB602EEBE03C3801C01CEA03801207EB00385AA3001E1370A4
14E0120E1301EA060238030DC0EA01F1EA0001A2EB0380A338700700EAF0065BEA6038EA
3FE0171F809417>I<13F0EA07E01200A3485AA4485AA448C7FCEB0F80EB30C0EB406038
0E8070EA0F00120EA24813E0A4383801C0A2EB0380148200701384EB07041408130300E0
1310386001E017237EA21C>I<13E0A21201EA00C01300A9121E1223EA4380A21283EA87
00A21207120EA35AA3EA38201340127013801230EA3100121E0B227EA111>I<147014F0
A214601400A9130FEB3180EB41C01381A2EA0101A238000380A4EB0700A4130EA45BA45B
A3EA7070EAF0605BEA6380003EC7FC142C81A114>I<13F0EA0FE01200A3485AA4485AA4
48C7FC1478EB0184EB021C380E0C3C1310EB2018EB4000485A001FC7FC13E0EA1C38487E
A27F140838701C10A3EB0C20EAE006386003C016237EA219>I<EA01E0EA0FC01201A3EA
0380A4EA0700A4120EA45AA45AA45AA31380EAE100A31262A2123C0B237EA20F>I<393C
07E01F3A46183061803A47201880C03A87401D00E0EB801E141C1300000E90383801C0A4
489038700380A2ED070016044801E01308150EA2ED0610267001C01320D83000EB03C026
157E942B>I<383C07C038461860384720303887403813801300A2000E1370A44813E0A2
EB01C014C1003813C2EB03821484130100701388383000F018157E941D>I<133EEBC180
380380C0380700E0120E4813F0123CA25AA338F001E0A214C0130300701380EB07001306
EA381C6C5AEA07E014157E9417>I<3803C0F03804631CEB740EEA0878EB7007A2140FEA
00E0A43801C01EA3143C38038038A2EBC07014E038072180EB1E0090C7FCA2120EA45AA3
B47E181F819418>I<EB7C103801C2303803017000071360380E00E05A123C383801C012
78A338F00380A4EB070012705BEA3017EA186EEA0F8EEA000EA25BA45BA33803FF80141F
7E9416>I<EA3C0F384630C0EA4741EA8783A2EB018090C7FC120EA45AA45AA45A123012
157E9416>I<137E138138030080EA0201EA0603140090C7FC120713F0EA03FC6CB4FCEA
003FEB07801303127000F01300A2EAE002EA4004EA3018EA0FE011157E9417>I<136013
E0A4EA01C0A4EA0380EAFFFCEA0380A2EA0700A4120EA45AA31308EA3810A21320EA1840
13C0EA0F000E1F7F9E12>I<001E131800231338EA438014701283A2EA8700000713E012
0EA3381C01C0A314C2EB0384A21307380C0988EA0E113803E0F017157E941C>I<001E13
E0EA2301384381F01380008313701430EA870000071320120EA3481340A21480A2EB0100
A21302EA0C04EA0618EA03E014157E9418>I<3801E0F03806310C38081A1C0010133CEA
201C14181400C65AA45BA314083860E01012F0142038E1704038423080383C1F0016157E
941C>120 D<001E131800231338EA438014701283EA8700A2000713E0120EA3381C01C0
A4EB0380A21307EA0C0B380E1700EA03E7EA0007A2130E1260EAF01C1318485AEA8060EA
41C0003FC7FC151F7E9418>I<EBE0103803F0203807F86038060FC038080080EB0100EA
00025B5B5B5B13C048C7FC1202481340481380EA1001383F8300EA61FEEA40FCEA807814
157E9417>I<14C0A31460B512F0A2C712E0EB0180EB03001302140A77A318>126
D E
%EndDVIPSBitmapFont
%DVIPSBitmapFont: Fw cmbx12 17.28 53
/Fw 53 128 df<EB0FF8EB7FFF3901FC1FC03903F007E048486C7E000F8048486C7EA200
3F80EB8000A2007F80A400FF1580B0007F1500A5003F5CEBC001001F5CA26C6C485A0007
5C6C6C485A3901FC1FC026007FFFC7FCEB0FF8212E7DAD28>48 D<EB01C01303130F137F
EA1FFFB5FC13BFEAE03F1200B3B1007FB512F0A31C2E7AAD28>I<EB3FE03801FFFE0007
EBFF80D80F8013C0391E003FE00038EB1FF0007CEB0FF8007EEB07FCB4FC018013FEA214
03A2EA7F00003E1307C7FC15FCA2EC0FF8A215F0EC1FE015C0EC3F80EC7F00147E14F849
5A495A495A49C7FC011E130E5B133849131E49131C485A48C7123C48B512FC5A5A5A4814
F8B6FCA31F2E7CAD28>I<EB1FF890B5FC000314C03907E01FF0390F0007F8D81F807FEA
3FC06E7EA4EA1F80380F0007C75BA25D4A5A4A5AEC3F8002FFC7FCEB3FF8ECFF80903800
1FE06E7E6E7E6E7E816E7EA21680A3121C123E127FEAFF801600A24A5AEA7F00007E495A
003C5C391FC01FF06CB512C0000391C7FC38003FF8212E7DAD28>I<157015F014011403
1407140FA2141F143F147714F714E7EB01C7EB0387EB0707130F130E131C1338137013F0
13E0EA01C0EA0380EA07005A120E5A5A5A5AB712E0A3C7380FF000A9010FB512E0A3232E
7EAD28>I<000C1430390FC007F090B512E015C0158015005C14F85C1480000EC8FCA8EB
1FF0EBFFFE390FE03F809038000FC0000EEB07E0000C14F0C713F8140315FCA215FEA212
18123E127F5AA215FCA25A0078EB07F815F06CEB0FE06CEB1FC0390FC07F806CB5120000
0113FC38003FE01F2E7CAD28>I<14FF010713E0011F7F90387F80F89038FE003CD801F8
137C484813FE00071301EA0FE0A2EA1FC0003F6D5A157892C7FC485AA338FF83FC90388F
FF8090389C0FC09038B003F06E7E01E07F01C07F140081A2491480A4127FA4003F15007F
121F5D000F495AEA07E06C6C485A3901FC0FE06CB55A013F90C7FCEB0FFC212E7DAD28>
I<1238123E003FB612C0A316804815005D5D5D0078C7123800705C5D00F0495A48495A4A
C7FCA2C7120E5C5C1478147014F0495AA213035C1307A2130FA2131F5CA2133FA4137FA8
6DC8FC131E22307CAF28>I<EB0FFC90387FFF8048B512E03903F00FF03907C003F84848
C67E48C7FC157E5AA37F7F01F05B01FC5B381FFE019038FF81F06CEBE3C06CEBFF806C49
C7FC6C7F6C14C0013F7F90B57ED803E37FD807C17F390F807FFE391F001FFF003E7F007E
01031380140048147F153F151FA316007E127E153E6C5CD81FC05B390FF007F00003B55A
C61480D91FF8C7FC212E7DAD28>I<EB0FF8EB7FFF48B57E3903F80FC03907E007E04848
6C7E001F6D7E003F80EA7F8081140000FF80A41680A4007F5BA2123F13C0001F5B000F13
06EA07E03801F81C3800FFF8EB1FE090C71300A4000F495AEA1F80D83FC05BA24A5A5D49
485A6C48485A001E495A260F807FC7FC3807FFFE000113F838007FC0212E7DAD28>I<12
1E123FEA7F80EAFFC0A4EA7F80EA3F00121EC7FCAC121E123FEA7F80EAFFC0A4EA7F80EA
3F00121E0A207A9F16>I<007FB812F8B912FCA26C17F8CCFCAC007FB812F8B912FCA26C
17F836147C9B3F>61 D<1578A215FCA34A7EA24A7EA24A7FA34A7FEC0E7F021E7FEC1C3F
A202387F151F02787FEC700FA202E07F1507010180ECC003A249486C7EA201078191C7FC
498191B6FCA24981011CC7123F013C810138141FA24981160F01F081491407A248488148
6C1403B549B512FCA336317DB03D>65 D<B712C016FC16FFD801FEC77FEE7FE0707E161F
707EA2831607A4160FA25FA24C5A4C5A4C5A4B485ADB1FFEC7FC90B65AEEFF8049C7EA3F
E0EE0FF0EE07FCA2707E83821880A718005E5F16074C5A4C5AEEFFF0B812C094C7FC16F8
31317DB039>I<913A03FF800180023FEBF00349B5EAFC0701079038003F0FD91FF8EB07
9FD93FC0EB01FFD9FF807F4848C8127F4848153F0007161F49150F485A001F1607A2485A
1703127FA24992C7FCA212FFA9127FA27FEF0380123FA26C7E1707000F17006C7E6D150E
0003161E6C6C151C6C6C6C1478D93FC05CD91FF8EB03E0D907FFEB3F800101D9FFFEC7FC
D9003F13F80203138031317CB03A>I<B712F016FF17C0C6D9800013F0EE0FF8EE03FE70
7E701380EF7FC0173FEF1FE018F0170F18F8A2EF07FCA418FEAB18FCA4EF0FF8A218F017
1F18E0173FEF7FC01880933801FF004C5AEE0FFCEE7FF0B812C094C7FC16F037317EB03E
>I<DA03FF1303027FEBF00749B5EAFC0F01079038007E1FD91FF0EB0FBFD97FC0EB03FF
49487F4848C87E485A0007824848815B001F82A2484881A2127FA24992C7FC12FFAA0307
B512F8127F7FDB00011300123FA26C7EA2120F7F6C7E12036C7E6C6C7E6D6C5BD91FF849
7ED907FFEB3E3F01019038FFFC1F6D6CEBF00F0203EB800335317CB03F>71
D<B6D8807FB512C0A3C60180C7387FC000B391B7FCA30280C7127FB3A3B6D8807FB512C0
A33A317EB03F>I<B61280A3C6EB8000B3B3A7B61280A319317EB01E>I<B6D88003B5FCA3
C60180C7EA1F80051EC7FC5F5F5FEE01C0EE07804CC8FC161E5E5E16E0ED03C04B5A4BC9
FC151E153E157F5D02837F02877F91388F7FE0EC9E3F9138BC1FF002F07F4A6C7EECC007
4A6C7E826F7F81707E83163F707E707E831607707E83707F8284B6D8801FEBFF80A33931
7EB03F>75 D<B67EA3000190C9FCB3A9EE0380A416071700A25EA35E5E5E5E4B5A150FB7
FCA329317DB030>I<B500C00303B5FCA26E5DC61900D9EFF0150EA3D9E7F85DA2D9E3FC
5DA2D9E1FE5DA2D9E0FF5DA26E6C495AA26E6C495AA36E6C495AA26E6C130EA26E6C5BA2
6E6C5BA26E6C5BA26E6C5BA392387F81C0A292383FC380A2DB1FE7C7FCA2ED0FFEA26F5A
A36F5A487EB526E001F090B6FCA26F5A48317EB04D>I<B56C49B512C08080C66D903900
03E0006E6E5AEBEFFC13E780EBE3FF01E17F01E07F6E7E143F816E7E6E7E6E7E14036E7E
16806E13C0ED7FE0ED3FF0151F16F8ED0FFCED07FEED03FF6F13818117C1EE7FE1EE3FF1
EE1FF9EE0FFD160717FF828282177F173FA2171F170F486C1507B500E014031701A23A31
7EB03F>I<B77E16F816FEC690398003FF809238007FE0EE1FF0707EA283160783A65F16
0F5F4C5A4C5A4C5ADB03FFC8FC91B512F816E091388007F8ED01FC6F7E167F83707EA283
A583A4F0038017F8161F1900706C5AB6398003FE0E933801FFFC9338001FF039317EB03C
>82 D<90391FF8018090B51203000314C73907F007EF390F8000FF48C7127F003E141F15
0F5A150712FCA215037EA26C91C7FC13C0EA7FF0EBFF806C13F8ECFF806C14F06C806C80
6C14FFC6FC013F1480010114C0D9001F13E01401EC003FED1FF0150F1507126000E01403
A316E07EA26CEC07C07EB4EC0F8001C0EB1F00D8FBFC13FE00F1B512F8D8E03F5BD8C003
138024317CB02D>I<007FB8FCA39039C00FF801D87E00EC003F007C82007882A2007082
00F01780A3481603A5C792C7FCB3AA017FB6FCA331307DAF38>I<B500FE91387FFFC0A3
000101C0913801E0006C4C5A6D6C5D6E14076D6C4AC7FC011F150E6E141E6D6C141C0107
5D6E14786D6D13706D15F06D6D485A03E05B027F13036E6C485A03F890C8FC021F5B9138
0FFC1EEDFE1C0207133C6E6C5A5E806E5B5E157FB1027FB57EA33A317FB03D>89
D<EBFFF0000313FF390F803F809038C00FE0486C6C7EA26E7ED80FC07FEA0780C7FCA414
FF131FEBFFE33803FC03EA0FF0EA1FC0123FEA7F80A2EAFF00A31407A2387F800D393FC0
1DFE3A1FE078FFF03907FFE07FC6EB803F24207E9F27>97 D<EA01F812FFA3120F1207AD
EC3FE0ECFFFC9038FBE07F9039FF001F8049EB0FC04914E049EB07F016F8A2ED03FCA316
FEA816FCA3ED07F8A216F06DEB0FE06D14C001E7EB3F809039C3C0FE00903880FFF89038
003FC027327EB12D>I<EB0FFF017F13C03901FC01F03803F0033907E007F8120FEA1FC0
003FEB03F0EC01E04848C7FCA312FFA8127FA36C6C131CA2001F14386C7E000714703903
F001E03901FC07C039007FFF00EB0FF81E207D9F24>I<ED0FC0EC07FFA3EC007F153FAD
EB07F8EB3FFF9038FE07BF3903F801FF3907E0007F120F4848133F123FA2485AA312FFA8
127FA36C7EA2121F6C6C137F000714FF2603F00313E03A01FC0F3FFE38007FFEEB0FF027
327DB12D>I<EB0FFC90387FFF803901FC0FC03903F003E03907E001F0000F14F8391FC0
00FC003F14FEA24848137E157FA212FFA290B6FCA20180C7FCA4127FA36C6C1307121F15
0E6C7E6C6C131C6C6C13783900FE03E090383FFFC0903807FE0020207E9F25>I<EB01FE
90380FFF8090381FC3C090387F07E09038FE0FF0120113FC1203EC07E0EC018091C7FCA8
B512FCA3D803FCC7FCB3A8387FFFF0A31C327EB119>I<90391FF007C09039FFFE3FE03A
01F83F79F03907E00FC3000F14E19039C007E0E0001FECF000A2003F80A5001F5CA2000F
5CEBE00F00075C2603F83FC7FC3806FFFE380E1FF090C9FC121EA2121F7F90B57E6C14F0
15FC6C806C801680000F15C0003FC7127F007EEC1FE0007C140F00FC1407A4007EEC0FC0
003E1580003F141FD80FC0EB7E003907F803FC0001B512F0D8001F90C7FC242F7E9F28>
I<EA01F812FFA3120F1207ADEC07F8EC3FFEEC783F02C013809039F9801FC0EBFB0001FE
14E05BA35BB3B500C3B5FCA328327DB12D>I<EA03C0487E487E487EA46C5A6C5A6C5AC8
FCA9EA01F8127FA31207B3A7B51280A311337DB217>I<EA01F812FFA3120F1207ADEDFF
F8A3ED3F00153C5D5DEC03C04A5A4AC7FC141E147814FCEBF9FE13FB90B5FC496C7E01FC
7FEBF83F496C7E6E7E816E7E14036E7E6E7E1680157F16C0B53881FFFEA327327EB12B>
107 D<EA01F812FFA3120F1207B3B3A6B512C0A312327DB117>I<2703F007F8EB1FE000
FFD93FFEEBFFF8913A783F01E0FC02C090388300FE280FF1801FC6137F2607F30013CC01
F602F8148001FC5CA3495CB3B500C3B5380FFFFCA33E207D9F43>I<3903F007F800FFEB
3FFEEC783F02C013803A0FF1801FC03807F30001F614E013FCA35BB3B500C3B5FCA32820
7D9F2D>I<EB07FC90387FFFC03901FC07F03903F001F848486C7E4848137E001F147F00
3F158049133F007F15C0A300FF15E0A8007F15C0A36C6CEB7F80A2001F15006C6C13FE00
075C3903F803F83901FE0FF039007FFFC0D907FCC7FC23207E9F28>I<3901F83FE000FF
EBFFFC9038FBE07F9039FF003F80D80FFEEB1FC06C48EB0FE04914F0ED07F8A216FC1503
A216FEA816FC1507A216F8A2ED0FF06D14E06DEB1FC06DEB3F809039FBC0FE009038F8FF
F8EC3FC091C8FCABB512C0A3272E7E9F2D>I<3803F03F00FFEB7FC09038F1C3E0148739
0FF30FF0EA07F6A29038FC07E0EC03C091C7FCA25BB2B512E0A31C207E9F21>114
D<3801FF86000713FEEA1F00003C133E48131E140E12F8A36C90C7FCB47E13FC387FFFC0
6C13F0806C7F00077F00017FEA003F01001380143F0060131F00E0130FA27E15007E6C13
1E6C131C38FF807838F3FFF038C07F8019207D9F20>I<131CA5133CA3137CA213FC1201
12031207381FFFFEB5FCA2D803FCC7FCB0EC0380A71201EC0700EA00FEEB7F0EEB3FFCEB
07F0192E7FAD1F>I<D801F8EB07E000FFEB03FFA3000FEB003F0007141FB3153FA20003
147FA26C6CEBDFF03A00FE039FFF90387FFF1FEB0FFC28207D9F2D>I<B5EB1FFCA3D80F
F8EB03C0000715806D1307000315007F0001140E7F6C5CA2EC803C017F1338ECC078013F
1370ECE0F0011F5B14F1010F5B14F9903807FB80A214FF6D90C7FCA26D5AA26D5AA21478
A226207E9F2B>I<B53A1FFFE03FF8A33C0FF000FE0007806D150300076EEB0700816D5D
00039138FF800EA26C6C486D5A15DF01FF153C6C9039038FE038A2D97F876D5A150702C7
14F0D93FCF6D5AECCE03D91FFEEBF9C09138FC01FD16FF010F5D4A7EA26D486DC7FCA201
03147E4A133EA26D48131C35207E9F3A>I<3A7FFF807FFCA33A03FC000F006C6C131E6C
6C5BEC803890387FC078013F5B90381FE1E090380FF3C0ECFF806D90C7FC6D5A13016D7E
81815B903803DFE09038078FF08190380F07FC90381E03FEEB3C01496C7E4914804848EB
7FC00003EC3FE026FFFC01B5FCA328207F9F2B>I<B5EB1FFCA3D80FF8EB03C000071580
6D1307000315007F0001140E7F6C5CA2EC803C017F1338ECC078013F1370ECE0F0011F5B
14F1010F5B14F9903807FB80A214FF6D90C7FCA26D5AA26D5AA21478A21470A214F05C13
01007C5BEAFE035C49C8FC5BEAFC1EEA787CEA3FF0EA0FC0262E7E9F2B>I<003FB512F8
A29038800FF0393E001FE0003C133F003814C00078EB7F8014FFD8700113005C1303495A
00005B130F495A5C495A137F9038FF801C14005A485A5B0007143C485A49133848481378
003F14F8EBC001387F8007B6FCA21E207E9F24>I<B712FEA22702809428>I<001E133C00
3F137E486CB4FCA200FF1480007F1400A2383F007E001E133C190979B228>127
D E
%EndDVIPSBitmapFont
%DVIPSBitmapFont: Fx cmr10 10 61
/Fx 61 122 df<137E3801C180EA0301380703C0120EEB018090C7FCA5B512C0EA0E01B0
387F87F8151D809C17>12 D<120EA2121E1238127012E012800707779C15>19
D<1380EA0100120212065AA25AA25AA35AA412E0AC1260A47EA37EA27EA27E12027EEA00
80092A7C9E10>40 D<7E12407E12307EA27EA27EA37EA41380AC1300A41206A35AA25AA2
5A12205A5A092A7E9E10>I<1203A4EAC30CEAE31CEA7338EA1FE0EA0780A2EA1FE0EA73
38EAE31CEAC30CEA0300A40E127D9E15>I<126012F0A212701210A41220A21240128004
0C7C830C>44 D<EAFFE0A20B0280890E>I<126012F0A2126004047C830C>I<EA03C0EA0C
30EA1818EA300CA2EA700EEA6006A2EAE007ADEA6006A2EA700EEA300CA2EA1818EA0C30
EA07E0101D7E9B15>48 D<5A1207123F12C71207B3A5EAFFF80D1C7C9B15>I<EA07C0EA
1830EA201CEA400C130EEAF00F12F81307A21270EA000F130EA2131CA213381370136013
C0EA0180EA0300EA0601120C1218EA1002EA3FFE127F12FF101C7E9B15>I<EA07E0EA18
30EA201CA2EA781E130E131E1238EA001CA2131813301360EA07C0EA0030131CA2130E13
0FA2127012F8A3EAF00EEA401C1220EA1830EA07C0101D7E9B15>I<130CA2131C133CA2
135C13DC139CEA011C120312021204120C1208121012301220124012C0B512C038001C00
A73801FFC0121C7F9B15>I<EA300CEA3FF813F013C0EA2000A6EA23E0EA2C30EA301813
1CEA200E1200130FA3126012F0A3EA800EEA401E131CEA2038EA1870EA07C0101D7E9B15
>I<13F0EA030CEA0404EA0C0EEA181E1230130CEA7000A21260EAE3E0EAE430EAE818EA
F00C130EEAE0061307A51260A2EA7006EA300E130CEA1818EA0C30EA03E0101D7E9B15>
I<1240387FFF801400A2EA4002485AA25B485AA25B1360134013C0A212015BA21203A412
07A66CC7FC111D7E9B15>I<EA03E0EA0C30EA1008EA200C13061260A21270A2EA7C0CEA
3E18EA3FB0EA1FE0EA07F013F8EA18FCEA307EEA601E130FEAC0071303A4EA60021304EA
300CEA1C10EA07E0101D7E9B15>I<EA03C0EA0C30EA1818EA300C1270EA600EEAE006A2
1307A51260EA700F1230EA1817EA0C27EA07C7EA0006A2130EEA300C127813181270EA20
30EA10C0EA0F80101D7E9B15>I<B612E0A2C9FCA8B612E0A21B0C7E8F20>61
D<1306A3130FA3EB1780A2EB37C01323A2EB43E01341A2EB80F0A338010078A2EBFFF838
02003CA3487FA2000C131F80001E5BB4EBFFF01C1D7F9C1F>65 D<B512C0380F00788080
140E140FA4140E141E5C14F8EBFFF0EB003C8080801580A5EC0F00A2141E1478B512E019
1C7F9B1D>I<90381F8080EBE0613801801938070007000E13035A14015A00781300A212
7000F01400A8007014801278A212386CEB0100A26C13026C5B380180083800E030EB1FC0
191E7E9C1E>I<B512C0380F00F0143C140E80A2EC038015C01401A215E0A815C0A21403
158014071500140E5C1470B512C01B1C7E9B20>I<B512FC380F003C140C1404A2140614
02A213011400A35B13FF13037FA3140113001402A31406A2140C143CB512FC181C7E9B1C
>I<B512F8380F007814181408A2140C1404A213011400A35B13FF13037FA490C7FCA8EA
FFF8161C7E9B1B>I<90381F8080EBE0613801801938070007000E13035A14015A007813
00A2127000F01400A6ECFFF0EC0F80007013071278A212387EA27E6C130B380180113800
E06090381F80001C1E7E9C21>I<39FFF0FFF0390F000F00AC90B5FCEB000FAD39FFF0FF
F01C1C7F9B1F>I<EAFFF0EA0F00B3A8EAFFF00C1C7F9B0F>I<B4EB1FF0390F8003809038
C00100120BEA09E0EA08F0A21378133C133E131E130F14811307EB03C1EB01E114F11300
1479147D143D141FA2808080121CB46C7E1C1C7F9B1F>78 D<EB3F80EBE0E03803803848
487E000E7F487F003C148000381303007814C0A20070130100F014E0A8007014C0007813
03A200381480003C1307001C14006C130E6C5B6C6C5A3800E0E0EB3F801B1E7E9C20>I<
B51280380F00E01478143C141C141EA5141C143C147814E0EBFF8090C7FCACEAFFF0171C
7E9B1C>I<B5FC380F01E0EB007880141C141EA4141C143C5CEB01E001FFC7FCEB01E0EB
0070147880A61510A2141CA239FFF00E20C7EA03C01C1D7E9B1F>82
D<3807E080EA1C19EA30051303EA600112E01300A36C13007E127CEA7FC0EA3FF8EA1FFE
EA07FFC61380130FEB07C0130313011280A300C01380A238E00300EAD002EACC0CEA83F8
121E7E9C17>I<007FB512C038700F010060130000401440A200C014201280A300001400
B1497E3803FFFC1B1C7F9B1E>I<39FFE00FF0391F0003C0EC01806C1400A238078002A2
13C000035BA2EBE00C00011308A26C6C5AA213F8EB7820A26D5AA36D5AA2131F6DC7FCA2
1306A31C1D7F9B1F>86 D<3AFFE1FFC0FF3A1F003E003C001E013C13186C6D1310A32607
801F1320A33A03C0278040A33A01E043C080A33A00F081E100A39038F900F3017913F2A2
017E137E013E137CA2013C133C011C1338A20118131801081310281D7F9B2B>I<39FFF0
03FC390F8001E00007EB00C06D13800003EB01006D5A000113026C6C5A13F8EB7808EB7C
18EB3C10EB3E20131F6D5A14C06D5AABEB7FF81E1C809B1F>89 D<EA1FC0EA3070EA7838
7F12301200A2EA01FCEA0F1C12381270126000E01340A3EA603C38304E80381F87001212
7E9115>97 D<12FC121CAA137CEA1D87381E0180381C00C014E014601470A6146014E014
C0381E018038190700EA10FC141D7F9C17>I<EA03F8EA0C0CEA181E1230EA700CEA6000
12E0A61260EA70021230EA1804EA0C18EA03E00F127F9112>I<EB1F801303AAEA03F3EA
0E0BEA1807EA30031270126012E0A6126012701230EA1807EA0E1B3803E3F0141D7F9C17
>I<EA07E0EA0C30EA1818EA300CEA700EEA600612E0EAFFFEEAE000A41260EA70021230
EA1804EA0C18EA03E00F127F9112>I<13F8EA018CEA071E1206EA0E0C1300A6EAFFE0EA
0E00B0EA7FE00F1D809C0D>I<EB03803807C4C0EA1C783838388038301800EA701CA4EA
3018EA38386C5AEA27C00020C7FCA21230EA3FF86CB4FC1480EA2003386001C0EAC000A3
3860018038300300EA1C0EEA07F8121C7F9215>I<12FC121CAA137C1387EA1D03001E13
80121CAD38FF9FF0141D7F9C17>I<1218123CA21218C7FCA712FC121CB0EAFF80091D7F
9C0C>I<12FC121CAAEB0FE0EB0780EB06005B13105B5B13E0121DEA1E70EA1C78133813
3C131C7F130F148038FF9FE0131D7F9C16>107 D<12FC121CB3A9EAFF80091D7F9C0C>I<
39FC7E07E0391C838838391D019018001EEBE01C001C13C0AD3AFF8FF8FF8021127F9124
>I<EAFC7CEA1C87EA1D03001E1380121CAD38FF9FF014127F9117>I<EA03F0EA0E1CEA18
06487E00701380EA600100E013C0A600601380EA700300301300EA1806EA0E1CEA03F012
127F9115>I<EAFC7CEA1D87381E0180001C13C0EB00E0A21470A614E0A2EB01C0001E13
80381D0700EA1CFC90C7FCA7B47E141A7F9117>I<3803E080EA0E19EA1805EA3807EA70
03A212E0A61270A2EA38071218EA0E1BEA03E3EA0003A7EB1FF0141A7F9116>I<EAFCE0
EA1D38EA1E78A2EA1C301300ACEAFFC00D127F9110>I<EA1F90EA2070EA4030EAC010A2
12E0EAF800EA7F80EA3FE0EA0FF0EA00F8EA8038131812C0A2EAE010EAD060EA8FC00D12
7F9110>I<1204A4120CA2121C123CEAFFE0EA1C00A91310A5120CEA0E20EA03C00C1A7F
9910>I<38FC1F80EA1C03AD1307120CEA0E1B3803E3F014127F9117>I<38FF07E0383C03
80381C0100A2EA0E02A2EA0F06EA0704A2EA0388A213C8EA01D0A2EA00E0A3134013127F
9116>I<39FF3FC7E0393C0703C0001CEB01801500130B000E1382A21311000713C4A213
203803A0E8A2EBC06800011370A2EB8030000013201B127F911E>I<38FF0FE0381E0700
EA1C06EA0E046C5AEA039013B0EA01E012007F12011338EA021C1204EA0C0E487E003C13
8038FE1FF014127F9116>I<38FF07E0383C0380381C0100A2EA0E02A2EA0F06EA0704A2
EA0388A213C8EA01D0A2EA00E0A31340A25BA212F000F1C7FC12F312661238131A7F9116
>I E
%EndDVIPSBitmapFont
%DVIPSBitmapFont: Fy cmsy7 7 4
/Fy 4 122 df<1204A3EAC460EAF5E0EA3F80EA0E00EA3F80EAF5E0EAC460EA0400A30B
0D7E8D11>3 D<133F3801FF80EA0307380403001208EA1006EA300448C7FCA2EAE0015B
5BA2EAF00EA2EA7C3EEA7FCCEA1F0CC65A1310EA1020EA3FC048C7FC11177F9314>71
D<3803F002000F13063810700E0020130C12403880601C0000131813E01438EBC0303807
FFF05A3801807014601203EB00E0A24813E1000613E214FC4813F818157F931C>I<120C
A6EAFFC0A2EA0C00B20A1A7E9310>121 D E
%EndDVIPSBitmapFont
%DVIPSBitmapFont: Fz cmmi10 10.95 1
/Fz 1 79 df<48B4EB1FF8D8001FEB03C091388001001317A2903823C002A2EB21E0A290
3841F0041340A2147801805B147C143CA248486C5AA2140FA2000214A01407A2EC03E048
5CA21401120C001E6D5AEAFFC0251F7E9E25>78 D E
%EndDVIPSBitmapFont
%DVIPSBitmapFont: FA cmr10 10.95 56
/FA 56 123 df<EB3FE013E0EA01C1EA0381EA0700A8B5FCEA0700B2383FE7FC1620809F
19>13 D<90381F81F89038F04F043901C07C06390380F80FEB00F05A0270C7FCA6B7FC39
07007007B23A3FE3FE3FE02320809F26>I<12E0A212F01238121C120C1206120308087B
9F17>18 D<1207A2120F121C12381230126012C00808779F17>I<127012F012F8A21278
1208A31210A31220A21240050E7C840D>44 D<EAFFF0A20C02808A0F>I<127012F8A312
7005057C840D>I<EA03F0EA0E1C487EEA1806EA380738700380A400F013C0AD00701380
A3EA780700381300EA1806EA1C0E6C5AEA03F0121F7E9D17>48 D<13801203120F12F312
03B3A6EA07C0EA7FFE0F1E7C9D17>I<EA03F0EA0C1CEA100E487E00401380128000F013
C0EAF803A3EA200712001480A2EB0F00130E5B5B5B13605B485A48C7FC000613405A5A00
101380EA3FFF5AB5FC121E7E9D17>I<EA03F0EA0C1CEA100EEA200F007813801307A2EA
380F12001400A2131E131C1370EA07F0EA003C130E130FEB0780A214C0122012F8A300F0
13801240EB0F00EA200EEA183CEA07F0121F7E9D17>I<1306A2130EA2131E132EA2134E
138EA2EA010E1202A212041208A212101220A2124012C0B512F038000E00A7EBFFE0141E
7F9D17>I<EA1803EA1FFE5B5B13E00010C7FCA6EA11F0EA161CEA180EEA10071480EA00
03A214C0A3127012F0A200E013801240EB0700EA20066C5AEA0838EA07E0121F7E9D17>
I<137CEA0182EA0701380E0380EA0C0712183838030090C7FC12781270A2EAF1F0EAF21C
EAF406EAF807EB0380A200F013C0A51270A214801238EB07001218EA0C0E6C5AEA01F012
1F7E9D17>I<EA03F0EA0E18487E487E13071270EB038012F0A214C0A5EA7007A21238EA
180BEA0E13EA03E338000380A3EB07001230EA7806130EEA700CEA2018EA1070EA0FC012
1F7E9D17>57 D<B612FCA2C9FCA8B612FCA21E0C7E9023>61 D<5B497EA3497EA3EB09E0
A3EB10F0A3EB2078A3497EA2EBC03EEB801EA248B5FCEB000FA20002EB0780A348EB03C0
A2120C001E14E039FF801FFE1F207F9F22>65 D<90380FE0109038381C309038E0027038
03C00139078000F048C71270121E15305A1510127C127800F81400A91278007C1410123C
A26C1420A27E6C6C13406C6C13803900E00300EB380CEB0FF01C217E9F21>67
D<B512F83807801EEC0780EC03C0EC01E0EC00F015701578A2153CA3153EA8153CA2157C
1578A215F0EC01E0EC03C0EC0780EC1E00B512F81F1F7F9E23>I<B61280380F000F1403
1401140015C01540A314401500A214C0130113FF130113001440A3EC0020A31540A315C0
1401EC0380140FB6FC1B1F7E9E1F>I<B61280380780071401A2140015C01540A4EC2000
A3146014E013FF138014601420A391C7FCA87FEAFFFE1A1F7F9E1E>I<90380FE0209038
7818609038E004E03803800238070001481300001E1460A25A1520127C127800F81400A7
EC7FFCEC03E000781301127C123CA27EA27E7E380380023900E00460903878182090380F
E0001E217D9F24>I<39FFF07FF8390F000780AD90B5FCEB0007AF39FFF07FF81D1F7E9E
22>I<EAFFF0EA0F00B3ABEAFFF00C1F7E9E10>I<EAFFF8EA0F8090C7FCB21402A4140614
04A2140C141C147CB512FC171F7E9E1C>76 D<B4EB0FF8390F8003E0EC0080EA0BC0EA09
E0A2EA08F01378A27F7FA27FEB0780A2EB03C0EB01E0A2EB00F01478A2143C141EA2140F
1407A214031401123E38FF80001D1F7E9E22>78 D<B512E0380F007C141E80EC0780A215
C0A41580A2EC0F00141E147CEBFFE090C8FCAEEAFFF01A1F7E9E1F>80
D<B512E0380F80780007131E80EC0780A215C0A41580A2EC0F00141E1478EBFFE0EB8060
1438143C141C141EA3141FA315011581140F390FC0078239FFFC03C4C812F820207F9E22
>82 D<3803F040380C0CC0EA1803EA3001EA6000A212E01440A36C13007E127CEA7F80EA
3FF86CB4FC00071380C613C0EB1FE013031301EB00F014707EA46C136014E06C13C038F8
018038C60300EA81FC14217E9F19>I<007FB512E038780F010060EB006000401420A200
C0143000801410A400001400B3497E3803FFFC1C1F7E9E21>I<39FFF00FF8390F0003E0
EC0080B3A46CEB01001380120314026C6C5A6C6C5AEB3830EB0FC01D207E9E22>I<3BFF
F07FF81FF03B1F000FC007C06C903907800180170015C001805C00071502EC09E013C000
035DEC19F01410D801E05CA2EC2078D800F05CA2EC403C01785CA2EC801E017C1460013C
144090383D000F133F6D5CA2011E1307010E91C7FCA2010C7F010413022C207F9E2F>87
D<EA1FE0EA3030EA7818131CEA300E1200A313FEEA0F8EEA1E0E1238127800F01310A313
1E127838386720380F83C014147E9317>97 D<121C12FC121CAA137CEA1D87381E0180EB
00C0001C13E01470A21478A6147014F014E0001E13C0381A018038198700EA107C15207E
9F19>I<EA01FCEA0706EA1C0F123813060078C7FC127012F0A61270127800381380A238
1C0100EA0706EA01F811147F9314>I<EB01C0130F1301AAEA01F1EA070DEA0C03EA1801
12381278127012F0A61270A21238EA1803120CEA070D3801F1F815207F9F19>I<EA03F0
EA0E1C487E487EA238700380A212F0B5FC00F0C7FCA41270A26C1380A2381C0100EA0706
EA01F811147F9314>I<137CEA01C6EA030F1207EA0E061300A7EAFFF0EA0E00B2EA7FE0
1020809F0E>I<14E03803E330EA0E3CEA1C1C38380E00EA780FA5EA380E6C5AEA1E38EA
33E00020C7FCA21230A2EA3FFE381FFF8014C0383001E038600070481330A4006013606C
13C0381C03803803FC00141F7F9417>I<121C12FC121CAA137C1386EA1D03001E1380A2
121CAE38FF8FF014207E9F19>I<1238127CA31238C7FCA6121C12FC121CB1EAFF80091F
7F9E0C>I<121C12FC121CB3ABEAFF8009207F9F0C>108 D<391C3E03E039FCC30C30391D
019018001EEBE01CA2001C13C0AE3AFF8FF8FF8021147E9326>I<EA1C7CEAFC86EA1D03
001E1380A2121CAE38FF8FF014147E9319>I<EA01F8EA070E381C0380383801C0A23870
00E0A200F013F0A6007013E0A2383801C0A2381C038038070E00EA01F814147F9317>I<
EA1C7CEAFD87381E018014C0381C00E014F014701478A6147014F014E0381E01C0EB0380
381D8700EA1C7C90C7FCA8B47E151D7E9319>I<3801F04038070CC0EA0E02EA1C03EA38
011278127012F0A6127012781238EA1C03EA0C05EA0709EA01F1EA0001A8EB0FF8151D7F
9318>I<EA1CF0EAFD18EA1E3CA21318EA1C00AEEAFFC00E147E9312>I<EA0FC8EA3038EA
6018EAC008A3EAE000127CEA3FE0EA1FF0EA07F8EA003CEA800E130612C0A21304EAE00C
EAD818EA87E00F147F9312>I<1202A31206A2120EA2123EEAFFF8EA0E00AB1304A5EA07
081203EA01F00E1C7F9B12>I<381C0380EAFC1FEA1C03AE1307120CEA061B3803E3F014
147E9319>I<38FF83F8383E00E0001C13C06C1380A338070100A21383EA0382A2EA01C4
A213E4EA00E8A21370A3132015147F9318>I<39FF9FE1FC393C078070391C030060EC80
20000E1440A214C0D80704138014E0A239038861001471A23801D032143A143E3800E01C
A2EB6018EB40081E147F9321>I<38FF87F8381E03C0380E0180EB0300EA0702EA0384EA
01C813D8EA00F01370137813F8139CEA010E1202EA060738040380000C13C0003C13E038
FE07FC16147F9318>I<38FF83F8383E00E0001C13C06C1380A338070100A21383EA0382
A2EA01C4A213E4EA00E8A21370A31320A25BA3EAF080A200F1C7FC1262123C151D7F9318
>I<EA7FFFEA700E1260EA401C133813781370EA00E0120113C0EA038012071301120E12
1EEA1C03EA3802EA7006130EEAFFFE10147F9314>I E
%EndDVIPSBitmapFont
%DVIPSBitmapFont: FB cmsy8 8 21
/FB 21 122 df<B512F0A214027D881B>0 D<126012F0A2126004047D890A>I<EA4001EA
C003EA6006EA300CEA1818EA0C30EA0660EA03C0EA0180A2EA03C0EA0660EA0C30EA1818
EA300CEA6006EAC003EA400110127B901B>I<1202A3EAC218EAF278EA3AE0EA0F80A2EA
3AE0EAF278EAC218EA0200A30D0E7E8E12>I<13101330AAB512FCA238003000A9B512FC
A216187E961B>6 D<B512FCA238003000A9B512FCA238003000AA131016187E901B>I<13
FC38070380380800404813200028135000241390004413883842010838810204EA808413
481330A213481384EA810238420108384400880024139000281350001013206C13403807
03803800FC0016187E931B>10 D<EA0F80EA1FC0EA3FE0EA7FF0EAFFF8A5EA7FF0EA3FE0
EA1FC0EA0F800D0D7E8E12>15 D<3801FFF01207000EC7FC12185A5AA35AA61260A37E7E
120E3807FFF0120114167D921B>26 D<1406A380A2EC0180EC00C01560B612FCA2C81260
15C0EC0180EC0300A21406A31E127E9023>33 D<1206120FA2120E121EA2121C123C1238
A212301270A2126012E012C0124008117F910A>48 D<390F8007C03919E01C2039203030
10394018400839C00C8004EA80071400EB03801307903804C00C39400860083920303010
3910E01E60390F8007C01E0E7E8D23>I<90380FFFF0133F9038C38060D80103C7FC1203
EA06071204EA0006A2130E130CEB0FFEEB1FF80118C7FC5BA25BA25BA2EA7180B4C8FC12
7C1C17809619>70 D<EB1F80EBFFC0EA0183EA0601000C138000181300EA1002EA300400
70C7FC12601480EAE001EB0300A25BA2EAF00EEAF81EEA7C2CEA3FCCEA1F1812005B1320
EA7FC048C7FC121A7E9615>I<D801F013C0000FEB0180EA18700020EB0300126000C05B
38006006A2EBE00E140CA2EBC01C3803FFF85A38018038A200031330A2EB0070A2481440
0006EB7880EC7F0048133C1A187F961E>I<48131F00071363380F018238070600131813
205B5BA3120F7F120C7FEA1C60EA18701330EA383838301801EB1C0238600E04EB070838
C003F018177F961B>75 D<EB07C0131FEB21E01341EBC0C038018000A248C7FCA25A1206
A2120EA2120CA25A1410481330383F8060387FF0403843FF8038807E0014177E9618>I<
01041408010E1418011E1438167016F0011F130115030117147001271306EC800CED1C60
01431338ED70E0ECC0E0903883C1C0903881E3800001EBE700EB00EE4813FC00025B00C6
137000FC012013F891C712F00038150025187F962A>I<12C0B3AF02217C980A>106
D<150815181530A21560A215C0A2EC0180EC0300A21406A25CA25CA200305B12D800185B
7E5C7E495A120349C7FCEA0186A2EA00CCA21378A21330A21D227F811D>112
D<1206A8EAFFF0A2EA0600B30C1D7E9611>121 D E
%EndDVIPSBitmapFont
%DVIPSBitmapFont: FC cmr8 8 23
/FC 23 106 df<B512C0EA1C01EB0040A21420A31400AFEAFFC013177F9616>0
D<1318A2133CA2134EA21387A238010380000313C0EA0201000613E0EA04004813F01470
481378143848133C141C48131E387FFFFEB6FCA218177E961D>I<13201370A313F813B8
A2EA01BC131CA2EA031EEA020EA2EA040F7FA2000813801303A2001013C01301123838FE
0FF815177F9618>3 D<B512FE381C0070B3A338FF83FE17177F961A>5
D<B512E0EA700000781360003813206C1330001E1310120E6C13007F12036C7E7F6C5A5B
48C7FC000213105A481330A24813604813E0EA7FFFB5FC14177E9619>I<120112021204
120C1218A21230A212701260A312E0AA1260A312701230A21218A2120C12041202120108
227D980E>40 D<12801240122012301218A2120CA2120E1206A31207AA1206A3120E120C
A21218A2123012201240128008227E980E>I<1330ABB512FCA238003000AB16187E931B>
43 D<EA07C0EA1830EA3018EA701CEA600CA2EAE00EA9EA600CA2EA701CEA3018EA1C70
EA07C00F157F9412>48 D<1206120E12FE120EB1EAFFE00B157D9412>I<EA0F80EA30E0
EA4070EA8030EAC03812E0124012001370A2136013C0EA0180EA03001206EA0C081208EA
1018EA3FF0127F12FF0D157E9412>I<EA0FE0EA3030EA6018EA701CA212001318133813
60EA07E0EA00301318130C130EA212E0A2EAC00CEA4018EA3030EA0FE00F157F9412>I<
1330A2137013F012011370120212041208121812101220124012C0EAFFFEEA0070A5EA03
FE0F157F9412>I<EA6030EA7FE013C0EA44001240A4EA4F80EA70E0EA4070EA00301338
A2124012E0A2EA8030EA4060EA20C0EA1F000D157E9412>I<EA01F0EA0608EA080CEA18
1C1230EA7000126012E0EAE3E0EAEC30EAF018130CEAE00EA31260A2EA300C1318EA1830
EA07C00F157F9412>I<1240EA7FFE13FC13F8EAC008EA80101320EA00401380A2EA0100
5AA212021206A2120EA512040F167E9512>I<EA07E0EA1830EA2018EA600CA21270EA78
18EA3E10EA1F60EA07C0EA0FF0EA18F8EA607C131EEAC00E1306A21304EA600CEA3830EA
0FE00F157F9412>I<B512FCA2C8FCA6B512FCA2160A7E8C1B>61
D<EAFFE0EA0E00B3A3EAFFE00B177F960D>73 D<EAFFFC381C0380EB00C014E01470A414
E014C0EB0380381FFE00381C0780EB01C0EB00E0A514E1A2147238FF803C18177F961A>
82 D<12FCA212C0B3AB12FCA206217D980A>91 D<12FCA2120CB3AB12FCA2062180980A>
93 D<12301278A212301200A512F81238AC12FE07177F960A>105
D E
%EndDVIPSBitmapFont
%DVIPSBitmapFont: FD cmbx12 12 58
/FD 58 128 df<EB0FF0EB7FFC3801F80E3803E01F48485AEA0F80A2141E140C91C7FCA4
B6FCA2380F801FB2397FF0FFE0A21B237FA21F>12 D<EB0FFF137F3801F83FEA03E0EA07
C0EA0F8080A7B6FCA2380F801FB2397FF0FFE0A21B237FA21F>I<EA03C01207120FA2EA
1F80EA3E005A12F012600A0975A21C>19 D<1238127C12FE12FFA2127F123B1203A31206
A2120C121C12181270122008117CA210>39 D<13181330136013C01201EA0380EA0700A2
120E121E121C123CA35AA412F85AAB7E1278A47EA3121C121E120E7EA2EA0380EA01C012
001360133013180D317BA416>I<12C012607E7E121C7E7EA2EA038013C0120113E0A3EA
00F0A413F81378AB13F813F0A4EA01E0A313C012031380EA0700A2120E5A12185A5A5A0D
317DA416>I<1238127C12FE12FFA2127F123B1203A31206A2120C121C12181270122008
117C8610>44 D<1238127C12FEA3127C123807077C8610>46 D<13FE3807FFC0380F83E0
381F01F0383E00F8A248137CA312FC147EAD007C137CA36C13F8A2381F01F0380F83E038
07FFC03800FE0017207E9F1C>48 D<13181378EA01F812FFA21201B3A7387FFFE0A21320
7C9F1C>I<EA03FCEA0FFF383C1FC0387007E0007C13F0EAFE0314F8A21301127CEA3803
120014F0A2EB07E014C0EB0F80EB1F00133E13385BEBE018EA01C0EA0380EA0700000E13
38380FFFF05A5A5AB5FCA215207D9F1C>I<13FE3807FFC0380F07E0381E03F0123FEB81
F8A3EA1F0314F0120014E0EB07C0EB1F803801FE007F380007C0EB01F014F8EB00FCA200
3C13FE127EB4FCA314FCEA7E01007813F8381E07F0380FFFC03801FE0017207E9F1C>I<
14E013011303A21307130F131FA21337137713E7EA01C71387EA03071207120E120C1218
1238127012E0B6FCA2380007E0A790B5FCA218207E9F1C>I<00301320383E01E0383FFF
C0148014005B13F8EA33C00030C7FCA4EA31FCEA37FF383E0FC0383807E0EA3003000013
F0A214F8A21238127C12FEA200FC13F0A2387007E0003013C0383C1F80380FFF00EA03F8
15207D9F1C>I<EB1F80EBFFE03803E0703807C0F0380F01F8121F123EA2387E00F0007C
1300A2EAFC08EB7FC0EBFFE038FD80F038FF00F848137CA248137EA4127CA3003C137C12
3E001E13F86C13F0380783E03803FFC0C6130017207E9F1C>I<12601278387FFFFEA214
FC14F8A214F038E0006014C038C00180EB0300A2EA00065B131C131813381378A25BA312
01A31203A76C5A17227DA11C>I<13FE3803FFC0380703E0380E00F05A1478123C123E12
3F1380EBE0F0381FF9E0EBFFC06C13806C13C06C13E04813F0381E7FF8383C1FFCEA7807
EB01FEEAF000143E141EA36C131C007813387E001F13F0380FFFC00001130017207E9F1C
>I<EA01FE3807FF80380F83E0381E01F0EA3E004813F8147800FC137CA3147EA4007C13
FEA2EA3E01381E037EEA0FFEEA07FCEA0020EB007CA2121E003F13F8A214F0EB01E0381E
03C0381C0F80380FFE00EA03F817207E9F1C>I<1470A214F8A3497EA2497EA3EB067FA2
010C7F143FA2496C7EA201307F140F01707FEB6007A201C07F90B5FC4880EB8001A2D803
007F14004880000680A23AFFE007FFF8A225227EA12A>65 D<B67E15F03907F001F86E7E
157EA2157FA5157E15FE5DEC03F890B55AA29038F001FCEC007E811680151F16C0A6ED3F
80A2ED7F00EC01FEB612F815C022227EA128>I<D903FE138090381FFF819038FF01E339
01F8003FD803E0131F4848130F48481307121F48C71203A2481401127EA200FE91C7FCA8
127EED0180127F7E15036C6C1400120F6C6C1306D803F05B6C6C13386CB413F090381FFF
C0D903FEC7FC21227DA128>I<B67E15F03907F003FCEC007E81ED1F80ED0FC0ED07E0A2
16F01503A316F8A916F0A3ED07E0A2ED0FC0ED1F80ED3F00157EEC03FCB612F015802522
7EA12B>I<B612FCA23807F000153C151C150C150EA21506140CA31500141C143CEBFFFC
A2EBF03C141C140CA21503A214001506A3150EA2151E153EEC01FCB6FCA220227EA125>
I<B612F8A23807F001EC007815381518151CA2150CA21418A21500A214381478EBFFF8A2
EBF07814381418A491C7FCA8B512C0A21E227EA123>I<B538803FFCA23A07F0000380ED
0700150E15185D15E04A5A4A5A4AC7FC140E1418143C14FCEBF1FEEBF3FFEBF77F9038FE
3F8001F87F496C7E140F6E7E816E7E1401816E7E81ED3F8016C0ED1FE0B53881FFFEA227
227EA12C>75 D<B512C0A2D807F0C7FCB31518A41538A21570A215F014011407B6FCA21D
227EA122>I<D8FFF0EC0FFF6D5C000716E0D806FC1437A3017E1467A26D14C7A290391F
800187A290390FC00307A3903807E006A2903803F00CA2903801F818A3903800FC30A2EC
7E60A2EC3FC0A2EC1F80A3EC0F00D8FFF091B5FC140630227EA135>I<B6FC15E03907F0
07F0EC01FC1400157EA2157FA5157EA215FC1401EC07F090B512E0150001F0C7FCADB57E
A220227EA126>80 D<EB07FC90383FFF809038FC07E03903F001F848486C7E4848137E48
487FA248C7EA1F80A24815C0007E140FA200FE15E0A9007E15C0007F141FA26C15809038
81F03F261F83F81300390FC70C7E3907E606FC3903F607F8D800FF13E090383FFF800107
1420EB0003EC01C0EDE0E015FF16C080A2ED7F801600151E232C7DA12A>I<B512FEECFF
C03907F007F0EC01F86E7E157E157FA6157E5D4A5AEC07F090B512C05D9038F00FE06E7E
6E7E6E7EA81606EC00FEEDFF0CB538803FF8ED0FF027227EA12A>I<3801FE023807FF86
381F01FE383C007E007C131E0078130EA200F81306A27E1400B4FC13E06CB4FC14C06C13
F06C13F86C13FC000313FEEA003F1303EB007F143FA200C0131FA36C131EA26C133C12FC
B413F838C7FFE00080138018227DA11F>I<007FB61280A2397E03F80F00781407007014
030060140100E015C0A200C01400A400001500B3A248B512F0A222227EA127>I<B5EB0F
FEA2D807F0EB00C0A26C6CEB0180A26D1303000115007F000014067F6D5BA2EC801C013F
1318ECC038011F133014E0010F5BA26D6C5AA214F901035B14FD6DB4C7FCA26D5AA3147C
A21438A227227FA12A>86 D<3A7FFFC1FFF8A23A03FC000C006C6C5B15386C6C13306D6C
5A15E090383FC1C090381FE18002E3C7FCEB0FF7EB07FE6D5AA26D7E13008081497F14BF
9038031FE0496C7E130E90380C07F8496C7E1338496C7E90386000FF5B0001EC7F8049EB
3FC03AFFFC03FFFEA227227FA12A>88 D<B5EB0FFEA2D807F8EB00C015016C6C14806DEB
030000015C6C6C13065D90387F801C90383FC018153890381FE0306D6C5A15E06D6C5A90
3803FD8014FF6D90C7FC5C1300AC90381FFFF0A227227FA12A>I<EA0FFC383FFF80387E
07C0EB03E0130114F0123C1200A2133FEA03FDEA1FC1EA3F01127E12FCA4EA7E02EB0CF8
381FF87F3807E03F18167E951B>97 D<B4FCA2121FABEB0FE0EB3FF8EBE07CEB803E497E
EC0F80A215C0A81580141F01801300EBC03E381EE07C381C3FF838180FC01A237EA21F>
I<EBFF80000713E0380F83F0EA1F03123E127E387C01E090C7FC12FCA6127C127EA2003E
13186C1330380FC0603807FFC0C6130015167E9519>I<EB01FEA2EB003EABEA01FC3807
FFBE380F81FE381F007E003E133E127E127C12FCA8127CA26C137E6C13FE380F83BE3907
FF3FC0EA01FC1A237EA21F>I<13FE3807FF80380F87C0381E01E0003E13F0EA7C0014F8
12FCA2B5FCA200FCC7FCA3127CA2127E003E13186C1330380FC0703803FFC0C613001516
7E951A>I<EB1FC0EB7FE0EBF1F0EA01E31203EA07C3EBC1E0EBC000A6EAFFFEA2EA07C0
B2EA3FFCA2142380A211>I<3801FE0F3907FFBF80380F87C7381F03E7391E01E000003E
7FA5001E5BEA1F03380F87C0EBFF80D809FEC7FC0018C8FCA2121C381FFFE06C13F86C13
FE001F7F383C003F48EB0F80481307A40078EB0F006C131E001F137C6CB45A000113C019
217F951C>I<B4FCA2121FABEB07E0EB1FF8EB307CEB403CEB803EA21300AE39FFE1FFC0
A21A237EA21F>I<121C123E127FA3123E121CC7FCA7B4FCA2121FB2EAFFE0A20B247EA3
10>I<B4FCA2121FB3ADEAFFE0A20B237EA210>108 D<3AFF07F007F090391FFC1FFC3A1F
303E303E01401340496C487EA201001300AE3BFFE0FFE0FFE0A22B167E9530>I<38FF07
E0EB1FF8381F307CEB403CEB803EA21300AE39FFE1FFC0A21A167E951F>I<13FE3807FF
C0380F83E0381E00F0003E13F848137CA300FC137EA7007C137CA26C13F8381F01F0380F
83E03807FFC03800FE0017167E951C>I<38FF0FE0EB3FF8381FE07CEB803E497E1580A2
EC0FC0A8EC1F80A29038803F00EBC03EEBE0FCEB3FF8EB0FC090C8FCA8EAFFE0A21A207E
951F>I<EBFE033807FF87380FC1C7381F006F48133F127E80127C12FCA7127EA2003E5B
6C5B380FC1DF3807FF9F3801FC1FC7FCA8ECFFE0A21B207E951E>I<EAFE1FEB3FC0381E
67E013C71387A2381F83C090C7FCADEAFFF0A213167E9517>I<EA0FF3EA3FFFEA781FEA
6007EAE003A212F000FCC7FCEA7FE013F8EA3FFEEA0FFF120138000F80EAC007130312E0
A238F00700EAFC0EEAEFFCEAC7F011167E9516>I<487EA41203A21207A2120F123FB5FC
A2EA0F80ABEB8180A5EB8300EA07C3EA03FEEA00F811207F9F16>I<38FF01FEA2381F00
3EAF147E14FE380F81BE3907FF3FC0EA01FC1A167E951F>I<39FFE07FC0A2390F801C00
6C6C5A6C6C5AEBF0606C6C5A3800F980137F6DC7FC7F80497E1337EB63E0EBC1F03801C0
F848487E3807007E000E133E39FF80FFE0A21B167F951E>120 D<39FFE01FE0A2391F80
0700000F1306EBC00E0007130C13E000035BA26C6C5AA26C6C5AA2EB7CC0A2137F6D5AA2
6DC7FCA2130EA2130CA25B1278EAFC3813305BEA69C0EA7F80001FC8FC1B207F951E>I<
B612E0A21B02808E1C>123 D<EA380EEA7C1F38FE3F80A3387C1F00EA380E11077BA31C>
127 D E
%EndDVIPSBitmapFont
%DVIPSBitmapFont: FE cmsy10 12 53
/FE 53 115 df<B612FCA21E027C8C27>0 D<6C13026C13060060130C6C13186C13306C
13606C13C03803018038018300EA00C6136C1338A2136C13C6EA018338030180380600C0
48136048133048131848130C4813064813021718789727>2 D<13C0A538E0C1C0EAF0C3
3838C700EA0EDCEA03F0EA00C0EA03F0EA0EDCEA38C738F0C3C0EAE0C13800C000A51215
7D9619>I<801301AFB7FCA23900018000AEB7FCA220227DA027>6
D<B7FCA23900018000AEB7FCA23900018000AF130020227D9827>I<EB0FF0EB708E3901
8081803902008040481420481410481408A2481404A2481402A3481401A3B7FC39800080
01A400401402A36C1404A26C1408A26C14106C14206C144039018081803900708E00EB0F
F020227D9C27>I<EB0FF0EB700E39018001800002C71240481420000C14300012144800
1114883920800104A23940400202EB2004EB10083980081001EB0420EB0240EB0180A2EB
0240EB0420EB08103940100802EB2004EB40023920800104A20011C7128800121448000C
1430000414206C144039018001803900700E00EB0FF020227D9C27>10
D<EA03F0EA0FFCEA1C0EEA300338600180A238C000C0A638600180A238300300EA1C0EEA
0FFCEA03F012127D9519>14 D<B7FC7EC9FCA8B7FCA2C9FCA8007FB6FCB7FC20167D9627
>17 D<150C153C15F0EC03C0EC0F00143C14F0EB03C0010FC7FC133C13F0EA03C0000FC8
FC123C12F0A2123C120FEA03C0EA00F0133C130FEB03C0EB00F0143C140FEC03C0EC00F0
153C150C1500A8007FB512F8B612FC1E287C9F27>20 D<12C012F0123C120FEA03C0EA00
F0133C130FEB03C0EB00F0143C140FEC03C0EC00F0153CA215F0EC03C0EC0F00143C14F0
EB03C0010FC7FC133C13F0EA03C0000FC8FC123C127012C0C9FCA8007FB512F8B612FC1E
287C9F27>I<D807E01301EA0FF8EA3FFCD8381E130338700780396003C00639C001E00E
903800781C48EB3FFCEC1FF0EC07E0200B7D9127>24 D<90380FFFFC137FD801F0C7FCEA
03800006C8FC5A5A5AA25AA25AA81260A27EA27E7E7E6C7EEA01E039007FFFFC131F1E1E
7C9A27>26 D<B512C014F0C7123C140E1403EC0180EC00C01560A21530A21518A81530A2
1560A215C0EC0180EC0300140E147CB512F014801D1E7B9A27>I<4B7EA46F7EA2166082
A2161C8282B812E0A2C9EA0700160E5E1630A25E5EA24B5AA42B1A7D9832>33
D<01601303A4496D7EA248486D7E48C81260A2000E153848814881B812C0A20038C8EA0E
006C5D6C5D00031560A26C6C5C6C6C495AA2016049C7FCA42A1A7C9832>36
D<D807E01301EA0FF8EA3FFCD8381E130338700780396003C00639C001E00E903800781C
48EB3FFCEC1FF0EC07E0C9FCA9007FB6FCB7FC20167D9627>39 D<14C0495AA249C9FCA2
13065B5B013FB612E090B7FCD801C0C9FC0007CAFC123E12F8123C120FEA0380C67E017F
B612E07F0118C9FC7F7F7FA26D7EA26D7E2B1C7D9932>I<156081A281A2818181B77E16
E0C91270161CEE0F80EE03E0EE0780EE1E0016381660B75A5EC80003C7FC15065D5DA25D
A25D2B1C7D9932>I<D803F8EB01F8D807FEEB0FFE3A1E3F801C033B3807C03001803A20
03E06000486C6C481340903800F98000C0017FC71220487F143E806E7E141F6F13600040
D933E01340EC61F06CD9C0F813803A3001807C033B1807003F8F00D80FFEEB0FFCD803F0
EB03F82B157D9432>49 D<EB1FFF137F3801E000EA03800006C7FC5A5A5AA25AA35AA2B6
FCA200C0C7FCA21260A37EA27E7E7E6C7EEA01E038007FFF131F181E7C9A21>I<1403A2
1406A2140CA21418A21430A21460A214C0A3EB0180A2EB0300A21306A25BA25BA25BA25B
A25BA2485AA248C7FCA31206A25AA25AA25AA25AA25A1240183079A300>54
D<0040141000C0143000601460A36C14C0A36CEB0180A26CEB0300A33807FFFEA2380300
0CA36C6C5AA36C6C5AA2EB6060A36D5AA2EB1980A3010FC7FCA31306A21C2480A21D>56
D<B512F8A2C71218AE383FFFF85AC71218AFB512F8A215237DA21C>I<1506150E151E15
3EA2157E155E15DE159E1401151E140314021406140CA21418A214301460A214C0130114
80EB03009038077FFF91B5FC5B90381C000F5BEA407001F01480EAE1E0B44813074914F8
90C713F0007EEC03C0003C91C7FC25267EA328>65 D<143F903801FF80010713C0EB0E07
EB30030160138013C038018007D803001300481306000E130E141848131091C7FC123C12
38A212781270A212F0A76C13031406007C5B5C6C5B383F80C06CB45A6C48C7FCEA03F81A
2480A21A>67 D<90380FFFE0017F13FC48B6FC260387801380D80C07EB1FC00018EC07E0
003890380003F000701401D8600FEB00F812C000001578A2130EA2131E1670A2011C14F0
16E0133C0138EB01C0A20178EB038001701400150601F05B495B1520000114C0D9C007C7
FC147E3803FFF8000F13C0D81FFCC8FC25227FA126>I<91387FFFFE49B6FC130790390C
1E000C0130140801701400EBE01CA23801C03C1300C71238A21478A21470A291B5FCA249
13FC02C0C7FCA213035CA249C8FCA2130EA25B1220EA703812F86C5AEA7FC06C5A001EC9
FC28247FA124>70 D<147F903803FFC0010F13E0EB1C07EB600101C013C0EA0180390300
038000061400000E5B48130C14084890C7FCA212781270A200F0EB01801403140715005C
A25C6C131E143E007C137E007E13DC383F839C381FFE3C380FFC38EA03E0C75AA25C5C38
180180D83E03C7FCEAFFFCEA3FF8EA0FE01B297EA21E>I<D91F801304D97FC0131CD801
FF1438EA0303000C15701218003815F0007015E000605B00C01401D8000714C0A2150314
0016805B1507017FB5120090B6FC4814EF39001E000F011C130EA2013C131E1338A21378
0170131CA201F0133C491406160C0001151849EB3FF04914C048C7EA1F0027247FA12A>
I<0107B5FC017F13FE90B512F83903C00C003806001C000E5B5A00101378C71270A214F0
5CA21301A25CA213035CA21307A291C7FCA25B130EA25B15304913E0013013C0001FB512
00007F5BB512F8202281A11B>I<0110EB07800170EB1FC0D801F013630003EB01810004
903806018000000108C7FC143014405C01E3C8FC13E4EA01EC13F8A4120313BCA2EA079C
139E131E7F120FEA0E0780121E381C03C06E1380D83C0113013A3800F00300ECF8020078
EB7C040070EB3E180060EB1FE00080EB0F8022247FA226>75 D<EC03E0EC0FF0EC3FF814
43EB01C1EB038090380700F015E0010E13C0011E1300A25BA35BA35BA312015BA3485AA3
485A90C7120C151CD80FFC1338391FFF8070ECF06039387FFFC0D8600F130038C001FC1E
247FA222>I<0218151002781530186014F818E017016E1403EF07C002BC140FEB013C17
1F173B023E1473010215E3021E01011380EE03C301041587021FEB0707160E496C131C16
38DB80781300011014F091390781E00FED83C00120EBC780EDCF0090384003FE5D9038C0
01F801805B00616D5A007FC75A4891C713F04817E0EF0780003C93C7FC34257EA23C>I<
171E17FEEE01FC1603026014F8D901E014C0EE06006E130401035CA3EB02F85E1478A2D9
067C5B1304143CA2023E5B1308141E141F5E497EA2158001200181C7FC140715C11340EC
03E2A290388001F212010063C712FE007F5C48147C481478481430003891C8FC2F2980A6
29>I<90380181F890380207FE90380C0FFF903910303F80903960600FC09038C0C007D8
018113032603038013E000071300D80E071301130E121C131848C7FCA21278007015C0A2
00F014031680A2150716001506150E6C5C151800785C007C5C007E5C6C495A261F8006C7
FC380FE03C3807FFF06C13C0C648C8FC23247DA228>I<90380FFFE0017F13FC48B6FC26
0387801380D80C07EB1FC000181407003890380003E01270D8600F130112C0120016C013
0EED0380131EED07001506011C5B1510013C13609038380380027FC7FCEB79FCEB7BE001
70C8FCA213F05BA212015BA2485AA248C9FC120623247FA123>I<EC3F80903801FFE001
0713F090380E03F890383000FC0140137E4848133E48C7121E48141F120E000C140F121C
5AA212781270150E12F0151E151CA215387E1570007C1460007EEB60E0393F0181C0391F
FF0180390FFC03003807F004C712181460EB07C0D80FFFC7FCD83FFC1303486C13073903
FFC00E39007FF80C90380FFFF0010113E09038003F8020297BA229>I<90380FFFF8017F
13FF48B612803A0387803FC0D80C07EB07E0001814030038EB00011270EA600F00C015C0
1200ED0380010E14001506011E5B5D15E090381C1FC04AC7FCEB3C7FEB381F6E7E137890
387007C0A29038F003E013E06E7E000115039039C000F806160C0003EC7C1849EB7FE090
C7EA3FC00004EC1F0028237FA12A>I<EC1FC0ECFFF04913F890380701FC90380C007C49
133C5B0170133801F013201500A27F7F137E6D7EEB1FE0EB0FF8EB03FCEB00FE143FEC1F
80EC0FC00006130748130312385A158012F0EC07006C13065C007E5B387F80F0383FFFC0
000F90C7FCEA03F81E247FA21E>I<1602160C013FB512F890B612F0000315C02604001C
C7FC001C133C123C48137C1478127012C0C712F85CA313015CA313035CA313075CA3130F
91C8FCA3131EA2131C133C13385B136027277FA31B>I<01F01440D803F8EB01C0000F14
03D81878148000201407D800701400A201F05B49130E151E485A5D485A157C48C7FC5D12
0E1401001E495A001C1470EC07F048130EEC0CE00078131800701331146100F0EBC1C0EB
0181EB03031306EAF80CEAFC30D87FE013F8D83F805B391E0001C0222381A11F>I<007C
14C0B414F0383F8001000F14F8EA07C0EC00786C6C1338151800011410A27F1530000014
201560154015C0EC0180140315005C140E5C5C14785CEBE1E0EBE3C03801E78001EFC7FC
13FE5B5B5B5BEA038090C8FC1D247EA11F>I<EB7F803801FFE038078078380E001C0018
1306487F48EB0180A248EB00C0B3A4004014401A1F7D9D21>92 D<130CA2131EA31333A2
EB6180A2EBC0C0A338018060A248487EA300067FA2487FA3487FA2487FA248EB0180A348
EB00C015401A1F7D9D21>94 D<EB03C0EB1E0013385B5BB1485A485A000FC7FC12F8120F
EA03806C7E6C7EB113707F131EEB03C012317DA419>102 D<12F8120FEA03806C7E6C7E
B113707F131EEB03C0EB1E0013385B5BB1485A485A000FC7FC12F812317DA419>I<1320
136013C0A3EA0180A3EA0300A21206A35AA35AA25AA35AA35AA21260A37EA37EA27EA37E
A37EA2EA0180A3EA00C0A3136013200B327CA413>I<12C0A21260A37EA37EA27EA37EA3
7EA2EA0180A3EA00C0A31360A213C0A3EA0180A3EA0300A21206A35AA35AA25AA35AA35A
A20B327DA413>I<12C0B3B3AD02317AA40E>I<EA8010EAC030B3B3ACEA80100C327AA419
>I<160116031606A2160CA21618A21630A21660A216C0A2ED0180A2ED0300A21506A25D
A25DA25D1206001E5C122F004F5CEA87800007495AEA03C04AC7FCA23801E006A26C6C5A
A2EB7818A26D5AA26D5AA26D5AA26D5AA26DC8FCA228327D812A>112
D<B712F86C15F0A2003CC81220123E001E1540121F6C15806D1301000715006D5B000314
026D1306000114046D130C000014086D1318017813106D5B133E011E5B131F6D5B1480D9
0781C7FC14C1EB03C214E2EB01E414F4EB00F8A21470A2142025237EA12A>114
D E
%EndDVIPSBitmapFont
%DVIPSBitmapFont: FF cmti12 17.28 24
/FF 24 122 df<EA0780EA0FC0121FA4EA0F401200A21380A2EA0100A21202A25A5A5A5A
5A5A0A157B8616>44 D<123C127E12FEA212FCA212700707788616>46
D<92387F8004913903FFF00C91390FC0381C91383E000C02F8EB06384948EB0378D907C0
14F84948130149C713F0013E14005B5B17E0485A485A12074915C0120F5B001F1600A248
CAFCA3127EA4127C12FCA4160CA3007C5DA25EA26C5D5E001E4A5A001F14036C6C49C7FC
0007140C6C6C5BD801F013703900FE03C0D93FFFC8FCEB07F82E3376B132>67
D<92387F8008913907FFE01891391FC0703891387E001802F8EB0C70D903E0EB06F04948
13074948130349C713E0013E14015B5B000116C05B485A1207491580120F5B001F92C7FC
A248CAFCA3127EA4127C12FC92387FFFC0A2923800FC005EA3007C4A5AA46C4A5AA2121E
001F14076C5D6C6C130F6C6C133BD801F013713A00FC03C18090383FFF00D907F890C7FC
2D3375B136>71 D<D90FFEED0FFF60D9007E16C0026FED3F80A2186F18CF02CFEDDF00EF
019FA2EF031FD9018F153E1706170CEC8780D903074A5AA21730176001065E17C0A2EE01
80010C91380301F0A21606EC03C001184A485AA21618163001304B5A1660A216C0016090
39C1800F80A2913801E300A201C001E649C7FC15ECA215F8D80180153E5DEA03C0D80FE0
49137ED8FFFE9039C01FFFF801FC5E40317BB03F>77 D<913807F00491381FFE0C91387C
0F1C9138E0039C903901C001B89039038000F849C7FC130E011E1470131C133CA2491460
A4017C1400A3137E6D7E14F0EB1FFE90380FFFC06D13F06D7F9038007FFC1407EC00FE15
7E8181A4120C48141EA3151C0038143C15381578003C1470007C5C007E495A0077495A26
738007C7FC38E1F01E38C07FF838801FE026337BB127>83 D<EB07C0EB18639038703780
EBE0173801C01FD80380130000077FEA0F00A248131E121E123EA2485BA4485BA31510EC
F0305AA2D870011320903803E060EA7802D8380413C03918086080380C30313907C01E00
1C1F789E24>97 D<EB03F0EB1C0CEB3806EBF0033801E0073803C00F3807801FA2380F00
1E481300121E123EA25AA45AA5140400781306140C1418003813306C1360EB01C0380607
00EA03F8181F789E20>99 D<157CEC07FC140FEC007C1578A415F0A4EC01E0A4EC03C0A3
EB07C39038186780EB7037EBE0173801C01FD80380130000077FEA0F00A248131E121E12
3EA2485BA4485BA31510ECF0305AA2D870011320903803E060EA7802D8380413C0391808
6080380C30313907C01E001E3278B124>I<EB07C0EB3830EBF0183801C00CEA03801207
EA0F00121E1418123E48133014E0EB078038FFFC0000F8C7FCA35AA51408140C14180070
133014606C13C038180380380C0E00EA03F0161F779E20>I<143EECC31890380381BCEB
0700010E13FC4913F8013C13785BA201F813F05B1201A23903E001E0A43907C003C0A4EC
07801380A20003130FEC1F0013C00001132F0000134FEB619EEB3E1E1300A25CA45CA200
385B00785B38F801C0495AD8700EC7FCEA1FF81E2D7D9E20>103
D<131F48B4FC5AEA001F131EA45BA45BA45BA3147E3801E3839038E603809038EC01C013
F8D803F013E013E0A201C013C0000713031380A3390F000780A3EC0F00121EA2141E1502
481406143CA2150C48133815181510152048EB18400060EB0F801F327BB124>I<1307EB
0F80A21400130690C7FCACEA01E0EA0630EA08381218EA103C123012605BA212C05B1200
485AA3485AA3485AA21381485AA2120EEA1E06A21304130CEA0E18EA0630EA03C011307A
AF16>I<133CEA07FCA2EA007C1378A413F0A4EA01E0A4EA03C0A4EA0780A4EA0F00A412
1EA45AA45AA31320EAF060A4EAE0C0A213801261EA7300121E0E3279B112>108
D<3B07C00FC007E03B0C60706038303B1870C07060383B10798038C01C3A307B00398001
7E90383F001ED8607C133EA20178013C131CD8C0F8017C133C4913781200A24848495BA3
5F4848485AA24C5A182027078003C01460EE03C0A218C0270F0007801380EF8180180017
83001E90390F000184000C0106EB00F8331F7A9E39>I<3907801F803908C060E03918E1
80703930F3003813F6EA60FC49133CA249133800C114785B1201A248485BA34A5AEA0780
A24A5A1680D80F0013C1EC0781A21600001E5C15021506150448EB03180018EB01F0211F
7A9E27>I<EB03F0EB0E1CEB3806EB70073901E00380EA03C0018013C01207EA0F005A12
1E123EA2481307A448EB0F80A215005C141EA200785B5C147000385B6C485A380C0380D8
060EC7FCEA01F81A1F789E24>I<90383E01F0903863030C9038C38C0E903883D8070001
13F002E01380EA030314C0A22606078013C0A21200168090380F000FA4011EEB1F00A315
3E5B153C5DA2017C5B017E5B4A5A90387A0380D9F10EC7FCEBF0F891C8FCA2485AA4485A
A4485A7FEA7FFC12FF222D7F9E24>I<3907C03F80390C60E0E03818718039107B01F0EA
307E017C13E0006014C00178C7FCA2485AA21200A2485AA4485AA4485AA448C8FCA4121E
120C1C1F7A9E1E>114 D<EB0FE0EB3038EBE00C380180061203EB000E48131EA2140C14
007F13E013FE3803FF806C13C06C13E0EB0FF01301EB00F81478A20070137012F8A24813
604813E04813C03840018038600300EA181CEA07F0171F7A9E1D>I<130C131E5BA45BA4
5BA3387FFFE0B512C03801E000A3485AA4485AA448C7FCA4121EA35B485AA213021306EA
3804130C5BEA1810EA1C60EA0780132C79AB17>I<D801E01338D806381378EA0C18EA18
1C1210D8303C13F0122012605B00C0EB01E0A2EA00F0A2EC03C0EA01E0A33903C00780A3
15819038800F031207A215020003EB1E06A29038C02E0C0001EB46083900E1831890383E
01E0201F7A9E26>I<3903C001C039047003E0EA0830EA18381230EB7801126014005B00
C014C0A2EA01E0A2EC0180EA03C0A33907800300A31406A2EB0004140C14081418EB8010
00035B00015B3800E180013FC7FC1B1F7A9E20>I<D801E01338D806381378EA0C18EA18
1C1210D8303C13F0122012605B00C0EB01E0A2EA00F0A2EC03C0EA01E0A33903C00780A4
9038800F001207A30003131EA2EBC03E0001135E3800E1BCEB3E3C1300A25CA21470003C
13F0007C5B495A3878038012600106C7FC6C5AEA1838EA07C01D2D7A9E22>121
D E
%EndDVIPSBitmapFont
%DVIPSBitmapFont: FG cmr17 20.74 28
/FG 28 122 df<B512F8A415047F941A>45 D<EB1FE0EBFFFC3801C07F3903001F800006
EB07C048EB03E04814F048EB01F8A248EB00FCA215FE12F86C147E7EA315FE127CC812FC
A3EC01F8A215F0140315E0EC07C0A2EC0F80EC1F00141E5C5C5C5C495A495A49C7FC130E
130C5B5B4913065B485A90C7120C12025A120C48141C003FB512FCA24814F8B6FCA21F38
7CB727>50 D<1238127C12FEA3127C12381200B3A51238127C12FEA3127C1238072579A4
15>58 D<B912FCA27ECCFCAD007FB812FCB9FCA236137C9E3E>61
D<4AB41480021FEBE00191387F0078D901F8EB0E03D903E0EB0707D90FC0EB018749C812
CF013E156F49153F5B4848151F0003160F485A491507120FA248481503A2123F90C91201
A25AA2007E93C7FCA212FEAB007E92387FFFFEA2007F9238007FC0EF1F807EA27F121FA2
6C7EA26C7EA26C7E12016C7E017C153F7F6D157FD90FC014E7D903E0EB01C7D901FCEB07
83903A007F803E0191391FFFF800020101801300373D7CBB3F>71
D<D8FFF893381FFF806D5E0003F0E00000016001BE166FA3019F16CFA3D98F80EC018FA2
D987C0EC030FA3D983E01406A3D981F0140CA3D980F81418A2027C1430A36E1460A36E14
C0A391390F800180A2913907C00300A3913803E006A36E6C5AA36E6C5AA2ED7C30A36F5A
A36F5AA3486C6D5A487E486C6DC7487EB50307B51280A2413B7CBA49>77
D<D8FFF891380FFFF07FD801FE02001300177E6D153CD9BF801418139F80138FEB87E080
1383801381EB80FC80147E8081141F81140F6E7E8114036E7E81140081157E811680151F
16C0ED0FE0150716F01503ED01F816FC150016FE167E163F1798161FEE0FD817F81607A2
16031601A21600486C1578487E486C1538B5FC1718343B7CBA3C>I<D90FF0138090387F
FE013901F00F813903C001C348C712E3000E143748143F003C141F0038140F1278007014
07A200F01403A415017EA27E007C91C7FC127E7E13C0EA1FF06CB4FC6C13F06C13FE6CEB
FFC06C14F0011F7F010313FE9038003FFF14039138007F80ED1FC0150FED07E01503A2ED
01F012C0A21500A37EA216E07E15016C15C0A26CEC03806C140700F71500D8E1C0131ED8
E0F05BD8C07E13F090380FFFE0D8800190C7FC243D7CBB2C>83 D<007FB812C0A2903AC0
03FC003F277E0001F8130F007C160300781601127017001260A200E017E0A2481760A7C7
1600B3B3EC07FE0107B512FEA2333B7DBA39>I<B500C091380FFFC0A2D807FEC83803FE
006C48ED01F80001EE00E06C6C5E1701017F5E6D4BC7FC6E5C6D6C1406170E6D6C140C01
075D6E14386D6C14305F6D7E6D6C5C1601027F5C6E49C8FC6F5A91381FC006160E91380F
E00C02075BEDF038913803F8305EEC01FC02005B15FF6F5A93C9FC81B3A34B7E91381FFF
FEA23A3B7FBA3C>89 D<EB3F803801C0F03803003C00047F000C7F486D7E001C80003E13
03003F80A3121EC7FCA3143FEB0FF3EB7E03EA01F8EA03E0EA0FC0EA1F80EA3F00123E12
7E16605AA31407A2007C130B127E003E903811F0C06C13603A07C1807F803A00FE003E00
23257CA427>97 D<EB07F8EB3C0E9038F001803901E000C0484813604848133048C71270
4814F81401123EA2007EEB00F0007C1400A212FCA9127CA2127E123E150C7E15186C7E00
0714306C6C13606C6C13C03900F0018090383C0E00EB07F81E257DA423>99
D<ED0F80EC03FFA2EC001F150FB3EB03F8EB1E07903870018F9038E0004FD803C0132F48
48131F120F90C7120F5A123EA2127E127CA212FCA9127CA2127E123EA2121E121F6C141F
6C6C133F6C6C136F6C6C13CF3A0070018FC090393C0E0FFEEB07F0273C7DBB2C>I<EB07
F8EB3C1E9038F007803901C003C00003EB01E039078000F048C712F8481478001E147C12
3EA2007E143E127CA212FCA2B612FE00FCC8FCA6127CA2127E123E15067E6C140C7F0007
14186C6C1330C66C1360017013C090381E0700EB03FC1F257EA423>I<14FCEB07839038
0E038090381C07C0EB3C0F137813F8EC078049C7FC1201AEB512FCA2D801F0C7FCB3AE48
7E387FFFE0A21A3C7FBB18>I<ED07C090390FE018609039383820709039F01E40F03901
E00F802603C00713600007ECC00048486C7EA3001F80A6000F5CA36C6C485A00035C6C6C
48C7FC3802F01EEB383838060FE00004C9FCA2120CA2120EA27E7F6CB5FC15F06C14FC6C
8039078000FF000EC7EA1F8048EC07C048140312780070EC01E012F0A50078EC03C00038
1580003C14076CEC0F000007141CD803C0137839007803C0D90FFEC7FC24387EA527>I<
EA03E012FFA212071203B3EC1FE0EC607CEC801E9038E3000F01E41480A201E8130716C0
13F0A25BB3A6486CEB0FE0B50081B5FCA2283C7EBB2C>I<1207EA0F80EA1FC0A3EA0F80
EA0700C7FCADEA07C012FFA2120F1207B3ACEA0FE0EAFFFEA20F397DB815>I<EA07C012
FFA2120F1207B3B3B1EA0FE0EAFFFEA20F3C7DBB15>108 D<3903E01FE000FFEB607CEC
801E3907E3000FD803E41480A201E8130716C013F0A25BB3A6486CEB0FE0B50081B5FCA2
28257EA42C>110 D<EB07FCEB1C0790387001C03901E000F04848137848487F48C77E48
141F001E80003E1580A248EC07C0A300FC15E0A9007C15C0A2007E140F003E1580A2001E
1500001F5C6C141E6C6C5B6C6C5B6C6C5B39007001C0D91C07C7FCEB07FC23257EA427>
I<3903E03FC000FFEBE0789038E3001CD807E6130FD803E8EB078001F8EB03C04914E049
EB01F0A2ED00F8A216FCA2167C167EA9167C16FCA216F8150116F0ED03E07F6DEB07C001
E8EB0F8001E4EB0E0001E3133C9038E1C0F09038E03F8091C8FCAE487EB57EA227367EA4
2C>I<3803E03E00FF13C39038E107803907E20FC0EA03E413E8EC0780EC030001F0C7FC
A35BB3A5487EB512C0A21A257EA41E>114 D<EBFF02380700C6000C132E0010131E1230
48130EA200E01306A37E7E6C90C7FC127FEA3FF0EBFF80000F13E06C7F000113FC38003F
FE1301EB003F00C07FEC0F8014076C1303A46C1400A26C5B140600E45B00E25B38C18070
38807F8019257DA41F>I<1330A61370A413F0A21201A212031207381FFFFEB5FCD801F0
C7FCB3EC0180A9000014006D5AA2EB78026D5AEB0E08EB03F019357FB41E>I<D803E0EB
07C000FFEB01FFA20007EB000F00031407B3A5150FA300011417A26C6C132715470178EB
87E090391E0307FFEB03FC28257EA42C>I<D8FFFEEB0FFFA2D807F0EB07F86C48EB03E0
ED01C06C7E16807F0000EC0300A2017C1306A2137E013E5BA2013F131C6D1318A26D6C5A
A2ECC07001071360A26D6C5AA214F101015BA2D900FBC7FCA214FF147EA2143CA3141828
257FA42A>I<D8FFFEEB0FFFA2D807F0EB07F86C48EB03E0ED01C06C7E16807F0000EC03
00A2017C1306A2137E013E5BA2013F131C6D1318A26D6C5AA2ECC07001071360A26D6C5A
A214F101015BA2D900FBC7FCA214FF147EA2143CA31418A25CA35CA214E05C1218383C01
80127E49C8FCA2EA7C06EA300CEA1C38EA07E028367FA42A>121
D E
%EndDVIPSBitmapFont
%DVIPSBitmapFont: FH cmr12 12 96
/FH 96 128 df<B512FE381F003E6C130E14061402A214031401A41400B3A3487EEAFFFC
18227DA11E>0 D<1460A214F0A2497E1478EB027C143CEB043E141EEB081F8001107F14
0701207F140301407F140101807F140048C77E15780002147C153C48143E151E48141F81
48158015074815C01503007FB612E0A2B712F024237EA229>I<EB0FE0EB783CEBE00E39
03C0078039078003C0390F0001E0000E1300001E14F0003E14F8003C1478007C147CA200
78143CA239F840043EA2EB7FFCA3EB4004A290C7FCA20078143C007C147CA2003C1478A2
6C14F0000E14E0000F130139078003C03903C007803900E00E00EB783CEB0FE01F247DA2
26>I<5B497EA3497EA4EB09E0A3EB10F0A3EB2078A3497EA3497EA348487EA30002EB07
80A348EB03C0A3000C14E0121E39FF801FFE1F237FA222>I<B612E038780007007C1300
003C14607E001F14206C14306D13106C7E12037F6C6C130012007F13787F133E131E131C
13085B5B4913105BA248C7FC000214305A4814605A15E0481307007FB5FCB6FC1C227DA1
23>6 D<3803FFFC38001F806DC7FCA4EB3FC03801EF7838078F1E380E0F07001E148000
3CEB03C0007C14E00078130100F814F0A6007814E0007C1303003C14C0001EEB0780000E
140038078F1E3801EF7838003FC0010FC7FCA4497E3803FFFC1C227DA123>8
D<EB1FE0EBF03C3801C00E3907800780390F0003C04814E0001E1301003E14F0003C1300
007C14F8A7003C14F0003E1301A2001E14E0A2000E14C0000F13036C14806C14006D5A00
011306008114040080130400401408EBC00CEB4008397FC00FF8003F14F0A21E237EA223
>10 D<90381FC1F090387037189038C03E3C3801807C000313783907003800A9B612C039
07003800B2143C397FE1FFC01E2380A21C>I<EB1FC0EB7020EBC0103801803800031378
EA0700143091C7FCA7B512F8380700781438B2397FE1FF80192380A21B>I<EB1FD8EB70
38EBC078EA0180120338070038A9B512F838070038B3397FF3FF80192380A21B>I<9038
0FC07F90397031C0809039E00B00402601801E13E00003EB3E013807003C91381C00C016
00A7B712E03907001C011500B23A7FF1FFCFFE272380A229>I<12E0A212F01278123812
1C12061202120108097BA218>18 D<1207A2120F121E121C1238126012401280080976A2
18>I<B5128011017D9C18>22 D<127012F8A71270AC1220A61200A5127012F8A3127005
247CA30E>33 D<EA7038EAF87CEAFC7EA2EA743AEA0402A4EA0804A2EA1008A2EA2010EA
40200F0F7EA218>I<ECC018A349485AA449485AA501065BA449485AB712C0A226001803
C7FCA4EB3006A4B712C0A22600600CC7FC495AA448485AA448485AA400065BA3222D7DA2
29>I<127012F812FCA212741204A41208A21210A212201240060F7CA20E>39
D<132013401380EA01005A12061204120CA25AA25AA312701260A312E0AE1260A3127012
30A37EA27EA2120412067E7EEA0080134013200B327CA413>I<7E12407E7E12187E1204
1206A27EA2EA0180A313C01200A313E0AE13C0A312011380A3EA0300A21206A21204120C
5A12105A5A5A0B327DA413>I<497EB0B612FEA23900018000B01F227D9C26>43
D<127012F812FCA212741204A41208A21210A212201240060F7C840E>I<EAFFF8A20D02
808B10>I<127012F8A3127005057C840E>I<14801301A2EB0300A31306A35BA35BA35BA3
5BA35BA3485AA448C7FCA31206A35AA35AA35AA35AA35AA311317DA418>I<EA01F0EA07
1CEA0C06487E00381380A2387001C0A400F013E0AE007013C0A3EA780300381380A2381C
0700EA0C06EA071CEA01F013227EA018>I<13801203120F12F31203B3A9EA07C0EAFFFE
0F217CA018>I<EA03F0EA0C1CEA100700201380384003C0A2008013E012F0EAF801A3EA
2003120014C0A2EB07801400130E5B13185B5B5B485A90C7FC000213205A5A0018136048
1340383FFFC05AB5FC13217EA018>I<EA03F8EA0C1EEA100F38200780004013C0127813
031307123800001380A214005B130C1338EA03F0EA001C130FEB0780A2EB03C0A214E012
20127012F8A200F013C01240EB0780122038100F00EA0C1CEA03F013227EA018>I<1303
A25BA25B1317A21327136713471387120113071202120612041208A212101220A2124012
C0B512F838000700A7EB0F80EB7FF015217FA018>I<00101380381E0700EA1FFF5B13F8
EA17E00010C7FCA6EA11F8EA120CEA1C07381803801210380001C0A214E0A4127012F0A2
00E013C01280EA4003148038200700EA1006EA0C1CEA03F013227EA018>I<137EEA01C1
38030080380601C0EA0C03121C381801800038C7FCA212781270A2EAF0F8EAF30CEAF406
7F00F81380EB01C012F014E0A51270A3003813C0A238180380001C1300EA0C06EA070CEA
01F013227EA018>I<12401260387FFFE014C0A23840008038C0010012801302A2485A5B
A25B5BA21360134013C0A21201A25B1203A41207A76CC7FC13237DA118>I<EA01F8EA06
0EEA0803381001801220386000C0A31270A238780180003E1300EA3F02EA1FC4EA0FF812
036C7EEA067EEA083F38100F80383007C0EA6003EB00E05A1460A40060134014C06C1380
38180300EA0E0EEA03F013227EA018>I<EA01F0EA060C487EEA1807383803801270A238
F001C0A314E0A5127013031238EA1805120CEA0619EA03E1380001C0A3EB0380A2123038
7807001306EA700CEA20186C5AEA0FC013227EA018>I<127012F8A312701200AB127012
F8A3127005157C940E>I<127012F8A312701200AB127012F8A312781208A41210A31220
1240A2051F7C940E>I<B612FEA2C9FCA8B612FEA21F0C7D9126>61
D<EA07E0EA1838EA201CEA400EEA800F12F0A31200130E131C13381330136013C0A21380
A212011300A6C7FCA5EA0380EA07C0A3EA038010237DA217>63 D<497EA3497EA3EB05E0
A2EB09F01308A2EB1078A3497EA3497EA2EBC01F497EA248B51280EB0007A20002EB03C0
A348EB01E0A348EB00F0121C003EEB01F839FF800FFF20237EA225>65
D<B512F8380F800E0007EB0780EC03C015E0140115F0A515E01403EC07C0EC0F80EC3E00
EBFFFE9038800780EC03C0EC01E015F0140015F8A6EC01F0A2EC03E0EC07C0000FEB0F00
B512FC1D227EA123>I<903807E0109038381830EBE0063901C0017039038000F048C7FC
000E1470121E001C1430123CA2007C14101278A200F81400A812781510127C123CA2001C
1420121E000E14407E6C6C13803901C001003800E002EB381CEB07E01C247DA223>I<B5
12F0380F801E00071307EC0380EC01C0EC00E015F01578A2157C153CA3153EA9153CA215
7C1578A215F015E01401EC03C0EC0700000F131EB512F01F227EA125>I<B612C0380F80
070007130114001540A215601520A314201500A3146014E013FF138014601420A3150814
00A21510A31530A2157015E0000F1303B6FC1D227EA121>I<B612C0380F800700071301
14001540A215601520A314201500A3146014E013FF138014601420A491C7FCA9487EEAFF
FE1B227EA120>I<903807F00890383C0C18EBE0023901C001B839038000F848C7127848
1438121E15185AA2007C14081278A200F81400A7EC1FFF0078EB00F81578127C123CA27E
A27E7E6C6C13B86C7E3900E0031890383C0C08903807F00020247DA226>I<39FFFC3FFF
390FC003F039078001E0AE90B5FCEB8001AF390FC003F039FFFC3FFF20227EA125>I<EA
FFFCEA0FC0EA0780B3ACEA0FC0EAFFFC0E227EA112>I<3803FFE038001F007FB3A61270
12F8A2130EEAF01EEA401C6C5AEA1870EA07C013237EA119>I<D8FFFCEBFF80D80FC0EB
7C006C48133015205D5D4AC7FC14025C5C5C5C5C5CEB81C0EB83E01385EB88F01390EBA0
78EBC03C13808080A26E7E8114036E7EA26E7E81486C7F3AFFFC07FF8021227EA126>I<
EAFFFCEA1F806CC7FCB3A21401A41403A214021406A2141E48137EB512FE18227DA11E>
I<D8FFC0EB03FF000F15F0000715E0D805E01305A2D804F01309A301781311A36D1321A3
6D1341A26D1381A39038078101A3EB03C2A2EB01E4A3EB00F8A31470120E001FEC03F03A
FFE0203FFF28227EA12D>I<39FF8007FF3907C000F81570D805E01320EA04F0A2137813
7C133C7F131F7FEB0780A2EB03C0EB01E0A2EB00F014F81478143C143E141E140FA2EC07
A0EC03E0A21401A21400000E1460121FD8FFE0132020227EA125>I<EB0FE0EB783CEBE0
0E3903C0078039078003C0390F0001E0000E1300001E14F0481478A2007C147CA2007814
3CA200F8143EA90078143C007C147CA2003C1478003E14F8001E14F06CEB01E0A2390780
03C03903C007803900E00E00EB783CEB0FE01F247DA226>I<B512F0380F803C0007130F
EC078015C0140315E0A615C014071580EC0F00143CEBFFF00180C7FCAE487EEAFFFC1B22
7EA121>I<EB0FE0EB783CEBE00E3903C0078039078003C0390F0001E0000E1300001E14
F0003E14F8003C1478007C147CA20078143CA200F8143EA90078143C007C147CA2003C14
78A2391E0380F0390E0420E0380F080139078813C03903C817803900E80E0090387C3C02
EB0FECEB000CA2EC0E06EC0F0EEC07FCA215F81403EC01E01F2D7DA226>I<B512E0380F
803C0007130E6E7E81140381A55D14075D020EC7FC143CEBFFE0EB80708080141E140E14
0FA481A3168015C014073A0FC003C10039FFFC01E2C8127C21237EA124>I<3803F02038
0C0C60EA1802383001E0EA70000060136012E0A21420A36C1300A21278127FEA3FF0EA1F
FE6C7E0003138038003FC0EB07E01301EB00F0A214707EA46C1360A26C13C07E38C80180
38C60700EA81FC14247DA21B>I<007FB512F839780780780060141800401408A300C014
0C00801404A400001400B3A3497E3801FFFE1E227EA123>I<39FFFC07FF390FC000F86C
4813701520B3A5000314407FA2000114806C7E9038600100EB3006EB1C08EB03F020237E
A125>I<D8FFF0EB7FC0D81F80EB1F006CC7120C7F00071408A26C6C5BA36C6C5BA26D13
6000001440A201785BA2137CD93C01C7FCA2EB1E02A36D5AA2148CEB0788A2EB03D0A214
F06D5AA26D5AA322237FA125>I<3BFFF03FFC03FE3B1F8007E000F86C486C4813701720
6E7ED807801540A24A7E2603C0021480A39039E004780100011600A2EC083CD800F01402
A2EC101E01785CA2EC200F013C5CA20260138890391E400790A216D090391F8003F0010F
5CA2EC00016D5CA20106130001025C2F237FA132>I<397FF803FF390FE001F83907C000
E06C6C5B00015CEBF001D800F890C7FCEB7802EB7C04133EEB1E08EB1F10EB0FB0EB07A0
14C06D7E130180497EEB0278EB047CEB0C3EEB081EEB101F496C7E140701407F496C7E14
01D801007F486D7E5AD81F807F3AFFC003FFC022227FA125>I<D8FFF0EB7FC0D81F80EB
1F00000F140C000714087F00035C6C6C5B7F00005C6D13C0017C5BD93C01C7FC133EEB1E
02EB1F06EB0F84EB078814D8EB03D014E01301AC1303EB3FFE22227FA125>I<387FFFFE
387E003E0078133C007013781260004013F012C0EB01E0388003C0A2EB07801200EB0F00
5B131E5BA25BA25B1201EBE001EA03C0A2EA07801403EA0F00001E1302A2481306140E48
131E00F8137EB512FE18227DA11E>I<12FEA212C0B3B3A912FEA207317BA40E>I<EA0804
EA1008EA2010A2EA4020A2EA8040A4EAB85CEAFC7EA2EA7C3EEA381C0F0F7AA218>I<12
FEA21206B3B3A912FEA207317FA40E>I<EA1FE0EA3038EA780C130EEA30071200A313FF
EA07C7EA1E07123C1278127000F01308A3130FEA7817383C2390380FC1E015157E9418>
97 D<120E12FE121E120EAB131FEB61C0EB8060380F0030000E1338143C141C141EA714
1C143C1438000F1370380C8060EB41C038083F0017237FA21B>I<EA01FEEA0703380C07
80121C383803000078C7FC127012F0A712700078134012386C1380380C0100EA0706EA01
F812157E9416>I<14E0130F13011300ABEA01F8EA0704EA0C02EA1C01EA380012781270
12F0A7127012781238EA1801EA0C0238070CF03801F0FE17237EA21B>I<EA01FCEA0707
380C0380381C01C01238007813E0EA700012F0B5FC00F0C7FCA512700078132012386C13
406C138038070300EA00FC13157F9416>I<133E13E33801C780EA0387130748C7FCA9EA
FFF80007C7FCB27FEA7FF0112380A20F>I<14703803F198380E1E18EA1C0E38380700A2
00781380A400381300A2EA1C0EEA1E1CEA33F00020C7FCA212301238EA3FFE381FFFC06C
13E0383000F0481330481318A400601330A2003813E0380E03803803FE0015217F9518>
I<120E12FE121E120EABEB1F80EB60C0EB80E0380F0070A2120EAF38FFE7FF18237FA21B
>I<121C123EA3121CC7FCA8120E127E121E120EB1EAFFC00A227FA10E>I<13E0EA01F0A3
EA00E01300A81370EA07F012001370B3A51260EAF0E013C0EA6180EA3F000C2C83A10F>
I<120E12FE121E120EABEB03FCEB01F014C01480EB02005B5B5B133813F8EA0F1CEA0E1E
130E7F1480EB03C0130114E0EB00F014F838FFE3FE17237FA21A>I<120E12FE121E120E
B3ADEAFFE00B237FA20E>I<390E1FC07F3AFE60E183803A1E807201C03A0F003C00E0A2
000E1338AF3AFFE3FF8FFE27157F942A>I<380E1F8038FE60C0381E80E0380F0070A212
0EAF38FFE7FF18157F941B>I<EA01FCEA0707380C0180381800C0003813E0481370A200
F01378A700701370007813F0003813E0381C01C0380E038038070700EA01FC15157F9418
>I<EA0E1F38FE61C0381E8060380F0070000E1338143CA2141EA7143CA21438000F1370
380E80E0EB41C0EB3F0090C7FCA9EAFFE0171F7F941B>I<3801F82038070460EA0E02EA
1C01003813E0EA7800A25AA71278A2EA3801121CEA0C02EA070CEA01F0C7FCA9EB0FFE17
1F7E941A>I<EA0E3CEAFE46EA1E8FEA0F0F13061300120EAD120FEAFFF010157F9413>I<
EA0F88EA3078EA601812C01308A212E0EAF000127FEA3FE0EA0FF0EA01F8EA003CEA801C
130CA212C01308EAE018EAD030EA8FC00E157E9413>I<1202A41206A3120E121E123EEA
FFFCEA0E00AB1304A6EA07081203EA01F00E1F7F9E13>I<000E137038FE07F0EA1E0000
0E1370AD14F0A238060170380382783800FC7F18157F941B>I<38FF80FE381E00781430
000E1320A26C1340A2EB80C000031380A23801C100A2EA00E2A31374A21338A313101715
7F941A>I<39FF8FF87F393E01E03C001CEBC01814E0000E1410EB0260147000071420EB
04301438D803841340EB8818141CD801C81380EBD00C140E3900F00F00497EA2EB6006EB
400220157F9423>I<38FF83FE381F00F0000E13C06C1380EB8100EA0383EA01C2EA00E4
1378A21338133C134E138FEA0187EB0380380201C0000413E0EA0C00383E01F038FF03FE
17157F941A>I<38FF80FE381E00781430000E1320A26C1340A2EB80C000031380A23801
C100A2EA00E2A31374A21338A31310A25BA35B12F05B12F10043C7FC123C171F7F941A>
I<383FFFC038380380EA300700201300EA600EEA401C133C1338C65A5B12015B38038040
EA07005A000E13C04813805AEA7801EA7007B5FC12157F9416>I<B512FE1701808C18>I<
EA6030EAF078EAF8F8EAF078EA60300D057BA118>127 D E
%EndDVIPSBitmapFont
end
%%EndProlog
%%BeginSetup
%%Feature: *Resolution 300dpi
TeXDict begin
%%BeginPaperSize: a4
a4
%%EndPaperSize

HPSdict begin
/TargetAnchors
640 dict dup begin
(equation.A.40) [61 [235 441 360 425] 653] def
(equation.A.42) [61 [146 364 165 271] 576] def
(equation.A.45) [61 [205 215 390 199] 426] def
(equation.A.47) [61 [228 137 368 121] 349] def
(equation.A.48) [62 [239 763 357 755] 841] def
(equation.A.49) [62 [222 707 382 606] 841] def
(equation.2.1) [4 [212 103 384 115] 315] def
(equation.2.2) [5 [219 737 327 677] 841] def
(equation.2.3) [5 [200 605 395 617] 817] def
(equation.2.4) [5 [103 550 468 562] 762] def
(equation.2.5) [5 [81 465 490 477] 676] def
(equation.2.6) [5 [231 345 364 357] 557] def
(cite.dere) [80 [71 211 71 223] 423] def
(equation.2.7) [5 [212 282 383 294] 493] def
(equation.2.8) [5 [159 217 437 229] 428] def
(equation.2.9) [5 [244 144 320 134] 355] def
(equation.A.51) [62 [142 377 453 389] 589] def
(cite.hklr) [80 [71 702 71 714] 841] def
(equation.A.52) [62 [178 338 418 350] 550] def
(equation.A.53) [62 [127 265 280 255] 476] def
(equation.A.54) [62 [80 192 323 116] 403] def
(cite.GomLopII) [79 [71 309 71 321] 521] def
(cite.CDF) [78 [71 158 71 170] 369] def
(equation.A.55) [63 [264 403 361 415] 615] def
(equation.A.56) [63 [244 380 380 392] 592] def
(equation.A.57) [63 [242 347 361 320] 559] def
(cite.pols) [80 [71 420 71 432] 631] def
(equation.A.60) [63 [240 252 385 264] 464] def
(equation.A.61) [64 [71 800 71 812] 841] def
(equation.A.61) [63 [261 103 303 85] 314] def
(equation.A.62) [64 [248 561 347 573] 773] def
(equation.A.63) [64 [234 515 361 527] 727] def
(equation.A.64) [64 [204 433 391 445] 645] def
(equation.A.65) [64 [211 359 276 335] 571] def
(equation.A.68) [64 [190 255 406 267] 467] def
(section.10) [47 [71 617 71 629] 829] def
(cite.sergius_3) [79 [71 285 71 297] 496] def
(cite.sergius_4) [79 [71 246 71 258] 457] def
(cite.gal) [80 [71 663 71 675] 841] def
(cite.skgsugra_13) [82 [71 755 71 767] 841] def
(subsection.7.1) [30 [71 294 71 306] 506] def
(subsection.7.2) [34 [71 775 71 787] 841] def
(subsection.7.3) [35 [71 775 71 787] 841] def
(subsection.7.4) [37 [71 526 71 538] 738] def
(cite.pincopallo) [82 [71 570 71 582] 781] def
(equation.9.47) [44 [151 389 444 401] 601] def
(cite.skgmat_1) [81 [71 191 71 203] 402] def
(equation.9.48) [44 [239 264 335 241] 476] def
(cite.CDFp) [80 [71 775 71 787] 841] def
(equation.9.49) [44 [147 175 448 187] 387] def
(subsection.10.1) [47 [71 286 71 298] 497] def
(subsection.10.2) [51 [71 454 71 466] 665] def
(subsection.10.3) [55 [71 775 71 787] 841] def
(equation.9.50) [45 [157 735 438 747] 841] def
(equation.9.51) [45 [157 684 438 696] 841] def
(equation.9.52) [45 [203 622 392 634] 833] def
(equation.9.53) [45 [205 541 391 553] 752] def
(equation.6.1) [27 [114 373 422 363] 585] def
(equation.9.54) [45 [217 500 379 512] 712] def
(equation.6.2) [27 [157 182 203 155] 394] def
(equation.9.55) [45 [253 407 342 419] 619] def
(equation.6.3) [28 [248 564 376 576] 775] def
(equation.9.56) [45 [232 372 364 384] 583] def
(equation.6.4) [28 [237 493 387 505] 704] def
(equation.9.57) [45 [191 303 404 315] 515] def
(equation.6.5) [28 [247 417 377 429] 629] def
(equation.9.58) [45 [217 214 378 226] 425] def
(equation.6.6) [28 [216 317 409 329] 529] def
(equation.9.59) [45 [138 150 457 162] 362] def
(equation.6.7) [28 [182 250 362 234] 462] def
(equation.6.8) [29 [258 716 366 728] 841] def
(equation.6.9) [29 [204 356 404 347] 568] def
(cite.pertgauging) [82 [71 668 71 680] 841] def
(equation.9.60) [46 [262 681 333 693] 841] def
(equation.9.61) [46 [172 601 423 613] 813] def
(equation.9.62) [46 [238 552 357 564] 764] def
(equation.9.63) [46 [211 324 384 336] 535] def
(equation.9.64) [46 [197 252 398 264] 463] def
(equation.9.65) [46 [237 141 358 153] 352] def
(equation.9.66) [47 [237 679 358 691] 841] def
(definizione.5.1) [25 [137 386 137 398] 597] def
(definizione.5.2) [25 [123 230 123 242] 442] def
(cite.dWLVP) [80 [71 575 71 587] 787] def
(equation.10.10) [49 [169 732 426 744] 841] def
(equation.10.11) [49 [298 451 298 463] 662] def
(equation.10.12) [49 [298 293 298 305] 504] def
(equation.10.13) [49 [265 210 330 222] 422] def
(equation.10.14) [49 [277 112 318 124] 323] def
(equation.10.15) [50 [235 709 360 721] 841] def
(equation.10.16) [50 [195 623 400 635] 835] def
(equation.10.17) [50 [298 381 298 393] 593] def
(equation.10.18) [50 [208 277 384 216] 489] def
(equation.10.19) [50 [156 149 440 161] 360] def
(cite.SW12) [78 [71 223 71 235] 435] def
(equation.1.1) [4 [167 465 423 444] 676] def
(equation.10.20) [51 [120 720 454 707] 841] def
(equation.10.21) [51 [142 632 453 624] 841] def
(Item.10) [4 [71 641 71 653] 841] def
(equation.10.22) [51 [177 341 418 353] 553] def
(Item.11) [4 [71 617 71 629] 828] def
(equation.10.23) [52 [71 800 71 812] 841] def
(equation.10.23) [51 [160 235 303 85] 446] def
(Item.12) [4 [71 563 71 575] 775] def
(equation.10.24) [52 [154 589 441 601] 800] def
(Item.13) [4 [71 525 71 537] 736] def
(equation.10.25) [52 [112 541 112 221] 753] def
(Item.14) [4 [71 365 71 377] 577] def
(Item.15) [12 [71 273 71 285] 485] def
(Item.16) [12 [71 249 71 261] 461] def
(Item.17) [28 [71 629 71 641] 841] def
(Item.18) [28 [71 479 71 491] 691] def
(Item.19) [29 [71 775 71 787] 841] def
(cite.ferscherzum) [82 [71 643 71 655] 841] def
(cite.BDW) [80 [71 265 71 277] 476] def
(equation.4.10) [17 [222 519 384 496] 731] def
(equation.4.11) [17 [243 359 352 371] 571] def
(equation.4.12) [17 [183 302 412 314] 513] def
(equation.4.13) [17 [222 226 373 238] 437] def
(equation.4.14) [17 [252 169 344 181] 381] def
(equation.4.15) [17 [151 116 444 128] 328] def
(equation.10.31) [53 [170 763 342 607] 841] def
(Item.20) [29 [71 535 71 547] 747] def
(equation.4.16) [18 [263 724 332 736] 841] def
(Item.21) [29 [71 484 71 496] 696] def
(equation.4.17) [18 [184 676 412 688] 841] def
(equation.10.33) [54 [175 685 328 638] 841] def
(Item.22) [30 [71 590 71 602] 802] def
(equation.4.18) [18 [168 461 431 438] 672] def
(equation.10.34) [54 [160 528 388 485] 740] def
(Item.23) [30 [71 566 71 578] 777] def
(equation.4.19) [18 [193 239 402 251] 450] def
(equation.10.35) [54 [159 354 276 120] 565] def
(Item.24) [38 [71 701 71 713] 841] def
(equation.10.36) [55 [263 524 332 536] 736] def
(Item.25) [38 [71 632 71 644] 841] def
(cite.kltold) [78 [71 196 71 208] 408] def
(equation.10.37) [55 [170 461 425 473] 673] def
(Item.26) [38 [71 531 71 543] 743] def
(equation.10.38) [55 [273 389 322 401] 600] def
(Item.27) [55 [71 693 71 705] 841] def
(equation.10.39) [55 [252 336 343 348] 547] def
(Item.28) [55 [71 665 71 677] 841] def
(Item.29) [63 [71 713 71 725] 841] def
(Doc-Start) [1 [71 775 71 787] 841] def
(equation.4.20) [18 [212 111 383 123] 322] def
(equation.4.21) [19 [232 715 363 727] 841] def
(equation.4.22) [19 [254 624 346 619] 836] def
(equation.4.23) [19 [218 547 377 559] 758] def
(equation.4.24) [19 [233 436 363 448] 648] def
(equation.10.40) [55 [250 283 345 295] 495] def
(equation.4.25) [19 [169 365 426 377] 576] def
(Item.30) [63 [71 494 71 506] 705] def
(equation.10.41) [55 [177 218 418 230] 430] def
(equation.4.26) [19 [193 291 402 303] 503] def
(equation.10.42) [55 [210 110 385 122] 322] def
(equation.4.27) [19 [206 231 390 243] 442] def
(equation.10.43) [56 [108 662 452 674] 841] def
(equation.4.28) [19 [217 174 378 186] 385] def
(equation.10.44) [56 [204 519 391 485] 731] def
(equation.4.29) [19 [194 111 401 123] 322] def
(equation.10.45) [56 [212 385 384 397] 597] def
(equation.10.46) [56 [271 292 324 304] 504] def
(equation.10.47) [56 [179 225 357 218] 436] def
(equation.10.48) [56 [233 130 363 142] 342] def
(equation.10.49) [57 [239 710 356 722] 841] def
(cite.sugraprimo) [81 [71 390 71 402] 602] def
(equation.4.30) [20 [245 749 350 761] 841] def
(equation.4.31) [20 [238 644 306 604] 841] def
(equation.10.50) [57 [196 626 399 610] 837] def
(equation.4.35) [20 [211 496 385 508] 707] def
(equation.10.51) [57 [205 528 390 540] 739] def
(equation.4.36) [20 [207 435 389 447] 647] def
(table.1) [77 [210 612 210 624] 824] def
(equation.10.52) [57 [272 458 324 470] 669] def
(equation.4.37) [20 [241 384 355 396] 595] def
(table.2) [78 [197 744 197 756] 841] def
(equation.10.53) [57 [191 408 404 420] 620] def
(equation.4.38) [20 [139 243 482 170] 455] def
(equation.10.54) [57 [191 361 405 373] 572] def
(equation.10.55) [57 [228 279 367 291] 491] def
(equation.10.56) [57 [209 222 386 234] 433] def
(equation.10.57) [57 [195 119 400 131] 331] def
(equation.10.58) [58 [198 734 397 746] 841] def
(cite.kltnew) [79 [71 363 71 375] 574] def
(equation.10.59) [58 [130 683 326 606] 841] def
(cite.corto) [80 [71 304 71 316] 515] def
(page.10) [11 [71 800 71 812] 841] def
(page.11) [12 [71 800 71 812] 841] def
(page.12) [13 [71 800 71 812] 841] def
(page.13) [14 [71 800 71 812] 841] def
(page.14) [15 [71 800 71 812] 841] def
(page.15) [16 [71 800 71 812] 841] def
(page.16) [17 [71 800 71 812] 841] def
(page.17) [18 [71 800 71 812] 841] def
(page.18) [19 [71 800 71 812] 841] def
(page.19) [20 [71 800 71 812] 841] def
(equation.7.10) [32 [247 737 348 749] 841] def
(equation.7.11) [32 [227 670 368 682] 841] def
(equation.7.12) [32 [254 615 342 627] 826] def
(equation.4.43) [21 [221 457 374 469] 668] def
(equation.7.13) [32 [266 580 329 592] 791] def
(equation.4.44) [21 [233 383 362 395] 594] def
(equation.7.14) [32 [239 417 356 429] 628] def
(equation.4.45) [21 [207 299 388 311] 510] def
(equation.10.61) [58 [198 390 397 402] 601] def
(equation.7.15) [32 [231 324 364 336] 536] def
(equation.4.46) [21 [254 232 344 227] 444] def
(equation.10.62) [58 [249 321 346 333] 532] def
(equation.7.16) [32 [210 272 385 284] 483] def
(equation.4.47) [21 [219 158 376 170] 370] def
(equation.7.17) [32 [262 205 333 217] 416] def
(equation.4.48) [22 [234 702 361 714] 841] def
(equation.7.18) [32 [259 150 336 162] 361] def
(equation.4.49) [22 [184 628 411 640] 839] def
(equation.7.19) [32 [249 103 346 115] 314] def
(page.20) [21 [71 800 71 812] 841] def
(page.21) [22 [71 800 71 812] 841] def
(page.22) [23 [71 800 71 812] 841] def
(page.23) [24 [71 800 71 812] 841] def
(page.24) [25 [71 800 71 812] 841] def
(cite.petropaolo) [81 [71 166 71 178] 378] def
(page.25) [26 [71 800 71 812] 841] def
(page.26) [27 [71 800 71 812] 841] def
(page.27) [28 [71 800 71 812] 841] def
(page.28) [29 [71 800 71 812] 841] def
(page.29) [30 [71 800 71 812] 841] def
(equation.4.50) [22 [244 576 351 588] 788] def
(equation.7.20) [33 [216 718 379 730] 841] def
(equation.4.51) [22 [245 534 350 546] 745] def
(equation.7.21) [33 [162 614 433 626] 825] def
(equation.4.52) [22 [296 443 340 418] 655] def
(equation.7.22) [33 [218 529 377 541] 740] def
(equation.7.23) [33 [200 433 425 427] 644] def
(equation.7.24) [33 [162 317 433 329] 529] def
(equation.4.55) [22 [218 324 366 301] 536] def
(equation.7.25) [34 [179 657 416 669] 841] def
(equation.4.56) [22 [264 234 331 246] 445] def
(equation.7.26) [34 [206 597 389 609] 808] def
(equation.4.57) [22 [244 196 351 208] 407] def
(equation.7.27) [34 [273 500 322 512] 712] def
(equation.4.58) [22 [174 133 421 145] 344] def
(equation.7.28) [34 [218 447 377 459] 659] def
(equation.4.59) [23 [209 474 387 486] 686] def
(equation.7.29) [34 [227 395 368 407] 606] def
(equation.5.1) [24 [185 511 410 523] 723] def
(equation.C.1) [68 [107 132 462 144] 344] def
(equation.5.2) [24 [262 378 333 390] 590] def
(equation.C.2) [69 [142 722 454 734] 841] def
(equation.5.3) [24 [181 260 414 255] 472] def
(equation.C.3) [69 [216 668 379 680] 841] def
(equation.5.4) [24 [186 149 409 161] 361] def
(equation.C.4) [69 [246 609 349 621] 820] def
(equation.5.5) [24 [172 103 423 115] 314] def
(equation.C.5) [69 [258 528 338 540] 740] def
(equation.5.6) [25 [235 738 360 750] 841] def
(equation.C.6) [69 [227 433 368 445] 645] def
(equation.5.7) [25 [139 687 456 699] 841] def
(equation.C.7) [69 [202 261 393 273] 472] def
(page.30) [31 [71 800 71 812] 841] def
(equation.5.8) [25 [177 635 418 647] 841] def
(equation.C.8) [69 [170 179 426 191] 391] def
(page.31) [32 [71 800 71 812] 841] def
(equation.5.9) [25 [216 426 380 438] 637] def
(equation.C.9) [69 [158 119 437 131] 330] def
(page.32) [33 [71 800 71 812] 841] def
(page.33) [34 [71 800 71 812] 841] def
(page.34) [35 [71 800 71 812] 841] def
(page.35) [36 [71 800 71 812] 841] def
(page.36) [37 [71 800 71 812] 841] def
(page.37) [38 [71 800 71 812] 841] def
(page.38) [39 [71 800 71 812] 841] def
(Hfootnote.1) [5 [89 103 89 115] 314] def
(Hfootnote.2) [9 [89 115 89 127] 326] def
(equation.4.60) [23 [204 403 391 415] 615] def
(Hfootnote.3) [21 [89 115 89 127] 326] def
(Hfootnote.4) [34 [89 138 89 150] 350] def
(equation.7.30) [34 [212 342 383 354] 553] def
(equation.4.61) [23 [240 368 355 380] 580] def
(equation.7.31) [34 [166 287 429 299] 498] def
(equation.4.62) [23 [243 330 352 342] 542] def
(equation.7.32) [34 [235 217 360 229] 429] def
(equation.4.63) [23 [274 255 321 267] 467] def
(equation.7.33) [34 [192 163 403 175] 375] def
(equation.4.64) [23 [244 206 352 218] 417] def
(section.1) [2 [71 775 71 787] 841] def
(equation.7.34) [35 [267 630 328 642] 841] def
(equation.4.65) [23 [157 154 438 166] 366] def
(section.2) [4 [71 260 71 272] 472] def
(equation.7.35) [35 [232 569 363 581] 780] def
(equation.4.66) [23 [245 103 350 115] 314] def
(section.3) [9 [71 479 71 491] 690] def
(equation.7.36) [35 [241 516 354 528] 728] def
(equation.4.67) [24 [225 728 371 740] 841] def
(section.4) [15 [71 775 71 787] 841] def
(equation.7.37) [35 [183 429 412 441] 641] def
(section.5) [24 [71 665 71 677] 841] def
(equation.7.38) [35 [198 362 398 374] 574] def
(section.6) [27 [71 503 71 515] 714] def
(equation.7.39) [35 [229 295 366 307] 506] def
(section.7) [30 [71 417 71 429] 629] def
(cite.ans123) [80 [71 614 71 626] 826] def
(section.8) [38 [71 775 71 787] 841] def
(section.9) [44 [71 492 71 504] 704] def
(page.42) [43 [71 800 71 812] 841] def
(page.43) [44 [71 800 71 812] 841] def
(definizione.4.1) [18 [195 551 195 563] 763] def
(page.44) [45 [71 800 71 812] 841] def
(definizione.4.2) [19 [71 521 71 533] 732] def
(page.45) [46 [71 800 71 812] 841] def
(definizione.4.3) [21 [71 133 71 145] 345] def
(page.46) [47 [71 800 71 812] 841] def
(page.47) [48 [71 800 71 812] 841] def
(page.48) [49 [71 800 71 812] 841] def
(page.49) [50 [71 800 71 812] 841] def
(equation.7.40) [35 [253 242 342 254] 454] def
(cite.GMS) [79 [71 532 71 544] 744] def
(equation.7.41) [35 [268 189 327 201] 401] def
(equation.7.42) [35 [185 108 410 120] 319] def
(equation.7.43) [36 [202 723 393 735] 841] def
(equation.7.44) [36 [245 657 351 669] 841] def
(equation.7.45) [36 [224 591 371 603] 803] def
(equation.7.46) [36 [254 536 342 548] 748] def
(equation.7.47) [36 [261 490 335 502] 702] def
(equation.7.48) [36 [253 438 342 450] 650] def
(equation.7.49) [36 [212 370 384 382] 581] def
(page.50) [51 [71 800 71 812] 841] def
(page.52) [53 [71 800 71 812] 841] def
(page.53) [54 [71 800 71 812] 841] def
(page.54) [55 [71 800 71 812] 841] def
(page.55) [56 [71 800 71 812] 841] def
(page.56) [57 [71 800 71 812] 841] def
(page.57) [58 [71 800 71 812] 841] def
(cite.skgsugra_2) [81 [71 229 71 241] 441] def
(page.58) [59 [71 800 71 812] 841] def
(page.59) [60 [71 800 71 812] 841] def
(equation.7.50) [36 [237 310 358 322] 521] def
(equation.7.51) [36 [239 263 356 275] 475] def
(equation.7.52) [36 [237 218 359 230] 430] def
(equation.7.53) [36 [212 169 383 181] 380] def
(equation.7.54) [36 [199 103 396 115] 314] def
(equation.7.55) [37 [239 737 356 749] 841] def
(equation.7.56) [37 [195 679 400 691] 841] def
(equation.7.57) [37 [85 266 510 278] 477] def
(equation.7.58) [37 [178 187 423 141] 398] def
(cite.CDFVP) [78 [71 133 71 145] 345] def
(page.61) [62 [71 800 71 812] 841] def
(page.62) [63 [71 800 71 812] 841] def
(page.64) [65 [71 800 71 812] 841] def
(page.66) [67 [71 800 71 812] 841] def
(page.68) [69 [71 800 71 812] 841] def
(page.69) [70 [71 800 71 812] 841] def
(page.70) [71 [71 800 71 812] 841] def
(page.71) [72 [71 800 71 812] 841] def
(page.72) [73 [71 800 71 812] 841] def
(page.73) [74 [71 800 71 812] 841] def
(page.74) [75 [71 800 71 812] 841] def
(page.75) [76 [71 800 71 812] 841] def
(page.76) [77 [71 800 71 812] 841] def
(page.77) [78 [71 800 71 812] 841] def
(page.78) [79 [71 800 71 812] 841] def
(page.79) [80 [71 800 71 812] 841] def
(cite.kava) [79 [71 455 71 467] 666] def
(page.80) [81 [71 800 71 812] 841] def
(page.81) [82 [71 800 71 812] 841] def
(cite.huto1) [79 [71 742 71 754] 841] def
(cite.KLM) [79 [71 140 71 152] 351] def
(lemma.7.1) [32 [342 375 342 387] 587] def
(equation.2.10) [6 [258 738 338 733] 841] def
(equation.2.11) [6 [209 671 386 683] 841] def
(equation.2.12) [6 [206 617 389 629] 828] def
(equation.2.13) [6 [199 554 396 566] 766] def
(equation.2.14) [6 [264 487 331 479] 699] def
(subsection.5.1) [24 [71 224 71 236] 435] def
(subsection.C.1) [72 [71 291 71 303] 502] def
(equation.2.16) [6 [251 418 344 411] 630] def
(equation.2.18) [6 [264 345 332 357] 556] def
(equation.2.19) [6 [223 283 373 295] 495] def
(Item.1) [3 [71 698 71 710] 841] def
(Item.2) [3 [71 659 71 671] 841] def
(Item.3) [3 [71 621 71 633] 832] def
(Item.4) [3 [71 182 71 194] 393] def
(Item.5) [3 [71 157 71 169] 369] def
(Item.6) [4 [71 775 71 787] 841] def
(Item.7) [4 [71 756 71 768] 841] def
(Item.8) [4 [71 718 71 730] 841] def
(equation.2.20) [6 [226 197 370 209] 409] def
(Item.9) [4 [71 694 71 706] 841] def
(cite.pietrolectures) [81 [71 541 71 553] 753] def
(equation.2.21) [6 [187 152 408 164] 364] def
(equation.2.22) [6 [229 103 366 115] 314] def
(equation.2.23) [7 [97 732 468 744] 841] def
(equation.2.24) [7 [188 617 407 629] 828] def
(equation.2.25) [7 [162 554 434 566] 766] def
(equation.2.26) [7 [158 503 437 515] 715] def
(equation.2.27) [7 [210 363 385 375] 574] def
(cite.sugkgeom_1) [81 [71 492 71 504] 704] def
(equation.2.28) [7 [197 317 391 306] 529] def
(cite.sugkgeom_2) [81 [71 305 71 317] 517] def
(equation.2.29) [7 [230 182 365 194] 394] def
(cite.sabarwhal) [82 [71 716 71 728] 841] def
(cite.sugkgeom_3) [81 [71 278 71 290] 490] def
(cite.sugkgeom_4) [81 [71 341 71 353] 553] def
(cite.sugkgeom_5) [81 [71 468 71 480] 679] def
(cite.sugkgeom_6) [81 [71 429 71 441] 641] def
(equation.4.1) [15 [195 346 400 358] 557] def
(equation.B.1) [65 [255 664 340 676] 841] def
(equation.4.2) [15 [219 239 376 251] 451] def
(equation.B.2) [65 [144 237 451 249] 448] def
(equation.4.3) [15 [260 121 336 133] 333] def
(equation.B.3) [66 [71 800 71 812] 841] def
(equation.B.3) [65 [90 201 303 85] 413] def
(equation.4.4) [16 [171 732 425 744] 841] def
(equation.B.4) [67 [168 503 427 493] 715] def
(equation.4.5) [16 [147 350 448 362] 562] def
(equation.B.5) [68 [71 800 71 812] 841] def
(equation.B.5) [67 [75 206 303 85] 417] def
(equation.4.6) [16 [241 309 355 321] 521] def
(equation.B.6) [68 [195 598 401 610] 810] def
(equation.4.7) [16 [174 260 421 272] 471] def
(equation.4.8) [16 [269 198 326 210] 409] def
(equation.2.30) [7 [77 105 488 117] 316] def
(equation.4.9) [17 [222 636 364 613] 841] def
(equation.2.31) [8 [170 742 425 754] 841] def
(cite.vanderseypen) [82 [71 692 71 704] 841] def
(equation.2.32) [8 [168 697 428 709] 841] def
(equation.2.33) [8 [212 611 383 623] 822] def
(equation.2.34) [8 [197 539 399 551] 751] def
(equation.2.35) [8 [238 503 358 515] 715] def
(equation.2.36) [8 [137 146 458 117] 357] def
(equation.2.37) [9 [226 652 370 647] 841] def
(equation.2.38) [9 [176 500 419 512] 711] def
(cite.Wdy) [79 [71 716 71 728] 841] def
(cite.anche) [82 [71 531 71 543] 743] def
(equation.5.10) [25 [231 294 364 306] 505] def
(equation.5.11) [25 [278 251 317 263] 462] def
(equation.5.12) [25 [269 128 327 140] 340] def
(equation.5.13) [26 [187 724 322 701] 841] def
(equation.5.14) [26 [253 621 342 633] 832] def
(equation.5.15) [26 [242 586 353 598] 797] def
(cite.DWNi) [80 [71 148 71 160] 360] def
(equation.5.16) [26 [191 506 345 495] 718] def
(equation.5.17) [26 [226 430 370 442] 641] def
(equation.5.18) [26 [196 370 399 359] 581] def
(equation.5.19) [26 [264 293 331 305] 505] def
(cite.cynoi) [79 [71 207 71 219] 418] def
(equation.C.10) [70 [247 727 348 739] 841] def
(equation.5.20) [26 [174 238 421 250] 449] def
(equation.C.11) [70 [195 663 400 675] 841] def
(equation.5.21) [26 [182 182 413 194] 393] def
(equation.C.12) [70 [187 578 408 590] 789] def
(equation.5.22) [26 [214 103 381 115] 314] def
(equation.C.13) [70 [189 414 364 354] 626] def
(equation.5.23) [27 [207 723 388 735] 841] def
(equation.C.14) [70 [189 303 406 315] 514] def
(equation.5.24) [27 [190 643 406 655] 841] def
(equation.C.15) [70 [163 228 432 240] 439] def
(equation.5.25) [27 [208 592 387 604] 803] def
(equation.C.16) [70 [200 149 339 120] 361] def
(equation.5.26) [27 [231 547 365 559] 758] def
(equation.C.17) [71 [228 745 367 757] 841] def
(equation.C.18) [71 [225 673 370 685] 841] def
(equation.C.19) [71 [204 581 391 593] 793] def
(cite.SS) [79 [71 639 71 651] 841] def
(cite.zachos) [82 [71 594 71 606] 806] def
(cite.zachos) [81 [71 642 71 654] 841] def
(cite.FHSV) [79 [71 493 71 505] 705] def
(equation.C.20) [71 [267 432 328 444] 643] def
(equation.C.21) [71 [195 166 400 178] 377] def
(equation.C.22) [72 [184 702 412 714] 841] def
(equation.C.23) [72 [208 124 387 136] 335] def
(equation.C.24) [73 [161 737 434 749] 841] def
(equation.C.25) [73 [188 677 407 689] 841] def
(equation.C.26) [73 [265 625 330 637] 837] def
(equation.C.27) [73 [149 559 446 571] 771] def
(equation.C.28) [73 [152 479 443 491] 691] def
(equation.C.29) [73 [274 369 327 363] 580] def
(cite.ferratoine) [81 [71 517 71 529] 728] def
(equation.10.1) [47 [96 200 469 212] 412] def
(equation.10.2) [47 [167 135 428 147] 347] def
(equation.10.3) [48 [120 725 314 617] 841] def
(equation.10.4) [48 [188 433 407 445] 644] def
(equation.10.5) [48 [240 358 356 370] 570] def
(equation.10.6) [48 [263 288 333 300] 499] def
(equation.10.7) [48 [251 248 345 260] 460] def
(equation.10.8) [48 [160 198 435 210] 409] def
(equation.10.9) [48 [208 109 387 121] 321] def
(equation.C.30) [73 [184 284 362 277] 495] def
(equation.C.31) [73 [228 154 367 166] 366] def
(cite.ward) [81 [71 775 71 787] 841] def
(equation.C.32) [74 [193 719 402 703] 841] def
(equation.C.33) [74 [208 623 387 635] 835] def
(equation.8.12) [39 [179 492 417 450] 704] def
(equation.C.34) [74 [207 544 388 556] 756] def
(equation.C.35) [74 [208 490 387 502] 702] def
(equation.C.36) [74 [232 401 364 413] 613] def
(equation.8.15) [39 [212 365 383 377] 577] def
(equation.C.37) [74 [212 333 384 345] 544] def
(equation.8.16) [40 [71 800 71 812] 841] def
(equation.8.16) [39 [207 107 303 85] 319] def
(equation.C.38) [74 [244 217 351 229] 429] def
(equation.8.17) [41 [71 800 71 812] 841] def
(equation.8.17) [40 [102 556 303 85] 767] def
(equation.C.39) [74 [178 167 418 179] 379] def
(cite.ant) [81 [71 702 71 714] 841] def
(cite.sugrasecondo) [81 [71 366 71 378] 577] def
(equation.C.40) [74 [226 108 369 120] 319] def
(equation.C.41) [75 [112 737 224 679] 841] def
(equation.C.42) [75 [232 587 363 599] 798] def
(equation.C.43) [75 [231 531 364 543] 742] def
(equation.C.44) [75 [252 467 343 479] 679] def
(equation.8.23) [41 [178 471 433 378] 682] def
(equation.C.45) [75 [204 387 333 371] 598] def
(equation.8.24) [42 [71 800 71 812] 841] def
(equation.8.24) [41 [99 107 303 85] 319] def
(equation.C.46) [75 [199 297 331 281] 509] def
(equation.C.47) [75 [103 210 459 222] 422] def
(equation.C.48) [75 [198 143 397 117] 355] def
(equation.8.27) [42 [177 444 360 353] 655] def
(equation.8.1) [38 [273 546 351 558] 758] def
(equation.8.2) [38 [206 431 419 443] 642] def
(equation.8.3) [38 [218 374 407 386] 586] def
(equation.8.4) [38 [143 259 268 197] 471] def
(equation.8.8) [38 [178 103 417 115] 315] def
(equation.8.9) [39 [119 708 483 623] 841] def
(equation.C.51) [76 [186 734 397 696] 841] def
(equation.8.32) [42 [141 209 457 193] 421] def
(equation.C.54) [76 [264 631 331 643] 841] def
(equation.C.55) [76 [220 564 375 576] 775] def
(equation.8.34) [42 [100 137 496 120] 348] def
(equation.C.56) [76 [156 449 439 461] 660] def
(equation.C.57) [76 [197 374 399 386] 586] def
(equation.8.36) [43 [233 759 362 743] 841] def
(equation.C.58) [76 [195 348 401 360] 559] def
(equation.C.59) [76 [195 301 400 313] 512] def
(equation.8.38) [43 [151 682 351 610] 841] def
(subsection.4.1) [15 [71 429 71 441] 641] def
(subsection.4.2) [16 [71 558 71 570] 770] def
(cite.specspec1) [81 [71 254 71 266] 465] def
(subsection.4.3) [18 [71 620 71 632] 832] def
(subsection.4.4) [21 [71 571 71 583] 783] def
(subsection.4.5) [23 [71 775 71 787] 841] def
(cite.fsz) [80 [71 124 71 136] 335] def
(equation.C.60) [76 [198 248 398 260] 459] def
(equation.C.61) [76 [240 195 356 207] 407] def
(equation.8.40) [43 [182 549 414 561] 761] def
(equation.8.41) [43 [76 474 520 486] 686] def
(equation.8.42) [43 [210 260 385 272] 472] def
(cite.FGP1) [80 [71 476 71 488] 688] def
(equation.8.43) [43 [192 159 403 171] 370] def
(equation.8.44) [43 [232 115 364 127] 326] def
(cite.APT) [80 [71 342 71 354] 554] def
(equation.8.45) [44 [146 734 423 717] 841] def
(equation.8.46) [44 [105 629 460 641] 841] def
(page.0) [1 [71 800 71 812] 841] def
(page.1) [2 [71 800 71 812] 841] def
(page.2) [3 [71 800 71 812] 841] def
(page.3) [4 [71 800 71 812] 841] def
(page.4) [5 [71 800 71 812] 841] def
(page.5) [6 [71 800 71 812] 841] def
(page.6) [7 [71 800 71 812] 841] def
(page.7) [8 [71 800 71 812] 841] def
(page.8) [9 [71 800 71 812] 841] def
(page.9) [10 [71 800 71 812] 841] def
(cite.flatpotn1) [81 [71 678 71 690] 841] def
(cite.flatpotn2) [80 [71 187 71 199] 398] def
(cite.recpformcond) [81 [71 590 71 602] 801] def
(cite.calvis) [82 [71 619 71 631] 830] def
(equation.3.1) [9 [222 245 373 257] 457] def
(equation.A.1) [59 [143 722 387 641] 841] def
(equation.3.2) [9 [243 172 353 184] 384] def
(cite.Duff) [79 [71 678 71 690] 841] def
(equation.3.3) [10 [267 480 328 492] 691] def
(equation.3.4) [10 [182 390 414 402] 601] def
(equation.3.5) [10 [196 326 399 338] 537] def
(equation.3.6) [10 [256 257 340 269] 469] def
(equation.A.6) [59 [114 475 114 179] 687] def
(equation.3.7) [10 [173 203 422 215] 414] def
(equation.3.8) [10 [243 148 352 160] 359] def
(equation.3.9) [10 [265 103 330 115] 314] def
(cite.cremvanp) [81 [71 128 71 140] 339] def
(cite.alekseev) [82 [71 775 71 787] 841] def
(cite.bagwit) [80 [71 726 71 738] 841] def
(cite.CaDF) [80 [71 551 71 563] 763] def
(cite.scsc) [81 [71 726 71 738] 841] def
(cite.stromco) [79 [71 571 71 583] 782] def
(cite.DFF) [80 [71 639 71 651] 841] def
(cite.CaDFb) [80 [71 381 71 393] 593] def
(equation.3.10) [11 [102 737 463 749] 841] def
(equation.3.11) [11 [158 620 437 632] 832] def
(equation.3.12) [11 [171 557 425 569] 769] def
(equation.3.13) [11 [230 488 365 500] 700] def
(equation.3.14) [11 [253 419 342 431] 630] def
(equation.3.15) [11 [187 374 408 386] 586] def
(equation.3.16) [11 [113 299 483 289] 510] def
(equation.3.17) [11 [220 238 376 250] 449] def
(equation.3.18) [11 [273 168 322 180] 379] def
(equation.3.19) [12 [188 679 407 691] 841] def
(equation.3.20) [12 [255 567 352 562] 778] def
(equation.3.21) [12 [248 141 348 153] 353] def
(equation.3.22) [13 [204 734 392 746] 841] def
(equation.3.23) [13 [215 426 380 438] 637] def
(equation.3.24) [13 [236 377 359 389] 588] def
(equation.3.25) [13 [215 301 380 313] 512] def
(equation.3.26) [13 [149 147 446 159] 358] def
(equation.3.27) [14 [235 710 360 722] 841] def
(equation.3.28) [14 [138 649 457 661] 841] def
(equation.A.19) [60 [193 623 402 635] 835] def
(equation.3.29) [14 [112 582 196 540] 793] def
(cite.noi) [79 [71 416 71 428] 627] def
(equation.7.1) [30 [252 173 343 185] 384] def
(equation.7.2) [31 [226 679 370 691] 841] def
(equation.7.3) [31 [253 626 342 638] 838] def
(equation.7.4) [31 [180 574 415 586] 785] def
(equation.7.5) [31 [263 506 332 518] 718] def
(equation.7.6) [31 [227 410 368 422] 622] def
(equation.7.7) [31 [93 249 479 261] 461] def
(equation.7.8) [31 [253 156 342 168] 367] def
(equation.7.9) [31 [261 103 334 115] 315] def
(equation.A.20) [60 [271 599 324 611] 811] def
(equation.3.30) [14 [113 366 453 378] 577] def
(equation.A.21) [60 [239 577 356 589] 789] def
(equation.3.31) [14 [181 289 414 301] 501] def
(cite.CFGVP) [80 [71 512 71 524] 724] def
(equation.A.22) [60 [200 556 395 568] 767] def
(equation.3.32) [14 [100 216 466 228] 428] def
(equation.A.23) [60 [124 367 376 203] 578] def
(equation.3.33) [14 [209 170 386 182] 381] def
(equation.3.34) [14 [213 106 383 118] 317] def
(equation.A.27) [61 [71 800 71 812] 841] def
(equation.A.27) [60 [120 154 303 85] 366] def
(cite.fredas) [81 [71 614 71 626] 826] def
(subsection.3.1) [12 [71 775 71 787] 841] def
(equation.6.10) [29 [193 278 415 269] 490] def
(equation.A.32) [61 [165 702 391 677] 841] def
(equation.6.11) [29 [263 184 332 196] 395] def
(equation.6.12) [30 [227 729 368 741] 841] def
(cite.gaizum) [81 [71 566 71 578] 777] def
(equation.A.35) [61 [137 609 461 593] 821] def
(equation.A.37) [61 [165 547 430 559] 758] def
(equation.A.38) [61 [98 512 497 501] 723] def
end targetdump-hook def
TeXDict begin
%%EndSetup
%%Page: 0 1
gsave %matrix defaultmatrix setmatrix
90 rotate 270 -39 moveto /Times-Roman findfont 20 scalefont setfont
0.3 setgray (arXiv:hep-th/9605032 v1   6 May 1996) show grestore
0 0 bop 1030 3 a FH(POLFIS-TH.03/96)1030 63 y(UCLA/96/TEP/9)1030
123 y(hep-th/9605032)8 449 y FG(N=2)26 b(Sup)r(ergra)n(vit)n(y)i(and)f
(N=2)f(Sup)r(er)h(Y)-7 b(ang-Mills)28 b(Theory)441 553
y(on)e(General)h(Scalar)h(Manifolds:)15 631 y FF(Symple)l(ctic)f
(Covarianc)l(e,)e(Gaugings)g(and)g(the)h(Momentum)g(Map.)1839
605 y FE(\003)199 868 y FD(L.)18 b(Andrianop)r(oli)589
850 y FC(1)608 868 y FD(,)g(M.)h(Bertolini)948 850 y
FC(2)f FB(y)1002 868 y FD(,)g(A.)h(Ceresole)1320 850
y FC(2)1338 868 y FD(,)f(R.)g(D'Auria)1646 850 y FC(2)1666
868 y FD(,)506 946 y(S.)g(F)-5 b(errara)750 928 y FC(3)770
946 y FD(,)19 b(P)-5 b(.)18 b(F)-5 b(r)o(\023)-27 b(e)951
928 y FC(4)21 b FB(y)1026 946 y FD(and)f(T.)e(Magri)1355
928 y FC(4)48 1045 y(1)83 1062 y FA(Dipartimen)o(to)d(di)h(Fisica,)g
(Univ)o(ersit\023)-23 b(a)16 b(di)g(Geno)o(v)m(a,)e(via)i(Do)q
(decaneso)f(33,)f(I-16146)h(Geno)o(v)m(a,)f(Italy)470
1127 y FC(2)505 1143 y FA(Dipartimen)o(to)h(di)h(Fisica,)g(P)o
(olitecnico)g(di)g(T)l(orino,)434 1199 y(Corso)f(Duca)g(degli)h
(Abruzzi)h(24,)d(I-10129)g(T)l(orino,)h(Italy)516 1264
y FC(3)551 1281 y FA(CERN,)f(CH)h(1211)f(Genev)m(a)i(23,)e(Switzerland)
118 1337 y(and)h(Departmen)o(t)f(of)h(Ph)o(ysics,)g(Univ)o(ersit)o(y)h
(of)f(California,)h(Los)f(Angeles,)h(CA)f(90024,)e(USA)22
1402 y FC(4)57 1419 y FA(Dipartimen)o(to)i(di)h(Fisica)g(T)l(eorica,)f
(Univ)o(ersit\022)-23 b(a)16 b(di)g(T)l(orino,)f(via)g(P)l(.)g(Giuria,)
h(1)f(I-10125)f(T)l(orino,)h(Italy)833 1755 y FD(Abstract)-5
1869 y FA(The)20 b(general)f(form)f(of)h Fz(N)d FA(=)c(2)18
b(sup)q(ergra)o(vit)o(y)h(coupled)i(to)d(an)h(arbitrary)f(n)o(um)o(b)q
(er)i(of)e(v)o(ector)h(m)o(ultiplets)-5 1929 y(and)c(h)o(yp)q(erm)o
(ultiplets,)h(with)f(a)g(generic)g(gauging)g(of)f(the)h(scalar)f
(manifold)i(isometries)f(is)g(giv)o(en.)20 b(This)c(ex-)-5
1989 y(tends)e(the)g(results)g(already)g(a)o(v)m(ailable)i(in)e(the)g
(literature)g(in)h(that)e(w)o(e)g(use)h(a)g(co)q(ordinate)g(indep)q
(enden)o(t)i(and)-5 2050 y(manifestly)i(symplectic)g(co)o(v)m(arian)o
(t)f(formalism)g(whic)o(h)h(allo)o(ws)f(to)f(co)o(v)o(er)g(theories)i
(di\016cult)g(to)f(form)o(ulate)-5 2110 y(within)f(sup)q(erspace)g(or)f
(tensor)f(calculus)j(approac)o(h.)j(W)l(e)15 b(pro)o(vide)g(the)g
(complete)h(lagrangian)f(and)g(sup)q(er-)-5 2170 y(symmetry)f(v)m
(ariations)h(with)g(all)h(fermionic)f(terms,)f(and)h(the)f(form)g(of)g
(the)h(scalar)f(p)q(oten)o(tial)i(for)e(arbitrary)-5
2230 y(quaternionic)f(manifolds)g(and)f(sp)q(ecial)i(geometry)l(,)e
(not)f(necessarily)j(in)e(sp)q(ecial)i(co)q(ordinates.)19
b(Lagrangians)-5 2290 y(for)d(rigid)h(theories)f(are)g(also)f(written)h
(in)h(this)g(general)f(setting)g(and)g(the)g(connection)h(with)g(lo)q
(cal)g(theories)-5 2350 y(elucidated.)26 b(The)16 b(deriv)m(ation)i(of)
e(these)g(results)h(using)g(geometrical)g(tec)o(hniques)g(is)g
(brie\015y)h(summarized.)p -5 2604 355 2 v -5 2624 a
Fy(y)26 2639 y Fx(F)m(ello)o(w)13 b(b)o(y)h(Ansaldo)f(Ricerc)o(he)i
(srl)f(C.so)g(P)o(errone)h(24,)e(I-16152)f(Geno)o(v)n(a.)-5
2684 y Fy(\003)31 2699 y Fx(Supp)q(orted)17 b(in)f(part)g(b)o(y)h(DOE)f
(gran)o(t)g(DE-F)o(GO3-91ER40662)e(T)m(ask)i(C.,)g(EEC)g(Science)i
(Program)d(SC1*CT92-)-5 2760 y(0789,)e(NSF)h(gran)o(t)f(no.)18
b(PHY94-07194,)12 b(and)i(INFN.)p eop
%%Page: 1 2
1 1 bop -5 15 a Fw(1)81 b(In)n(tro)r(duction)-5 125 y
FH(Impressiv)o(e)14 b(results)j(o)o(v)o(er)f(the)h(last)g(y)o(ear)g(on)
g(non)h(p)q(erturbativ)o(e)e(prop)q(erties)h(of)h Fv(N)i
FH(=)15 b(2)j(sup)q(ersym-)-5 185 y(metric)h(Y)l(ang-Mills)i
(theories[1)p
 (#cite.SW12) [[212 723 218 735] [1 1 1 [3 3]] [0 0 1]] pdfm 
-1 w(,)g(2)p
 (#cite.kltold) [[226 723 232 735] [1 1 1 [3 3]] [0 0 1]] pdfm (])g
(and)h(their)f(extension)f(to)i(string)g(theory[3)p
 (#cite.CDF) [[432 723 438 735] [1 1 1 [3 3]] [0 0 1]] pdfm 
-1 w(]-[6)p  (#cite.Wdy) [[449 723 454 735] [1 1 1 [3 3]] [0 0 1]] pdfm 
(])f(through)h(the)-5 245 y(notion)e(of)f(string-string)g(dualit)o(y[7)
p  (#cite.Duff) [[228 708 234 720] [1 1 1 [3 3]] [0 0 1]] pdfm 
-1 w(,)f(8)p  (#cite.SS) [[241 708 247 720] [1 1 1 [3 3]] [0 0 1]] pdfm 
1 w(],)g(ha)o(v)o(e)g(used)h(the)g(deep)f(underlying)g(mathematical)e
(struc-)-5 306 y(ture)g(of)h(these)f(theories)g(and)g(its)g(relation)g
(to)h(algebraic)f(geometry)e([9)p
 (#cite.stromco) [[383 694 388 706] [1 1 1 [3 3]] [0 0 1]] pdfm (]-)i
([18)p  (#cite.cynoi) [[403 694 414 706] [1 1 1 [3 3]] [0 0 1]] pdfm 
1 w(].)68 366 y(In)22 b(the)f(case)g(of)h Fv(N)28 b FH(=)22
b(2)g(v)o(ector)f(m)o(ultiplets,)e(describing)i(the)g(e\013ectiv)o(e)f
(in)o(teractions)g(in)h(the)-5 426 y(Ab)q(elian)e(\(Coulom)o(b\))g
(phase)h(of)f(a)h(sp)q(on)o(taneously)h(brok)o(en)e(gauge)i(theory)l(,)
e(Seib)q(erg)h(and)g(Witten)-5 486 y([1)p
 (#cite.SW12) [[74 650 80 662] [1 1 1 [3 3]] [0 0 1]] pdfm (])15
b(ha)o(v)o(e)g(sho)o(wn)h(that)f(p)q(ositivit)o(y)f(of)i(the)f(metric)e
(on)i(the)h(underlying)e(mo)q(duli)g(space)h(iden)o(ti\014es)f(the)-5
546 y(geometrical)e(data)i(of)g(the)g(e\013ectiv)o(e)d
Fv(N)20 b FH(=)13 b(2)h(rigid)g(theory)f(with)h(the)f(p)q(erio)q(ds)h
(of)g(a)h(particular)e(torus.)68 607 y(In)i(the)f(coupling)g(to)h(gra)o
(vit)o(y)f(it)g(w)o(as)g(conjectured)g(b)o(y)g(some)g(of)g(the)h
(presen)o(t)e(authors)j([3)p
 (#cite.CDF) [[480 621 486 633] [1 1 1 [3 3]] [0 0 1]] pdfm (,)e(4)p
 (#cite.CDFVP) [[493 621 499 633] [1 1 1 [3 3]] [0 0 1]] pdfm (])g(and)
-5 667 y(later)g(con\014rmed)f(b)o(y)h(heterotic-T)o(yp)q(e)f(I)q(I)h
(dualit)o(y)g([11)p
 (#cite.FHSV) [[300 607 312 619] [1 1 1 [3 3]] [0 0 1]] pdfm (,)g(12)p
 (#cite.kava) [[319 607 330 619] [1 1 1 [3 3]] [0 0 1]] pdfm 
1 w(,)g(18)p
 (#cite.cynoi) [[337 607 349 619] [1 1 1 [3 3]] [0 0 1]] pdfm (,)g(19)p
 (#cite.KLM) [[355 607 367 619] [1 1 1 [3 3]] [0 0 1]] pdfm 
1 w(],)g(that)h(the)f(v)o(ery)f(same)g(argumen)o(t)-5
727 y(based)24 b(on)g(p)q(ositivit)o(y)e(of)h(the)g(v)o(ector)g(m)o
(ultiplet)d(kinetic)h(metric)g(iden)o(ti\014es)h(the)h(corresp)q
(onding)-5 787 y(geometrical)e(data)j(of)g(the)f(e\013ectiv)o(e)e
Fv(N)31 b FH(=)25 b(2)f(sup)q(ergra)o(vit)o(y)e(with)h(the)g(p)q(erio)q
(ds)h(of)g(Calabi-Y)l(au)-5 847 y(threefolds.)68 907
y(On)j(the)f(other)g(hand,)j(when)e(matter)e(is)h(added,)j(the)d
(underlying)f(geometrical)f(structure)-5 968 y(is)f(m)o(uc)o(h)e(ric)o
(her,)i(since)f Fv(N)30 b FH(=)c(2)d(matter)f(h)o(yp)q(erm)o(ultipl)o
(ets)e(are)j(asso)q(ciated)h(with)f(quaternionic)-5 1028
y(geometry[21)p
 (#cite.bagwit) [[122 520 133 532] [1 1 1 [3 3]] [0 0 1]] pdfm 
-1 w(,)13 b(22)p
 (#cite.hklr) [[139 520 151 532] [1 1 1 [3 3]] [0 0 1]] pdfm 
1 w(,)g(23)p
 (#cite.gal) [[158 520 169 532] [1 1 1 [3 3]] [0 0 1]] pdfm 
1 w(],)g(and)h(c)o(harged)f(h)o(yp)q(erm)o(ultiplets)e(are)i(naturally)
g(asso)q(ciated)i(with)e(the)h(gaug-)-5 1088 y(ing)j(of)f
(triholomorphic)f(isometries)f(of)i(these)g(quaternionic)g(manifolds)f
([24)p  (#cite.DFF) [[405 506 416 518] [1 1 1 [3 3]] [0 0 1]] pdfm (,)h
(25)p  (#cite.ans123) [[424 506 435 518] [1 1 1 [3 3]] [0 0 1]] pdfm 
1 w(].)68 1148 y(It)k(is)f(the)g(aim)f(of)i(this)g(pap)q(er)g(to)g
(complete)d(the)i(general)h(form)e(of)i(the)f Fv(N)25
b FH(=)20 b(2)g(sup)q(ergra)o(vit)o(y)-5 1208 y(lagrangian)i(coupled)e
(to)g(an)h(arbitrary)f(n)o(um)o(b)q(er)f(of)h(v)o(ector)g(m)o(ultiple)o
(ts)e(and)j(h)o(yp)q(erm)o(ultipl)o(ets)c(in)-5 1269
y(presence)g(of)h(a)g(general)f(gauging)i(of)f(the)f(isometries)f(of)i
(b)q(oth)g(the)g(v)o(ector)e(m)o(ultiplets)f(and)j(h)o(yp)q(er-)-5
1329 y(m)o(ultiplets)d(scalar)j(manifolds.)24 b(Actually)16
b(this)i(extends)f(results)g(already)h(obtained)f(y)o(ears)h(ago)h(b)o
(y)-5 1389 y(some)c(of)g(us)h([24)p
 (#cite.DFF) [[131 434 143 446] [1 1 1 [3 3]] [0 0 1]] pdfm (],)f(that)
h(in)f(turn)h(extended)e(previous)h(w)o(ork)g(b)o(y)g(Bagger)h(and)g
(Witten)f(on)h(ungauged)-5 1449 y(general)j(quaternionic)g(manifolds)f
(coupled)h(to)g Fv(N)24 b FH(=)19 b(2)h(sup)q(ergra)o(vit)o(y[21)p
 (#cite.bagwit) [[399 419 410 431] [1 1 1 [3 3]] [0 0 1]] pdfm (],)f(b)
o(y)f(de)i(Wit,)f(Lau)o(w)o(ers)-5 1509 y(and)13 b(V)l(an)f(Pro)q(ey)o
(en)g(on)h(gauged)g(sp)q(ecial)f(geometry)e(and)j(gauged)g
(quaternionic)f(manifolds)f(obtained)-5 1570 y(b)o(y)h(quaternionic)g
(quotien)o(t)g(in)g(the)g(tensor)h(calculus)f(framew)o(ork)f([26)p
 (#cite.dWLVP) [[368 390 379 402] [1 1 1 [3 3]] [0 0 1]] pdfm (],)h
(and)h(b)o(y)f(Castellani,)h(D'Auria)-5 1630 y(and)i(F)l(errara)g(on)f
(co)o(v)m(arian)o(t)g(form)o(ulation)f(of)i(sp)q(ecial)f(geometry)e
(for)j(matter)e(coupled)h(sup)q(ergra)o(vit)o(y)-5 1690
y([27)p  (#cite.CaDF) [[74 361 86 373] [1 1 1 [3 3]] [0 0 1]] pdfm 
1 w(].)68 1750 y(This)22 b(pap)q(er)f(\014rstly)g(pro)o(vides)g(in)g(a)
g(geometrical)e(setting)i(the)g(full)f(lagrangian)j(with)e(all)f(the)-5
1810 y(fermionic)f(terms)i(and)h(the)g(sup)q(ersymmetry)c(v)m
(ariations.)39 b(Secondly)l(,)21 b(it)h(uses)g(a)g(co)q(ordinate)g(in-)
-5 1871 y(dep)q(enden)o(t)e(and)i(manifestly)c(symplectic)g(co)o(v)m
(arian)o(t)i(formalism)e(whic)o(h)i(in)h(particular)f(do)q(es)i(not)-5
1931 y(require)16 b(the)g(use)h(of)h(a)f(prep)q(oten)o(tial)f(function)
h Fv(F)7 b FH(\()p Fv(X)t FH(\).)23 b(Whether)16 b(a)h(prep)q(oten)o
(tial)g Fv(F)7 b FH(\()p Fv(X)t FH(\))16 b(exists)h(or)-5
1991 y(not)e(dep)q(ends)f(on)g(the)g(c)o(hoice)e(of)i(a)g(symplectic)d
(gauge[4)p
 (#cite.CDFVP) [[317 289 322 301] [1 1 1 [3 3]] [0 0 1]] pdfm 
1 w(].)20 b(Moreo)o(v)o(er,)12 b(some)h(ph)o(ysically)f(in)o(teresting)
-5 2051 y(cases)17 b(are)f(precisely)e(instances)j(where)f
Fv(F)7 b FH(\()p Fv(X)t FH(\))16 b(do)q(es)h(not)f(exist[4)p
 (#cite.CDFVP) [[359 275 365 287] [1 1 1 [3 3]] [0 0 1]] pdfm 
-1 w(].)68 2111 y(Of)24 b(particular)e(relev)m(ance)h(is)g(the)g(fact)g
(that)h(w)o(e)e(exhibit)g(a)i(scalar)f(p)q(oten)o(tial)g(for)h
(arbitrary)-5 2171 y(quaternionic)18 b(geometries)f(and)j(for)f(sp)q
(ecial)g(geometry)e(not)i(necessarily)f(in)h(sp)q(ecial)f(co)q(ordian)o
(tes.)-5 2232 y(This)g(allo)o(ws)f(us)g(to)h(go)g(b)q(ey)o(ond)f(what)h
(is)f(obtainable)h(with)f(the)g(tensor)g(calculus)g(\(or)h(sup)q
(erspace\))-5 2292 y(approac)o(h.)j(Among)13 b(man)o(y)g(applications,)
g(our)i(results)e(allo)o(w)h(the)f(study)h(of)g(general)g(conditions)g
(for)-5 2352 y(sp)q(on)o(taneous)i(sup)q(ersymmetry)11
b(breaking)i(in)h(a)g(manner)f(analogous)j(to)e(what)g(w)o(as)h(done)f
(for)g Fv(N)19 b FH(=)14 b(1)-5 2412 y(matter)h(coupled)h(sup)q(ergra)o
(vit)o(y)g([28)p
 (#cite.CFGVP) [[223 188 234 200] [1 1 1 [3 3]] [0 0 1]] pdfm 
1 w(].)21 b(Man)o(y)16 b(examples)f(of)h(sup)q(ersymmetry)e(breaking)i
(studied)g(in)-5 2472 y(the)g(past)h(are)g(then)f(repro)q(duced)g(in)g
(a)h(uni\014ed)e(framew)o(ork.)68 2533 y(Recen)o(tly)h(the)h(p)q(o)o(w)
o(er)g(of)h(using)f(simple)f(geometrical)f(form)o(ulae)g(for)j(the)f
(scalar)h(p)q(oten)o(tial)f(w)o(as)-5 2593 y(exploited)23
b(while)h(studying)g(the)g(breaking)g(of)h(half)f(sup)q(ersymmetrie)o
(s)e(in)i(a)g(particular)g(simple)-5 2653 y(mo)q(del,)17
b(using)h(a)g(symplectic)d(basis)k(where)e Fv(F)7 b FH(\()p
Fv(X)t FH(\))18 b(is)f(not)i(de\014ned[29)p
 (#cite.FGP1) [[378 130 390 142] [1 1 1 [3 3]] [0 0 1]] pdfm (].)26
b(The)17 b(metho)q(d)h(has)g(p)q(oten-)-5 2713 y(tial)g(applications)g
(in)f(string)h(theory)g(to)g(study)g(non)h(p)q(erturbativ)o(e)e
(phenomena)g(suc)o(h)h(as)g(conifold)928 2892 y(1)p eop
%%Page: 2 3
2 2 bop -5 15 a FH(transitions)17 b([10)p
 (#cite.GMS) [[132 763 144 775] [1 1 1 [3 3]] [0 0 1]] pdfm (],)f
Fv(p)p FH(-forms)g(condensation)h([30)p
 (#cite.pols) [[270 763 282 775] [1 1 1 [3 3]] [0 0 1]] pdfm (])f(and)h
(F)l(a)o(y)o(et-Iliop)q(oulos)e(terms)g([29)p
 (#cite.FGP1) [[432 763 444 775] [1 1 1 [3 3]] [0 0 1]] pdfm (,)h(32)p
 (#cite.APT) [[451 763 463 775] [1 1 1 [3 3]] [0 0 1]] pdfm 
1 w(].)68 76 y Fv(N)k FH(=)13 b(2)f(sup)q(ergra)o(vit)o(y)f(displa)o
(ys)g(a)h(high)f(degree)g(of)h(complexit)o(y)c(in)j(its)g(structure,)g
(based)h(ho)o(w)o(ev)o(er)-5 136 y(on)17 b(the)f(simplici)o(t)o(y)d(of)
j(few)g(principles.)k(The)c(sup)q(ersymmetric)c(Lagrangian)18
b(and)f(the)f(transforma-)-5 196 y(tion)23 b(rules)f(are)h(indeed)f
(quite)g(in)o(v)o(olv)o(ed)e(but)j(all)f(the)h(couplings,)h(the)e(mass)
g(matrices)f(and)i(the)-5 256 y(v)m(acuum)15 b(energy)h(are)h
(completely)c(\014xed)j(and)h(organized)f(in)g(terms)f(of)h(three)g
(geometrical)e(data:)55 358 y(1.)24 b Fu(The)19 b(choic)n(e)f(of)g(a)g
(sp)n(e)n(cial)g(K\177)-25 b(ahler)19 b(manifold)g FE(S)t(M)e
Fu(describing)j(the)f(self-inter)n(actions)h(of)e(the)117
418 y(ve)n(ctor)g(multiplets)55 520 y FH(2.)24 b Fu(The)f(choic)n(e)f
(of)g(a)g(quaternionic)i(manifold)f FE(HM)f Fu(describing)i(the)e
(self-inter)n(action)j(of)d(the)117 580 y(hyp)n(ermultiplets)55
682 y FH(3.)i Fu(The)19 b(choic)n(e)g(of)f(a)h(gauge)h(gr)n(oup)e
FE(G)s Fu(,)g(that)h(in)g(the)g(non)g(ab)n(elian)g(c)n(ase)g(must)g(b)n
(e)g(a)f(sub)n(gr)n(oup)g(of)117 742 y(the)f(isometry)f(gr)n(oup)g(of)g
(the)h(sc)n(alar)f(manifold)h FE(M)1065 749 y Ft(scalar)1186
742 y FE(\021)22 b(S)t(M)8 b(\012)h(HM)17 b Fu(with)g(a)f(blo)n(ck)h
(diag-)117 802 y(onal)i(immersion)f(in)h(the)f(symple)n(ctic)h(gr)n
(oup)f Fv(S)s(p)p FH(\(2)p 1080 776 30 2 v Fv(n)12 b
FH(+)g(2)p Fv(;)c FH(I)-9 b(R\))18 b Fu(of)g(ele)n(ctric{magnetic)j
(duality)117 862 y(r)n(otations)16 b FH(\(see)g(eq.)f(6.4)p
 (#equation.6.4) [[191 560 206 572] [1 1 1 [3 3]] [0 0 1]] pdfm (\).)-5
964 y(F)l(or)i(this)g(reason)h(w)o(e)f(dev)o(ote)f(the)h(\014rst)g(and)
h(largest)f(part)g(of)h(the)e(pap)q(er)i(\(sections)f(2-7\))h(to)f
(review)-5 1024 y(and)e(discuss,)g(in)e(a)i(w)o(a)o(y)f(indep)q(enden)o
(t)f(from)h(sup)q(ersymmetric)c(Lagrangians)17 b(and)e(sup)q
(ersymmetry)-5 1084 y(algebras,)j(the)e(geometrical)f(ingredien)o(ts)h
(of)h(the)g(construction)g(that)g(w)o(e)g(listed)e(ab)q(o)o(v)o(e.)24
b(This)17 b(part)-5 1145 y(of)e(the)g(pap)q(er)g(can)g(b)q(e)f(read)h
(as)g(an)g(indep)q(enden)o(t)f(essa)o(y)h(and)g(should)g(b)q(e)g(quite)
e(accessible)h(to)h(math-)-5 1205 y(ematicians)g(as)i(w)o(ell)e(as)h
(to)h(readers)f(who)h(ha)o(v)o(e)f(no)g(bac)o(kground)h(or)g(in)o
(terest)e(in)h(sup)q(ersymmetry)l(.)68 1265 y(The)d(second)g(part)g(of)
g(the)f(pap)q(er)h(\(sections)g(8-9\))g(presen)o(ts)f(instead)h(the)f
(Lagrangian)j(and)e(sup)q(er-)-5 1325 y(symmetry)i(transformation)i
(rules)g(for)h(b)q(oth)h Fv(N)j FH(=)16 b(2)i(sup)q(ergra)o(vit)o(y)f
(and)h Fv(N)k FH(=)16 b(2)i(matter)e(coupled)-5 1385
y(rigid)k(Y)l(ang{Mills)f(theory)h(that)h(is)e(retriev)o(ed)f(from)h
(sup)q(ergra)o(vit)o(y)h(in)f(the)h(in\014nite)f(Planc)o(k)h(mass)-5
1446 y(limit)d Fv(\026)29 b FE(!)e(1)p FH(.)32 b(The)19
b(theory)h(is)f(presen)o(ted)g(in)g(a)h(completely)d(explicit)h(comp)q
(onen)o(t)g(formalism,)-5 1506 y(and)f(no)f(form)o(ulae)e(emplo)o(y)g
(or)i(require)f(the)g(use)h(of)h(sup)q(er\014elds,)e(sup)q(erspace)i
(or)f(conformal)f(tensor)-5 1566 y(calculus.)30 b(All)18
b(items)g(en)o(tering)g(suc)o(h)h(form)o(ulae)f(are)h(rather)h
(geometrical)d(ob)s(jects)i(whose)h(nature)-5 1626 y(and)d(prop)q
(erties)f(w)o(ere)g(describ)q(ed)g(and)g(explained)f(in)h(previous)g
(sections.)68 1686 y(The)g(reader)f(in)o(terested)f(in)g(applications)i
(of)f Fv(N)k FH(=)14 b(2)i(sup)q(ergra)o(vit)o(y)f(or)g(Y)l(ang{Mills)g
(theory)g(can)-5 1746 y(directly)g(jump)f(to)j(sections)f(8-9,)g(that)h
(are)f(self{con)o(tained,)f(and)h(insert,)f(in)h(the)g(ready-to-use)h
(for-)-5 1807 y(m)o(ulae)d(the)h(sp)q(eci\014c)g(geometrical)f(data)i
(corresp)q(onding)h(to)f(the)f(problem)f(considered.)21
b(References)-5 1867 y(to)c(form)o(ulae)d(in)i(previous)g(sections)g
(are)h(giv)o(en)e(to)i(\014x)f(normalizations.)68 1927
y(The)i(deriv)m(ation)f(of)h(the)g(results)f(presen)o(ted)g(in)g
(sections)h(8-9)g(w)o(as)h(obtained)f(b)o(y)f(means)f(of)i(the)-5
1987 y(geometric)13 b(\(\\rheonomic"\))h(approac)o(h)i(\(for)f(a)g
(general)f(review)g(see)h(the)f(b)q(o)q(ok)i(b)o(y)f(some)e(of)i(us)h
([31)p  (#cite.CaDFb) [[502 290 513 302] [1 1 1 [3 3]] [0 0 1]] pdfm 
(]\).)-5 2047 y(The)h(details)e(of)i(the)f(deriv)m(ation)g(are)g(giv)o
(en)g(in)f(the)i(App)q(endices)e(for)h(the)g(in)o(terested)f(reader,)h
(while)-5 2108 y(the)k(results)g(are)g(presen)o(ted)g(in)g(the)g(main)f
(text.)32 b(It)20 b(is)g(indeed)f(one)i(of)f(the)g(main)f(adv)m(an)o
(tages)j(of)-5 2168 y(the)15 b(geometrical)e(approac)o(h)j(to)g(sup)q
(ersymmetry)c(that)k(the)f(\014nal)g(outcome)f(of)i(the)f(construction)
g(is)-5 2228 y(directly)g(written)g(in)h(space{time)f(comp)q(onen)o(t)g
(formalism.)68 2288 y(As)h(emphasized)e(our)i(results)g(are)g(general)f
(and)i(apply)f(to)g(generic)f(c)o(hoice)f(of)i(the)g(scalar)g(mani-)-5
2348 y(fold.)21 b(As)16 b(an)g(illustration)f(of)h(our)g(form)o(ulae)e
(in)i(the)f(app)q(endix)h(w)o(e)f(sp)q(ecialize)f(them)g(to)j(the)e
(case)h(of)-5 2409 y(the)g(manifolds)32 b(1.1)p
 (#equation.1.1) [[148 189 163 201] [1 1 1 [3 3]] [0 0 1]] pdfm (.)21
b(More)16 b(sp)q(eci\014cally)l(,)f(our)h(pap)q(er)h(is)f(organized)h
(as)f(follo)o(ws:)55 2510 y(1.)24 b FD(Section)18 b(2)e
FH(reviews)g(dualit)o(y)f(rotations)i(and)g(symplectic)c(co)o(v)m
(ariance)j(in)g(\014eld)f(theory)l(.)55 2612 y(2.)24
b FD(Section)c(3)f FH(describ)q(es)e(the)h(symplectic)d(em)o(b)q
(edding)i(of)h(the)g(homogeneous)h(spaces,in)e(par-)117
2672 y(ticular)h(the)h(sp)q(ecial)g(symme)o(tric)d(spaces)j(whic)o(h)f
(app)q(ear)i(at)f(tree)g(lev)o(el)d(in)j(heterotic)f(string)117
2732 y(theory)l(.)928 2892 y(2)p eop
%%Page: 3 4
3 3 bop 55 15 a FH(3.)24 b FD(Section)13 b(4)g FH(reviews)e(Sp)q(ecial)
g(K\177)-24 b(ahler)12 b(geometry)l(,)f(b)q(oth)i(for)g(rigid)f(and)g
(lo)q(cal)g(sup)q(ersymmetry)l(.)55 116 y(4.)24 b FD(Section)17
b(5)e FH(describ)q(es)g(the)g(geometry)e(of)j(h)o(yp)q(erm)o(ultipl)o
(ets,)c(their)j(asso)q(ciated)h(quaternionic)117 176
y(and)h(h)o(yp)q(erK\177)-24 b(ahler)15 b(manifolds)h(in)g(lo)q(cal)g
(and)h(rigid)e(sup)q(ersymmetry)l(.)55 276 y(5.)24 b
FD(Section)18 b(6)e FH(faces)g(the)g(gauging)i(of)f(sp)q(ecial)e(and)i
(quaternionic)f(manifolds.)55 377 y(6.)24 b FD(Section)18
b(7)f FH(deals)g(with)f(the)g(so)i(called)d(momen)o(tum)e(map)i(on)j
(Sp)q(ecial)e(K\177)-24 b(ahler)16 b(and)h(quater-)117
437 y(nionic)12 b(manifolds)g(giving)g(rise)g(to)h(the)f(in)o(tro)q
(duction)h(of)g(prep)q(oten)o(tial)f(functions)g(whic)o(h)g(en)o(ter)
117 497 y(in)k(the)g(construction)g(of)h(the)f(scalar)h(p)q(oten)o
(tial.)55 598 y(7.)24 b FD(Section)18 b(8)e FH(rep)q(orts)h(the)f(full)
g Fv(N)j FH(=)13 b(2)k(Lagrangian)h(in)e(a)h(symplectic)c(co)o(v)m
(arian)o(t)j(form)55 698 y(8.)24 b FD(Section)16 b(9)e
FH(con)o(tains)h(the)f(rigid)g(limit)d(and)k(rep)q(orts)g(the)g
(general)f(form)f(of)i(a)f(matter)f(coupled)117 758 y
Fv(N)24 b FH(=)19 b(2)h(sup)q(er)g(Y)l(ang{Mills)e(theory)h(on)h(a)g
(generic)e(rigid)h(sp)q(ecial)g(manifold)f(and)h(a)h(generic)117
818 y(rigid)c(h)o(yp)q(erK\177)-24 b(ahler)15 b(manifold.)55
919 y(9.)24 b FD(App)r(endices)15 b(A,)h(B)e FH(giv)o(e)f(a)i(detailed)
e(deriv)m(ation)g(of)i(the)e(Lagrangian)k(and)d(transformation)117
979 y(rules)i(using)h(the)f(geometrical)e(approac)o(h.)31
1079 y(10.)24 b FD(App)r(endix)16 b(C)f FH(deals)f(with)g(the)g(relev)m
(an)o(t)f(form)o(ulas)h(for)g Fv(N)19 b FH(=)14 b(2)h(sup)q(ergra)o
(vit)o(y)f(based)g(on)h(the)117 1139 y(manifolds)397
1260 y(sp)q(ecial)h(manifold)40 b(=)i Fv(S)s(T)7 b FH([2)p
Fv(;)h(n)p FH(])20 b FE(\021)1121 1226 y Fv(S)s(U)5 b
FH(\(1)p Fv(;)j FH(1\))p 1121 1248 180 2 v 1161 1294
a Fv(U)d FH(\(1\))1325 1260 y FE(\012)1463 1226 y Fv(S)s(O)q
FH(\(2)p Fv(;)j(n)p FH(\))p 1388 1248 334 2 v 1388 1294
a Fv(S)s(O)q FH(\(2\))k FE(\002)f Fv(S)s(O)q FH(\()p
Fv(n)p FH(\))275 1394 y(quaternionic)16 b(manifold)40
b(=)50 b Fv(H)t(Q)p FH([)p Fv(m)p FH(])21 b FE(\021)1186
1360 y Fv(S)s(O)q FH(\(4)p Fv(;)8 b(m)p FH(\))p 1111
1383 347 2 v 1111 1428 a Fv(S)s(O)q FH(\(4\))k FE(\002)f
Fv(S)s(O)q FH(\()p Fv(m)p FH(\))1785 1394 y(\(1.1\))117
1525 y(This)19 b(is)g(done)g(as)h(an)f(exempli\014cation)e(of)i(the)g
(general)f(form)o(ulae)g(for)h(the)g(p)q(oten)o(tial,)g(mass)117
1585 y(matrices)c(and)h(kinetic)f(p)q(erio)q(d)i(matrices)d(and)j(for)f
(its)g(in)o(trinsic)f(in)o(terest)g(in)g(applications)i(to)117
1645 y(tree)f(lev)o(el)e(string)i(theory)31 1745 y(11.)24
b FD(App)r(endix)d(D)d FH(con)o(tains)h(a)f(list)g(of)h(con)o(v)o(en)o
(tions)e(and)i(normalizations)f(that)h(w)o(e)f(ha)o(v)o(e)f(em-)117
1806 y(plo)o(y)o(ed.)68 1903 y(An)e(expanded)h(v)o(ersion)e(of)i(this)f
(pap)q(er,)g(with)h(particular)e(atten)o(tion)h(to)h(the)f(geometrical)
e(prop-)-5 1964 y(erties)e(of)i(the)e(scalar)i(manifolds,)e(the)h
(rigidly)f(sup)q(ersymmetri)o(c)e(v)o(ersion)i(and)i(further)f(related)
f(issues)-5 2024 y(is)16 b(giv)o(en)g(in)g([33)p
 (#cite.corto) [[130 281 142 293] [1 1 1 [3 3]] [0 0 1]] pdfm (].)-5
2189 y Fw(2)81 b(Dualit)n(y)26 b(Rotations)i(and)e(Symplectic)g(Co)n(v)
l(ariance)-5 2299 y FH(In)17 b(this)g(section,)f(b)q(oth)i(for)f
(completeness)e(and)j(in)e(order)h(to)h(\014x)f(our)g(con)o(v)o(en)o
(tions)f(and)h(notations,)-5 2359 y(w)o(e)k(review)g(the)g(general)h
(structure)f(of)h(an)g(ab)q(elian)g(theory)f(of)h(v)o(ectors)f(and)i
(scalars)f(displa)o(ying)-5 2419 y(co)o(v)m(ariance)c(under)g(a)g
(group)h(of)g(dualit)o(y)e(rotations.)27 b(The)18 b(basic)g(reference)f
(is)h(the)f(1981)j(pap)q(er)f(b)o(y)-5 2480 y(Gaillard)i(and)g(Zumino)f
([46)p  (#cite.gaizum) [[189 172 200 184] [1 1 1 [3 3]] [0 0 1]] pdfm 
(].)35 b(A)20 b(general)g(presen)o(tation)h(in)g Fv(D)i
FH(=)f(2)p Fv(p)f FH(dimensions)f(w)o(as)h(recen)o(tly)-5
2540 y(giv)o(en)16 b(in)g([47)p
 (#cite.pietrolectures) [[119 157 130 169] [1 1 1 [3 3]] [0 0 1]] pdfm 
(].)21 b(Here)15 b(w)o(e)h(\014x)g Fv(D)f FH(=)f(4.)68
2600 y(W)l(e)23 b(consider)g(a)h(theory)f(of)p 627 2574
30 2 v 24 w Fv(n)g FH(gauge)h(\014elds)f Fv(A)993 2582
y FC(\003)993 2612 y Ft(\026)1019 2600 y FH(,)i(in)e(a)g
Fv(D)28 b FH(=)e(4)d(space{time)f(with)h(Loren)o(tz)-5
2660 y(signature.)f(They)16 b(corresp)q(ond)h(to)g(a)f(set)g(of)p
832 2634 V 17 w Fv(n)g FH(di\013eren)o(tial)f(1{forms)582
2765 y Fv(A)619 2745 y FC(\003)675 2765 y FE(\021)30
b Fv(A)781 2745 y FC(\003)781 2778 y Ft(\026)816 2765
y Fv(dx)869 2745 y Ft(\026)998 2765 y FH(\(\003)14 b(=)f(1)p
Fv(;)8 b(:)g(:)g(:)g(;)p 1250 2739 V 8 w(n)p FH(\))487
b(\(2.1\))928 2892 y(3)p eop
%%Page: 4 5
4 4 bop -5 15 a FH(The)17 b(corresp)q(onding)g(\014eld)e(strengths)i
(and)g(their)f(Ho)q(dge)g(duals)h(are)f(de\014ned)g(b)o(y)612
124 y Fv(F)651 104 y FC(\003)718 124 y FE(\021)42 b Fv(d)8
b(A)869 104 y FC(\003)917 124 y FE(\021)22 b(F)1019 104
y FC(\003)1014 136 y Ft(\026\027)1065 124 y Fv(dx)1118
104 y Ft(\026)1161 124 y FE(^)e Fv(dx)1267 104 y Ft(\027)598
225 y FE(F)639 205 y FC(\003)634 238 y Ft(\026\027)718
225 y FE(\021)803 192 y FH(1)p 803 214 25 2 v 803 259
a(2)849 177 y Fs(\020)874 225 y Fv(@)900 232 y Ft(\026)923
225 y Fv(A)960 205 y FC(\003)960 238 y Ft(\027)1006 225
y FE(\000)f Fv(@)1090 232 y Ft(\027)1111 225 y Fv(A)1148
205 y FC(\003)1148 238 y Ft(\026)1174 177 y Fs(\021)592
302 y Ft(?)612 322 y Fv(F)651 302 y FC(\003)718 322 y
FE(\021)821 306 y Fs(e)807 322 y FE(F)848 302 y FC(\003)843
335 y Ft(\026\027)894 322 y Fv(dx)947 302 y Ft(\026)989
322 y FE(^)h Fv(dx)1095 302 y Ft(\027)613 407 y Fs(e)598
423 y FE(F)639 403 y FC(\003)634 436 y Ft(\026\027)718
423 y FE(\021)803 390 y FH(1)p 803 412 V 803 458 a(2)833
423 y Fv(")856 430 y Ft(\026\027)r(\032\033)946 423 y
FE(F)987 403 y FC(\003)p FB(j)p Ft(\032\033)1785 423
y FH(\(2.2\))-5 545 y(De\014ning)d(the)f(space{time)e(in)o(tegration)i
(v)o(olume)e(as)535 673 y(d)562 651 y FC(4)582 673 y
Fv(x)22 b FE(\021)f(\000)743 639 y FH(1)p 736 661 38
2 v 736 707 a(4!)787 673 y Fv(")810 680 y Ft(\026)831
685 y Fr(1)849 680 y Ft(:::)o(\026)899 685 y Fr(4)927
673 y Fv(dx)980 652 y Ft(\026)1001 657 y Fr(1)1040 673
y FE(^)f Fv(:)8 b(:)g(:)18 b FE(^)12 b Fv(dx)1267 652
y Ft(\026)1288 657 y Fr(4)1324 673 y Fv(;)447 b FH(\(2.3\))-5
794 y(w)o(e)16 b(obtain)130 903 y Fv(F)169 882 y FC(\003)214
903 y FE(^)k Fv(F)306 882 y FC(\006)355 903 y FH(=)14
b Fv(")430 882 y Ft(\026\027)r(\032\033)520 903 y FE(F)561
882 y FC(\003)556 915 y Ft(\026\027)607 903 y FE(F)648
882 y FC(\006)643 915 y Ft(\032\033)693 903 y Fv(d)718
882 y FC(4)738 903 y Fv(x)97 b FH(;)105 b Fv(F)1021 882
y FC(\003)1067 903 y FE(^)1119 882 y Ft(?)1139 903 y
Fv(F)1178 882 y FC(\006)1219 903 y FH(=)13 b FE(\000)p
FH(2)8 b FE(F)1382 882 y FC(\003)1377 915 y Ft(\026\027)1429
903 y FE(F)1470 882 y FC(\006)p FB(j)p Ft(\026\027)1548
903 y Fv(d)1573 882 y FC(4)1593 903 y Fv(x)16 b(:)134
b FH(\(2.4\))-5 1011 y(In)20 b(addition)g(to)g(the)g(gauge)h(\014elds)f
(let)f(us)h(also)h(in)o(tro)q(duce)f(a)g(set)g(of)g(real)g(scalar)g
(\014elds)g Fv(\036)1723 993 y Ft(I)1762 1011 y FH(\()g
Fv(I)k FH(=)-5 1072 y(1)p Fv(;)8 b(:)g(:)g(:)g(;)p 129
1045 43 2 v 8 w(m)p FH(\))17 b(spanning)h(an)p 483 1045
V 17 w Fv(m)p FH({dimensional)d(manifold)h FE(M)1082
1079 y Ft(scalar)1198 1054 y FC(1)p
 (#Hfootnote.1) [[360 510 364 522] [1 1 1 [3 3]] [0 0 1]] pdfm 
1235 1072 a FH(endo)o(w)o(ed)g(with)h(a)g(metric)e Fv(g)1762
1079 y Ft(I)s(J)1805 1072 y FH(\()p Fv(\036)p FH(\).)-5
1132 y(Utilizing)f(the)i(ab)q(o)o(v)o(e)h(\014eld)e(con)o(ten)o(t)h(w)o
(e)g(can)g(write)g(the)g(follo)o(wing)g(action)g(functional:)38
1260 y FE(S)26 b FH(=)151 1226 y(1)p 151 1248 25 2 v
151 1294 a(2)197 1201 y Fs(Z)255 1212 y(nh)311 1260 y
Fv(\015)336 1267 y FC(\003\006)388 1260 y FH(\()p Fv(\036)p
FH(\))8 b Fv(F)502 1239 y FC(\003)548 1260 y FE(^)19
b Fv(?F)663 1239 y FC(\006)710 1260 y FH(+)g Fv(\022)790
1267 y FC(\003\006)842 1260 y FH(\()p Fv(\036)p FH(\))8
b Fv(F)956 1239 y FC(\003)1001 1260 y FE(^)20 b Fv(F)1093
1239 y FC(\006)1128 1212 y Fs(i)1167 1260 y FH(+)f Fv(g)1247
1267 y Ft(I)s(J)1290 1260 y FH(\()p Fv(\036)p FH(\))8
b Fv(@)1391 1267 y Ft(\026)1414 1260 y Fv(\036)1443 1239
y Ft(I)1471 1260 y Fv(@)1500 1239 y Ft(\026)1523 1260
y Fv(\036)1552 1239 y Ft(J)1585 1260 y FH(d)1612 1239
y FC(4)1632 1260 y Fv(x)1668 1212 y Fs(o)1720 1260 y
Fv(;)51 b FH(\(2.5\))-5 1384 y(where)24 b(the)f(scalar)h(\014elds)f
(dep)q(enden)o(t)p 756 1358 30 2 v 23 w Fv(n)16 b FE(\002)p
856 1358 V 16 w Fv(n)24 b FH(matrix)e Fv(\015)1100 1391
y FC(\003\006)1152 1384 y FH(\()p Fv(\036)p FH(\))i(generalizes)e(the)i
(in)o(v)o(erse)d(of)j(the)-5 1444 y(squared)18 b(coupling)f(constan)o
(t)584 1425 y FC(1)p 575 1433 36 2 v 575 1461 a Ft(g)593
1452 y Fr(2)633 1444 y FH(app)q(earing)h(in)f(ordinary)g(gauge)h
(theories.)24 b(The)17 b(\014eld)g(dep)q(enden)o(t)-5
1509 y(matrix)12 b Fv(\022)174 1516 y FC(\003\006)226
1509 y FH(\()p Fv(\036)p FH(\))h(is)g(instead)h(a)g(generalization)f
(of)g(the)g Fv(theta)p FH({angle)g(of)h(quan)o(tum)e(c)o(hromo)q
(dynamics.)-5 1570 y(Both)k Fv(\015)k FH(and)c Fv(\022)i
FH(are)e(symmetri)o(c)d(matrices.)20 b(In)o(tro)q(ducing)c(a)g(formal)f
(op)q(erator)j Fv(j)h FH(that)d(maps)g(a)h(\014eld)-5
1630 y(strength)g(in)o(to)f(its)g(Ho)q(dge)h(dual)673
1710 y Fs(\020)697 1758 y Fv(j)12 b FE(F)770 1737 y FC(\003)796
1710 y Fs(\021)821 1785 y Ft(\026\027)886 1758 y FE(\021)952
1724 y FH(1)p 952 1746 25 2 v 952 1792 a(2)989 1758 y
Fv(\017)1009 1765 y Ft(\026\027)r(\032\033)1099 1758
y FE(F)1140 1737 y FC(\003)p FB(j)p Ft(\032\033)1785
1758 y FH(\(2.6\))-5 1879 y(and)17 b(a)g(formal)e(scalar)h(pro)q(duct)
593 2022 y(\()p Fv(G)8 b(;)17 b(K)t FH(\))d FE(\021)g
Fv(G)858 2002 y Ft(T)886 2022 y Fv(K)26 b FE(\021)p 1038
1949 22 2 v 1038 1968 a Ft(n)1019 1981 y Fs(X)1014 2073
y FC(\003=1)1092 2022 y Fv(G)1130 2002 y FC(\003)1130
2035 y Ft(\026\027)1173 2022 y Fv(K)1218 2002 y FC(\003)p
FB(j)p Ft(\026\027)1785 2022 y FH(\(2.7\))-5 2164 y(the)16
b(total)h(Lagrangian)h(of)f(eq.)e(2.5)p
 (#equation.2.5) [[212 248 227 260] [1 1 1 [3 3]] [0 0 1]] pdfm 
17 w(can)h(b)q(e)g(rewritten)g(as)361 2292 y FE(L)395
2271 y FC(\()p Ft(tot)p FC(\))489 2292 y FH(=)22 b FE(F)590
2271 y Ft(T)634 2292 y FH(\()p FE(\000)p Fv(\015)14 b
FE(\012)d FH(1)-17 b(1)11 b(+)g Fv(\022)i FE(\012)d Fv(j)s
FH(\))f FE(F)24 b FH(+)1130 2258 y(1)p 1130 2280 25 2
v 1130 2326 a(2)1168 2292 y Fv(g)1191 2299 y Ft(I)s(J)1233
2292 y FH(\()p Fv(\036)p FH(\))8 b Fv(@)1334 2299 y Ft(\026)1358
2292 y Fv(\036)1387 2271 y Ft(I)1415 2292 y Fv(@)1444
2271 y Ft(\026)1466 2292 y Fv(\036)1495 2271 y Ft(J)1785
2292 y FH(\(2.8\))-5 2418 y(The)19 b(op)q(erator)i Fv(j)h
FH(satis\014es)d Fv(j)545 2400 y FC(2)592 2418 y FH(=)27
b FE(\000)8 b FH(1)-17 b(1)20 b(so)f(that)h(its)f(eigen)o(v)m(alues)f
(are)h FE(\006)p FH(i.)29 b(In)o(tro)q(ducing)19 b(self{dual)-5
2478 y(and)e(an)o(tiself{dual)f(com)o(binations)718 2597
y FE(F)759 2576 y FB(\006)830 2597 y FH(=)914 2563 y(1)p
914 2585 V 914 2631 a(2)952 2597 y(\()p FE(F)24 b(\006)11
b FH(i)d Fv(j)s FE(F)d FH(\))687 2688 y Fv(j)11 b FE(F)759
2668 y FB(\006)830 2688 y FH(=)41 b FE(\007)p FH(i)p
FE(F)1003 2668 y FB(\006)1785 2688 y FH(\(2.9\))p -5
2722 756 2 v 51 2753 a Fq(1)70 2768 y Fx(Whether)15 b(the)f
Fp(\036)338 2753 y Fo(I)371 2768 y Fx(can)g(b)q(e)h(arranged)f(in)o(to)
f(complex)g(\014elds)h(is)g(not)f(relev)n(an)o(t)h(at)g(this)g(lev)o
(el)g(of)f(the)h(discussion.)928 2892 y FH(4)p eop
%%Page: 5 6
5 5 bop -5 15 a FH(and)17 b(the)f(\014eld{dep)q(enden)o(t)g(symmetri)o
(c)d(matrices)774 119 y FE(N)48 b FH(=)42 b Fv(\022)20
b FE(\000)f FH(i)p Fv(\015)p 774 152 49 2 v 774 191 a
FE(N)48 b FH(=)42 b Fv(\022)12 b FH(+)f(i)p Fv(\015)19
b(;)661 b FH(\(2.10\))-5 295 y(the)16 b(v)o(ector)g(part)g(of)h(the)f
(Lagrangian)34 b(2.8)p
 (#equation.2.8) [[250 696 265 708] [1 1 1 [3 3]] [0 0 1]] pdfm 
17 w(can)16 b(b)q(e)h(rewritten)e(as)572 398 y FE(L)606
405 y Ft(v)q(ec)681 398 y FH(=)22 b(i)771 350 y Fs(h)791
398 y FE(F)832 377 y FB(\000)p Ft(T)p 886 359 V 886 398
a FE(N)8 b(F)976 377 y FB(\000)1016 398 y FE(\000)j(F)1107
377 y FC(+)p Ft(T)1162 398 y FE(N)c(F)1251 377 y FC(+)1280
350 y Fs(i)1760 398 y FH(\(2.11\))-5 501 y(In)o(tro)q(ducing)16
b(the)g(new)h(tensors)570 610 y Fs(e)560 627 y FE(G)593
606 y FC(\003)590 639 y Ft(\026\027)655 627 y FE(\021)721
593 y FH(1)p 721 615 25 2 v 721 661 a(2)777 593 y Fv(@)s
FE(L)p 755 615 108 2 v 755 661 a Fv(@)s FE(F)825 646
y FC(\003)820 673 y Ft(\026\027)881 627 y FE($)c(G)977
606 y FB(\007)p FC(\003)974 639 y Ft(\026\027)1053 627
y FE(\021)22 b(\007)1163 593 y FH(i)p 1158 615 25 2 v
1158 661 a(2)1222 593 y Fv(@)s FE(L)p 1192 615 124 2
v 1192 661 a Fv(@)s FE(F)1262 646 y FB(\007)p FC(\003)1257
673 y Ft(\026\027)1760 627 y FH(\(2.12\))-5 761 y(whic)o(h,)15
b(in)h(matrix)f(notation,)h(corresp)q(onds)i(to)531 887
y Fv(j)11 b FE(G)25 b(\021)683 853 y FH(1)p 683 875 25
2 v 683 921 a(2)742 853 y Fv(@)s FE(L)p 725 875 97 2
v 725 921 a Fv(@)s FE(F)795 906 y Ft(T)849 887 y FH(=)d
FE(\000)17 b FH(\()p Fv(\015)d FE(\012)d FH(1)-17 b(1)11
b FE(\000)g Fv(\022)h FE(\012)f Fv(j)s FH(\))17 b FE(F)415
b FH(\(2.13\))-5 1003 y(the)23 b(Bianc)o(hi)e(iden)o(tities)f(and)k
(\014eld)e(equations)g(asso)q(ciated)i(with)e(the)h(Lagrangian)47
b(2.5)p  (#equation.2.5) [[469 526 484 538] [1 1 1 [3 3]] [0 0 1]] pdfm 
23 w(can)23 b(b)q(e)-5 1063 y(written)16 b(as)802 1166
y Fv(@)831 1145 y Ft(\026)868 1150 y Fs(e)854 1166 y
FE(F)895 1145 y FC(\003)890 1178 y Ft(\026\027)974 1166
y FH(=)42 b(0)682 b(\(2.14\))808 1248 y Fv(@)837 1227
y Ft(\026)871 1231 y Fs(e)860 1248 y FE(G)893 1227 y
FC(\003)890 1260 y Ft(\026\027)974 1248 y FH(=)42 b(0)682
b(\(2.15\))-5 1351 y(or)17 b(equiv)m(alen)o(tly)745 1454
y Fv(@)774 1434 y Ft(\026)797 1454 y Fv(I)t(m)p FE(F)907
1434 y FB(\006)p FC(\003)902 1466 y Ft(\026\027)1001
1454 y FH(=)42 b(0)655 b(\(2.16\))753 1533 y Fv(@)782
1512 y Ft(\026)805 1533 y Fv(I)t(m)p FE(G)907 1512 y
FB(\006)p FC(\003)904 1545 y Ft(\026\027)1001 1533 y
FH(=)42 b(0)16 b Fv(:)625 b FH(\(2.17\))-5 1636 y(This)17
b(suggests)g(that)g(w)o(e)f(in)o(tro)q(duce)f(the)h(2)p
799 1610 30 2 v Fv(n)h FH(column)e(v)o(ector)798 1760
y FD(V)23 b FE(\021)924 1700 y Fs(\022)963 1730 y Fv(j)11
b FE(F)967 1791 y Fv(j)g FE(G)1043 1700 y Fs(\023)1760
1760 y FH(\(2.18\))-5 1885 y(and)17 b(that)g(w)o(e)f(consider)g
(general)g(linear)f(transformations)h(on)h(suc)o(h)f(a)h(v)o(ector)636
1954 y Fs(\022)675 1984 y Fv(j)11 b FE(F)679 2045 y Fv(j)g
FE(G)755 1954 y Fs(\023)786 1960 y FB(0)819 2015 y FH(=)880
1954 y Fs(\022)919 1984 y Fv(A)51 b(B)918 2045 y(C)i(D)1056
1954 y Fs(\023)8 b(\022)1134 1984 y Fv(j)j FE(F)1138
2045 y Fv(j)g FE(G)1214 1954 y Fs(\023)1760 2015 y FH(\(2.19\))-5
2172 y(F)l(or)k(an)o(y)f(matrix)328 2111 y Fs(\022)368
2142 y Fv(A)51 b(B)367 2202 y(C)h(D)505 2111 y Fs(\023)557
2172 y FE(2)23 b Fv(GL)p FH(\(2)p 727 2145 V Fv(n)q(;)8
b FH(I)-9 b(R)o(\))15 b(the)f(new)h(v)o(ector)f FD(V)1226
2154 y FB(0)1252 2172 y FH(of)h Fu(magnetic)i(and)f(ele)n(ctric)g
FH(\014eld{)-5 2253 y(strengths)j(satis\014es)g(the)f(same)f(equations)
37 b(2.15)p
 (#equation.2.14) [[274 226 294 238] [1 1 1 [3 3]] [0 0 1]] pdfm 
19 w(as)19 b(the)f(old)h(one.)27 b(In)18 b(a)h(condensed)f(notation)h
(w)o(e)-5 2313 y(can)e(write)640 2373 y Fv(@)10 b FD(V)24
b FH(=)e(0)63 b FE(\()-8 b(\))62 b Fv(@)10 b FD(V)1122
2353 y FB(0)1156 2373 y FH(=)22 b(0)520 b(\(2.20\))-5
2458 y(Separating)17 b(the)f(self{dual)g(and)h(an)o(ti{self{dual)f
(parts)479 2561 y FE(F)j FH(=)585 2513 y Fs(\020)610
2561 y FE(F)651 2541 y FC(+)692 2561 y FH(+)11 b FE(F)782
2541 y FB(\000)811 2513 y Fs(\021)941 2561 y FH(;)106
b FE(G)16 b FH(=)1159 2513 y Fs(\020)1184 2561 y FE(G)1217
2541 y FC(+)1257 2561 y FH(+)11 b FE(G)1339 2541 y FB(\000)1368
2513 y Fs(\021)1760 2561 y FH(\(2.21\))-5 2664 y(and)17
b(taking)g(in)o(to)e(accoun)o(t)i(that)f(w)o(e)g(ha)o(v)o(e)653
2768 y FE(G)686 2747 y FC(+)737 2768 y FH(=)22 b FE(N)7
b(F)886 2747 y FC(+)965 2768 y FE(G)998 2747 y FB(\000)1049
2768 y FH(=)p 1109 2729 49 2 v 22 w FE(N)g(F)1198 2747
y FB(\000)1760 2768 y FH(\(2.22\))928 2892 y(5)p eop
%%Page: 6 7
6 6 bop -5 15 a FH(the)16 b(dualit)o(y)g(rotation)h(of)f(eq.)f(2.19)p
 (#equation.2.19) [[207 763 228 775] [1 1 1 [3 3]] [0 0 1]] pdfm 
17 w(can)i(b)q(e)f(rewritten)f(as)112 86 y Fs(\022)151
116 y FE(F)192 98 y FC(+)155 177 y FE(G)188 158 y FC(+)229
86 y Fs(\023)260 92 y FB(0)294 146 y FH(=)354 86 y Fs(\022)394
116 y Fv(A)50 b(B)393 177 y(C)i(D)530 86 y Fs(\023)8
b(\022)632 116 y FE(F)673 98 y FC(+)608 177 y FE(N)f(F)697
158 y FC(+)735 86 y Fs(\023)871 146 y FH(;)990 86 y Fs(\022)1029
116 y FE(F)1070 98 y FB(\000)1033 177 y FE(G)1066 158
y FB(\000)1108 86 y Fs(\023)1138 92 y FB(0)1172 146 y
FH(=)1232 86 y Fs(\022)1272 116 y Fv(A)51 b(B)1271 177
y(C)h(D)1409 86 y Fs(\023)7 b(\022)1510 116 y FE(F)1551
98 y FB(\000)p 1486 138 49 2 v 1486 177 a FE(N)g(F)1575
158 y FB(\000)1613 86 y Fs(\023)1760 146 y FH(\(2.23\))-5
276 y(The)22 b(problem)f(is)g(that)i(the)e(transformation)h(rule)43
b(2.23)p
 (#equation.2.23) [[316 701 336 713] [1 1 1 [3 3]] [0 0 1]] pdfm 
23 w(of)22 b FE(G)1218 258 y FB(\006)1269 276 y FH(m)o(ust)f(b)q(e)h
(consisten)o(t)g(with)f(the)-5 336 y(de\014nition)d(of)g(the)f(latter)g
(as)i(v)m(ariation)f(of)g(the)g(Lagrangian)h(with)f(resp)q(ect)g(to)g
FE(F)1541 318 y FB(\006)1588 336 y FH(\(see)f(eq.)g(2.12)p
 (#equation.2.12) [[496 686 516 698] [1 1 1 [3 3]] [0 0 1]] pdfm (\).)
-5 420 y(This)g(request)e(restricts)h(the)g(form)f(of)h(the)g(matrix)f
(\003)e(=)1060 359 y Fs(\022)1100 390 y Fv(A)50 b(B)1099
450 y(C)i(D)1236 359 y Fs(\023)1267 420 y FH(.)21 b(As)16
b(w)o(e)g(are)g(going)h(to)g(sho)o(w,)f(\003)-5 501 y(m)o(ust)f(b)q
(elong)i(to)g(the)f(symplectic)d(subgroup)k(of)g(the)f(general)g
(linear)f(group)484 627 y(\003)f FE(\021)584 566 y Fs(\022)624
597 y Fv(A)50 b(B)623 657 y(C)i(D)760 566 y Fs(\023)813
627 y FE(2)22 b Fv(S)s(p)p FH(\(2)p 968 601 30 2 v Fv(n)q(;)8
b FH(I)-9 b(R\))22 b FE(\032)g Fv(GL)p FH(\(2)p 1281
601 V Fv(n)q(;)8 b FH(I)-9 b(R\))363 b(\(2.24\))-5 755
y(the)22 b(subgroup)h Fv(S)s(p)p FH(\(2)p 402 729 V Fv(n)q(;)8
b FH(I)-9 b(R\))22 b(b)q(eing)g(de\014ned)g(as)g(the)g(set)g(of)g(2)p
1173 729 V Fv(n)16 b FE(\002)e FH(2)p 1295 729 V Fv(n)23
b FH(matrices)d(that)i(satisfy)g(the)-5 816 y(condition)373
887 y(\003)13 b FE(2)h Fv(S)s(p)p FH(\(2)p 567 861 V
Fv(n)q(;)8 b FH(I)-9 b(R\))30 b FE(\000)-9 b(!)30 b FH(\003)857
867 y Ft(T)901 827 y Fs(\022)961 857 y FD(0)72 b FH(1)-17
b(1)940 917 y FE(\000)p FH(1)g(1)53 b FD(0)1103 827 y
Fs(\023)1151 887 y FH(\003)22 b(=)1267 827 y Fs(\022)1327
857 y FD(0)72 b FH(1)-17 b(1)1305 917 y FE(\000)p FH(1)g(1)54
b FD(0)1469 827 y Fs(\023)1760 887 y FH(\(2.25\))-5 993
y(that)17 b(is,)f(using)g Fv(n)11 b FE(\012)g Fv(n)17
b FH(blo)q(c)o(k)e(comp)q(onen)o(ts)360 1098 y Fv(A)397
1077 y Ft(T)424 1098 y Fv(C)g FE(\000)10 b Fv(C)562 1077
y Ft(T)589 1098 y Fv(A)k FH(=)g Fv(B)732 1077 y Ft(T)759
1098 y Fv(D)f FE(\000)d Fv(D)902 1077 y Ft(T)931 1098
y Fv(B)16 b FH(=)e(0)98 b Fv(A)1195 1077 y Ft(T)1222
1098 y Fv(D)13 b FE(\000)e Fv(C)1364 1077 y Ft(T)1391
1098 y Fv(B)16 b FH(=)e(1)240 b(\(2.26\))68 1202 y(T)l(o)14
b(pro)o(v)o(e)f(the)g(statemen)o(t)f(w)o(e)h(just)g(made,)f(w)o(e)h
(calculate)g(the)g(transformed)g(Lagrangian)i FE(L)1781
1184 y FB(0)1806 1202 y FH(and)-5 1263 y(then)g(w)o(e)f(compare)f(its)h
(v)m(ariation)655 1243 y Ft(@)r FB(L)700 1231 y Fn(0)p
642 1251 83 2 v 642 1280 a Ft(@)r FB(F)691 1270 y Fn(0)p
Fm(T)744 1263 y FH(with)g FE(G)886 1244 y FB(\0060)939
1263 y FH(as)i(it)e(follo)o(ws)g(from)f(the)i(p)q(ostulated)g
(transforma-)-5 1323 y(tion)i(rule)32 b(2.23)p
 (#equation.2.23) [[122 449 143 461] [1 1 1 [3 3]] [0 0 1]] pdfm (.)23
b(T)l(o)17 b(p)q(erform)e(suc)o(h)h(a)h(calculation)f(w)o(e)g(rely)g
(on)h(the)f(follo)o(wing)g(basic)g(idea.)22 b(While)-5
1383 y(the)17 b(dualit)o(y)f(rotation)i(2.23)p
 (#equation.2.23) [[176 435 197 447] [1 1 1 [3 3]] [0 0 1]] pdfm 
18 w(is)f(p)q(erformed)f(on)h(the)g(\014eld)g(strengths)h(and)f(on)h
(their)e(duals,)i(also)f(the)-5 1443 y(scalar)g(\014elds)g(are)g
(transformed)f(b)o(y)g(the)h(action)g(of)g(some)f(di\013eomorphism)f
Fv(\030)26 b FE(2)d FH(Di\013)12 b(\()p FE(M)1711 1450
y Ft(scalar)1810 1443 y FH(\))17 b(of)-5 1503 y(the)h(scalar)g
(manifold)f(and,)h(as)h(a)f(consequence)f(of)i(that,)f(also)h(the)e
(matrix)f FE(N)26 b FH(c)o(hanges.)g(In)18 b(other)-5
1563 y(w)o(ords)f(giv)o(en)d(the)i(scalar)g(manifold)e
FE(M)744 1570 y Ft(scalar)859 1563 y FH(w)o(e)h(assume)g(that)h(there)g
(exists)f(a)h(homomorphism)d(of)-5 1624 y(the)j(form)576
1684 y Fv(\023)593 1691 y Ft(\016)626 1684 y FH(:)22
b(Di\013)12 b(\()p FE(M)832 1691 y Ft(scalar)931 1684
y FH(\))22 b FE(\000)-9 b(!)22 b Fv(GL)p FH(\(2)p 1188
1657 30 2 v Fv(n)q(;)8 b FH(I)-9 b(R\))456 b(\(2.27\))-5
1769 y(so)17 b(that)520 1873 y FE(8)77 b Fv(\030)k FE(2)22
b FH(Di\013)12 b(\()p FE(M)953 1880 y Ft(scalar)1052
1873 y FH(\))22 b(:)g Fv(\036)1158 1853 y Ft(I)1232 1844
y(\030)1200 1873 y FE(\000)-9 b(!)22 b Fv(\036)1331 1853
y Ft(I)s FB(0)520 1970 y FE(9)41 b Fv(\023)606 1977 y
Ft(\016)625 1970 y FH(\()p Fv(\030)r FH(\))h(=)780 1909
y Fs(\022)819 1940 y Fv(A)856 1947 y Ft(\030)925 1940
y Fv(B)962 1947 y Ft(\030)820 2000 y Fv(C)855 2007 y
Ft(\030)923 2000 y Fv(D)963 2007 y Ft(\030)991 1909 y
Fs(\023)1043 1970 y FE(2)23 b Fv(GL)p FH(\(2)p 1213 1943
V Fv(n)q(;)8 b FH(I)-9 b(R)o(\))432 b(\(2.28\))-5 2098
y(\(In)15 b(the)g(sequel)e(the)i(sub\014x)g Fv(\030)j
FH(will)c(b)q(e)h(omitted)e(when)i(no)g(confusion)h(can)f(arise)g(and)g
(b)q(e)g(reinstalled)-5 2158 y(when)i(necessary)f(for)g(clarit)o(y)l(.)
k(\))68 2219 y(Using)h(suc)o(h)f(a)h(homomorphism)d(w)o(e)i(can)h
(de\014ne)f(the)h(sim)o(ultaneous)e(action)i(of)g Fv(\030)i
FH(on)e(all)f(the)-5 2279 y(\014elds)c(of)h(our)f(theory)h(b)o(y)e
(setting)660 2437 y Fv(\030)25 b FH(:)742 2337 y Fs(8)742
2374 y(>)742 2387 y(<)742 2462 y(>)742 2474 y(:)787 2377
y Fv(\036)d FE(\000)-8 b(!)22 b Fv(\030)r FH(\()p Fv(\036)p
FH(\))787 2437 y FD(V)h FE(\000)-8 b(!)22 b Fv(\023)972
2444 y Ft(\016)991 2437 y FH(\()p Fv(\030)r FH(\))8 b
FD(V)787 2497 y FE(N)f FH(\()p Fv(\036)p FH(\))22 b FE(\000)-8
b(!)22 b(N)1075 2479 y FB(0)1087 2497 y FH(\()p Fv(\030)r
FH(\()p Fv(\036)p FH(\)\))1760 2437 y(\(2.29\))-5 2595
y(where)12 b(the)g(notation)i(2.18)p
 (#equation.2.18) [[169 144 190 156] [1 1 1 [3 3]] [0 0 1]] pdfm 
13 w(has)f(b)q(een)f(utilized.)18 b(In)12 b(the)g(gauge)i(sector)e(the)
g(transformed)g(Lagrangian)-5 2655 y(is)20 2759 y FE(L)54
2739 y FB(0)54 2772 y Ft(v)q(ec)129 2759 y FH(=)22 b(i)211
2711 y Fs(h)230 2759 y FE(F)271 2739 y FB(\000)p Ft(T)334
2759 y FH(\()p Fv(A)10 b FH(+)h Fv(B)p 489 2720 49 2
v 3 w FE(N)c FH(\))556 2735 y Ft(T)p 583 2720 V 583 2759
a FE(N)631 2730 y FB(0)643 2759 y FH(\()p Fv(A)j FH(+)h
Fv(B)p 798 2720 V 3 w FE(N)c FH(\))p FE(F)906 2739 y
FB(\000)954 2759 y FE(\000)18 b(F)1052 2739 y FC(+)p
Ft(T)1115 2759 y FH(\()p Fv(A)11 b FH(+)f Fv(B)s FE(N)d
FH(\))1337 2735 y Ft(T)1364 2759 y FE(N)1412 2739 y FB(0)1424
2759 y FH(\()p Fv(A)j FH(+)h Fv(B)s FE(N)c FH(\))p FE(F)1687
2739 y FC(+)1716 2711 y Fs(i)1760 2759 y FH(\(2.30\))928
2892 y(6)p eop
%%Page: 7 8
7 7 bop -5 15 a FH(Consistency)16 b(with)h(the)f(de\014nition)f(of)i
FE(G)766 -3 y FC(+)811 15 y FH(requires)e(that)410 104
y FE(N)458 84 y FB(0)492 104 y FE(\021)22 b(N)601 84
y FB(0)613 104 y FH(\()p Fv(\030)r FH(\()p Fv(\036)p
FH(\)\))h(=)f(\()p Fv(C)14 b FH(+)d Fv(D)q FE(N)c FH(\()p
Fv(\036)p FH(\)\))i(\()p Fv(A)i FH(+)g Fv(B)s FE(N)c
FH(\()p Fv(\036)p FH(\)\))1415 80 y FB(\000)p FC(1)1760
104 y FH(\(2.31\))-5 193 y(while)16 b(consistency)f(with)h(the)g
(de\014nition)g(of)h FE(G)880 175 y FB(\000)925 193 y
FH(imp)q(oses)e(the)h(transformation)h(rule)p 399 254
49 2 v 399 293 a FE(N)447 264 y FB(0)481 293 y FE(\021)p
542 254 V 22 w(N)590 264 y FB(0)601 293 y FH(\()p Fv(\030)r
FH(\()p Fv(\036)p FH(\)\))23 b(=)812 245 y Fs(\020)837
293 y Fv(C)14 b FH(+)d Fv(D)p 976 254 V 1 w FE(N)d FH(\()p
Fv(\036)p FH(\))1092 245 y Fs(\021)g(\020)1150 293 y
Fv(A)j FH(+)g Fv(B)p 1287 254 V 3 w FE(N)c FH(\()p Fv(\036)p
FH(\))1402 245 y Fs(\021)1426 257 y FB(\000)p FC(1)1760
293 y FH(\(2.32\))-5 382 y(It)15 b(is)f(from)g(the)h(transformation)g
(rules)f(2.31)p
 (#equation.2.31) [[249 675 270 687] [1 1 1 [3 3]] [0 0 1]] pdfm 
16 w(and)30 b(2.32)p
 (#equation.2.32) [[299 675 320 687] [1 1 1 [3 3]] [0 0 1]] pdfm 
16 w(that)15 b(w)o(e)g(deriv)o(e)e(a)i(restriction)f(on)h(the)g(form)-5
442 y(of)f(the)f(dualit)o(y)g(rotation)h(matrix)e(\003)h
FE(\021)h Fv(\023)749 449 y Ft(\016)768 442 y FH(\()p
Fv(\030)r FH(\).)21 b(Indeed)13 b(b)o(y)f(requiring)h(that)h(the)f
(transformed)g(matrix)-5 503 y FE(N)43 484 y FB(0)68
503 y FH(b)q(e)g(again)g(symmetric)c(one)k(easily)f(\014nds)h(that)g
(\003)g(m)o(ust)e(ob)q(ey)i(eq.)20 b(2.25)p
 (#equation.2.25) [[380 646 400 658] [1 1 1 [3 3]] [0 0 1]] pdfm (,)14
b(namely)c(\003)k FE(2)g Fv(S)s(p)p FH(\(2)p 1756 476
30 2 v Fv(n)q(;)8 b FH(I)-9 b(R\).)-5 563 y(Consequen)o(tly)16
b(the)g(homomorphism)d(of)k(eq.)e(2.27)p
 (#equation.2.27) [[278 632 299 644] [1 1 1 [3 3]] [0 0 1]] pdfm 
17 w(sp)q(ecializes)g(as)583 651 y Fv(\023)600 658 y
Ft(\016)633 651 y FH(:)22 b(Di\013)12 b(\()p FE(M)839
658 y Ft(scalar)938 651 y FH(\))22 b FE(\000)-8 b(!)21
b Fv(S)s(p)p FH(\(2)p 1181 625 V Fv(n)q(;)8 b FH(I)-9
b(R\))463 b(\(2.33\))-5 740 y(Clearly)l(,)14 b(since)h
Fv(S)s(p)p FH(\(2)p 392 714 V Fv(n)q(;)8 b FH(I)-9 b(R)o(\))16
b(is)f(a)h(\014nite)e(dimensional)g(Lie)h(group,)h(while)e(Di\013)e(\()
p FE(M)1530 747 y Ft(scalar)1629 740 y FH(\))j(is)h(in\014nite{)-5
800 y(dimensional,)j(the)i(homomorphism)c Fv(\023)736
807 y Ft(\016)775 800 y FH(can)k(nev)o(er)e(b)q(e)i(an)f(isomorphism.)
32 b(De\014ning)20 b(the)g(T)l(orelli)-5 861 y(group)d(of)g(the)f
(scalar)g(manifold)f(as)519 949 y(Di\013)d(\()p FE(M)689
956 y Ft(scalar)788 949 y FH(\))22 b FE(\033)g FH(T)l(or)8
b(\()p FE(M)1051 956 y Ft(scalar)1150 949 y FH(\))22
b FE(\021)g FH(k)o(er)7 b Fv(\023)1342 956 y Ft(\016)1760
949 y FH(\(2.34\))-5 1038 y(w)o(e)16 b(alw)o(a)o(ys)g(ha)o(v)o(e)690
1098 y(dim)6 b(T)l(or)j(\()p FE(M)941 1105 y Ft(scalar)1040
1098 y FH(\))22 b(=)g FE(1)569 b FH(\(2.35\))-5 1176
y(The)21 b(reason)g(wh)o(y)f(w)o(e)g(ha)o(v)o(e)f(giv)o(en)h(the)g
(name)f(of)i(T)l(orelli)e(to)i(the)f(group)h(de\014ned)f(b)o(y)g(eq.)f
(2.34)p
 (#equation.2.34) [[491 485 511 497] [1 1 1 [3 3]] [0 0 1]] pdfm 
21 w(is)-5 1237 y(b)q(ecause)e(of)f(its)g(similarit)o(y)d(with)j(the)g
(T)l(orelli)g(group)h(that)f(o)q(ccurs)h(in)f(algebraic)g(geometry)l(.)
68 1297 y(What)h(should)g(b)q(e)g(clear)e(from)g(the)i(ab)q(o)o(v)o(e)f
(discussion)g(is)g(that)h(a)g(family)d(of)j(Lagrangians)h(as)f(in)-5
1357 y(eq.)e(2.5)p
 (#equation.2.5) [[89 441 104 453] [1 1 1 [3 3]] [0 0 1]] pdfm 
17 w(will)g(admit)g(a)h(group)h(of)g(dualit)o
(y{rotations/\014eld{rede\014nitions)f(that)h(will)e(map)g(elemen)o(ts)
-5 1417 y(of)20 b(the)g(family)d(in)o(to)i(eac)o(h)g(other,)i(as)f
(long)g(as)g(a)g Fu(kinetic)i(matrix)e FE(N)1295 1424
y FC(\003\006)1367 1417 y FH(can)f(b)q(e)h(constructed)g(that)-5
1477 y(transforms)15 b(as)h(in)f(eq.)g(2.31)p
 (#equation.2.31) [[175 413 196 425] [1 1 1 [3 3]] [0 0 1]] pdfm (.)21
b(A)15 b(w)o(a)o(y)g(to)h(obtain)g(suc)o(h)f(an)h(ob)s(ject)f(is)g(to)h
(iden)o(tify)d(it)i(with)g(the)g Fu(p)n(erio)n(d)-5 1538
y(matrix)e FH(o)q(ccurring)h(in)f(problems)f(of)i(algebraic)f(geometry)
l(.)18 b(A)o(t)13 b(the)g(lev)o(el)e(of)j(the)f(presen)o(t)f
(discussion,)-5 1598 y(ho)o(w)o(ev)o(er,)18 b(this)h(iden)o
(ti\014cation)f(is)g(b)o(y)h(no)g(means)f(essen)o(tial:)26
b(an)o(y)18 b(construction)h(of)h FE(N)1633 1605 y FC(\003\006)1704
1598 y FH(with)e(the)-5 1658 y(appropriate)12 b(transformation)g(prop)q
(erties)f(is)g(acceptable.)19 b(Note)11 b(also)h(that)g(so)g(far)f(w)o
(e)g(ha)o(v)o(e)g(used)g(the)-5 1718 y(w)o(ords)i Fu(duality{r)n
(otations/\014eld{r)n(e)n(de\014nitions)f FH(and)h(not)f(the)f(w)o(ord)
h(dualit)o(y)f(symmetry)l(.)16 b(Indeed)11 b(the)-5 1778
y(di\013eomorphisms)g(of)j(the)e(scalar)i(manifold)d(w)o(e)i(ha)o(v)o
(e)f(considered)h(w)o(ere)f(quite)g(general)h(and,)h(as)f(suc)o(h)-5
1838 y(had)18 b(no)g(pretension)g(to)g(b)q(e)f(symmetrie)o(s)e(of)j
(the)f(action,)h(or)f(of)h(the)f(theory)l(.)25 b(Indeed)17
b(the)g(question)-5 1899 y(w)o(e)e(ha)o(v)o(e)f(answ)o(ered)h(is)g(the)
g(follo)o(wing:)20 b(what)c(are)f(the)g(appropriate)h(transformation)f
(prop)q(erties)g(of)-5 1959 y(the)j(tensor)f(gauge)i(\014elds)e(and)h
(of)g(the)g(generalized)e(coupling)h(constan)o(ts)i(under)e
(di\013eomorphisms)-5 2019 y(of)g(the)f(scalar)g(manifold?)21
b(The)16 b(next)g(question)g(is)g(ob)o(viously)f(that)i(of)g(dualit)o
(y)e(symmetri)o(es.)68 2079 y(As)23 b(it)g(is)g(the)g(case)g(with)g
(the)g(di\013erence)g(b)q(et)o(w)o(een)f(general)h(co)o(v)m(ariance)f
(and)i(isometries)d(in)-5 2139 y(the)d(con)o(text)f(of)h(general)g
(relativit)o(y)l(,)e(dualit)o(y)h(symmetri)o(es)e(corresp)q(ond)k(to)g
(the)e(subset)i(of)f(dualit)o(y)-5 2200 y(transformations)f(for)g(whic)
o(h)e(w)o(e)h(obtain)h(an)g(in)o(v)m(ariance)f(in)g(form)f(of)i(the)f
(theory)l(.)21 b(In)c(this)f(resp)q(ect,)-5 2260 y(ho)o(w)o(ev)o(er,)g
(w)o(e)i(ha)o(v)o(e)e(to)i(stress)g(that)g(what)g(is)g(in)o(v)m(arian)o
(t)e(in)i(form)e(cannot)i(b)q(e)g(the)f(Lagrangian)j(but)-5
2320 y(only)e(the)g(set)g(of)g(\014eld)g(equations)g(plus)g(Bianc)o(hi)
f(iden)o(tities.)24 b(Indeed,)18 b(while)f(an)o(y)h(\003)f
FE(2)g Fv(S)s(p)p FH(\(2)p 1770 2294 V Fv(n)q(;)8 b FH(I)-9
b(R)o(\))-5 2380 y(can,)25 b(in)e(principle,)g(b)q(e)g(an)h(in)o(v)m
(ariance)e(in)h(form)f(of)h(eqs.)g(2.17)p
 (#equation.2.16) [[343 196 364 208] [1 1 1 [3 3]] [0 0 1]] pdfm (,)i
(the)e(same)f(is)h(not)h(true)f(for)g(the)-5 2440 y(Lagrangian.)28
b(One)17 b(can)g(easily)g(\014nd)h(that)g(the)f(v)o(ector)g(kinetic)f
(part)i(of)g(this)f(latter)g(transforms)g(as)-5 2501
y(follo)o(ws:)272 2589 y(Im)o FE(F)372 2569 y FB(\000)p
FC(\003)p 425 2550 49 2 v 425 2589 a FE(N)474 2596 y
FC(\003\006)526 2589 y FE(F)567 2569 y FB(\000)p FC(\006)663
2589 y FE(!)41 b FH(Im)827 2573 y Fs(e)812 2589 y FE(F)853
2569 y FB(\000)p FC(\003)926 2573 y Fs(e)915 2589 y FE(G)948
2569 y FB(\000)945 2602 y FC(\006)754 2668 y FH(=)14
b(Im)864 2620 y Fs(\020)889 2668 y FE(F)930 2647 y FB(\000)p
FC(\003)984 2668 y FE(G)1017 2647 y FB(\000)1014 2680
y FC(\003)1057 2668 y FH(+)d(2)p FE(F)1171 2647 y FB(\000)p
FC(\003)1233 2668 y FH(\()p Fv(C)1291 2647 y Ft(T)1318
2668 y Fv(B)s FH(\))1401 2644 y FC(\006)1377 2683 y(\003)1437
2668 y FE(G)1470 2647 y FB(\000)1467 2680 y FC(\006)754
2759 y FH(+)p FE(F)833 2739 y FB(\000)p FC(\003)895 2759
y FH(\()p Fv(C)953 2739 y Ft(T)980 2759 y Fv(A)p FH(\))1036
2774 y FC(\003\006)1088 2759 y FE(F)1129 2739 y FB(\000)p
FC(\006)1194 2759 y FH(+)g FE(G)1276 2739 y FB(\000)1273
2772 y FC(\003)1314 2759 y FH(\()p Fv(D)1374 2739 y Ft(T)1402
2759 y Fv(B)s FH(\))1461 2735 y FC(\003\006)1521 2759
y FE(G)1554 2739 y FB(\000)1551 2772 y FC(\006)1583 2711
y Fs(\021)1760 2759 y FH(\(2.36\))928 2892 y(7)p eop
%%Page: 8 9
8 8 bop -5 15 a FH(whence)17 b(w)o(e)f(conclude)g(that)h(prop)q(er)h
(symmetri)o(es)c(of)j(the)g(Lagrangian)h(are)f(to)h(b)q(e)f(lo)q(ok)o
(ed)f(for)h(only)-5 76 y(among)e(matrices)d(with)j Fv(C)i
FH(=)d Fv(B)i FH(=)e(0.)21 b(If)14 b Fv(C)j FE(6)p FH(=)d(0)h(and)g
Fv(B)i FH(=)d(0,)g(the)h(Lagrangian)h(v)m(aries)f(through)g(the)-5
136 y(addition)i(of)g(a)f(top)q(ological)h(densit)o(y)f(\(see)g(b)q
(elo)o(w)g(eq.)g(6.7)p
 (#equation.6.7) [[316 734 330 746] [1 1 1 [3 3]] [0 0 1]] pdfm (\).)22
b(Elemen)o(ts)14 b(of)i Fv(S)s(p)p FH(\(2)p 1498 109
30 2 v Fv(n)q(;)8 b FH(I)-9 b(R\))16 b(with)g Fv(B)h
FE(6)p FH(=)d(0,)-5 196 y(cannot)j(b)q(e)g(symme)o(tries)c(of)k(the)f
(classical)f(action)i(under)f(an)o(y)g(circumstance.)68
256 y(The)g(scalar)g(part)g(of)g(the)f(Lagrangian,)i(on)f(the)g(other)f
(hand,)h(is)g(in)o(v)m(arian)o(t)f(under)g(all)g(those)h(dif-)-5
316 y(feomorphisms)c(of)h(the)h(scalar)f(manifolds)g(that)h(are)f
Fu(isometries)h FH(of)f(the)h(scalar)f(metric)e Fv(g)1641
323 y Ft(I)s(J)1684 316 y FH(.)20 b(Naming)-5 377 y Fv(\030)18
359 y Ft(?)53 377 y FH(:)h Fv(T)7 b FE(M)184 384 y Ft(scalar)305
377 y FE(!)21 b Fv(T)7 b FE(M)472 384 y Ft(scalar)587
377 y FH(the)16 b(push{forw)o(ard)i(of)e Fv(\030)r FH(,)h(this)f(means)
f(that)735 478 y FE(8)8 b Fv(X)q(;)g(Y)33 b FE(2)22 b
Fv(T)7 b FE(M)1047 485 y Ft(scalar)682 550 y Fv(g)j FH(\()p
Fv(X)q(;)e(Y)k FH(\))22 b(=)g Fv(g)10 b FH(\()p Fv(\030)1013
532 y Ft(?)1034 550 y Fv(X)q(;)e(\030)1120 532 y Ft(?)1141
550 y Fv(Y)j FH(\))561 b(\(2.37\))-5 651 y(and)21 b Fv(\030)j
FH(is)c(an)h(exact)f(global)h(symmetry)d(of)j(the)f(scalar)h(part)g(of)
g(the)f(Lagrangian)j(in)d(eq.)g(2.5)p
 (#equation.2.5) [[487 611 502 623] [1 1 1 [3 3]] [0 0 1]] pdfm (.)34
b(In)-5 711 y(view)16 b(of)i(our)f(previous)g(discussion)g(these)g
(symmetri)o(es)d(of)j(the)g(scalar)g(sector)g(are)g(not)h(guaran)o
(teed)-5 772 y(to)f(admit)e(an)i(extension)e(to)i(symmetrie)o(s)d(of)i
(the)h(complete)d(action.)21 b(Y)l(et)15 b(w)o(e)h(can)h(insist)f(that)
h(they)-5 832 y(extend)k(to)i(symmetri)o(es)c(of)j(the)g(\014eld)f
(equations)h(plus)g(Bianc)o(hi)f(iden)o(tities,)g(namely)f(to)i(dualit)
o(y)-5 892 y(symmetrie)o(s)15 b(in)h(the)h(sense)g(de\014ned)g(ab)q(o)o
(v)o(e.)23 b(This)18 b(requires)d(that)j(the)f(group)h(of)f(isometries)
e(of)i(the)-5 952 y(scalar)d(metric)e FE(I)t FH(\()p
FE(M)391 959 y Ft(scalar)489 952 y FH(\))i(b)q(e)g(suitably)f(em)o(b)q
(edded)f(in)o(to)i(the)f(dualit)o(y)g(group)i Fv(S)s(p)p
FH(\(2)p 1574 926 V Fv(n)q(;)8 b FH(I)-9 b(R)o(\))14
b(and)h(that)-5 1012 y(the)h(kinetic)f(matrix)f FE(N)437
1019 y FC(\003\006)505 1012 y FH(satis\014es)j(the)f(co)o(v)m(ariance)g
(la)o(w:)434 1113 y FE(N)g FH(\()p Fv(\030)r FH(\()p
Fv(\036)p FH(\)\))23 b(=)f(\()p Fv(C)756 1120 y Ft(\030)785
1113 y FH(+)11 b Fv(D)874 1120 y Ft(\030)894 1113 y FE(N)c
FH(\()p Fv(\036)p FH(\)\))h(\()p Fv(A)1092 1120 y Ft(\030)1122
1113 y FH(+)j Fv(B)1208 1120 y Ft(\030)1227 1113 y FE(N)c
FH(\()p Fv(\036)p FH(\)\))1361 1089 y FB(\000)p FC(1)1432
1113 y Fv(:)314 b FH(\(2.38\))-5 1278 y Fw(3)81 b(Symplectic)25
b(em)n(b)r(eddings)h(of)h(homogenous)h(spaces)-5 1388
y FH(A)15 b(general)f(construction)h(of)g(the)g(kinetic)e(coupling)h
(matrix)f FE(N)22 b FH(can)15 b(b)q(e)g(deriv)o(ed)f(in)g(the)h(case)f
(where)-5 1448 y(the)19 b(scalar)f(manifold)g(is)g(tak)o(en)g(to)h(b)q
(e)g(a)g(homogeneous)f(space)h FE(G)s Fv(=)p FE(H)p FH(.)29
b(This)18 b(is)h(what)g(happ)q(ens)g(in)-5 1508 y(all)d(extended)g(sup)
q(ergra)o(vities)g(for)h Fv(N)j FE(\025)14 b FH(3)j(and)g(also)h(in)e
(sp)q(eci\014c)g(instances)h(of)f(N=2)h(theories.)22
b(F)l(or)-5 1569 y(this)16 b(reason)h(w)o(e)f(shortly)g(review)f(the)h
(construction)h(of)f(the)g Fu(kinetic)k(p)n(erio)n(d)c(matrix)g
FE(N)23 b FH(in)16 b(the)g(case)-5 1629 y(of)g(homogeneous)f(spaces.)21
b(Although)16 b(the)f(basic)g(construction)h(w)o(as)f(in)o(tro)q(duced)
g(in)g(the)g(literature)-5 1689 y(b)o(y)g(Gaillard)g(and)h(Zumino)e(in)
g(1981)j([46)p
 (#cite.gaizum) [[241 362 253 374] [1 1 1 [3 3]] [0 0 1]] pdfm (])e
(and)h(w)o(as)g(review)o(ed)d(b)o(y)i(some)f(of)i(us)f(in)g([31)p
 (#cite.CaDFb) [[442 362 454 374] [1 1 1 [3 3]] [0 0 1]] pdfm (],)g(a)g
(deriv)m(ation)-5 1749 y(of)21 b(the)f(basic)g(form)o(ulae)e(that)j
(matc)o(hes)e(completely)e(with)j(the)g(mo)q(dern)f(notations)j(of)e
(N=2)g(and)-5 1809 y(N=4)g(theories,)g(suc)o(h)g(as)h(they)e(emerge)g
(in)g(string)h(compacti\014cations)f(and)i(in)f(the)g(discussion)g(of)
-5 1870 y(S{dualit)o(y)l(,)j(is)f(not)h(a)o(v)m(ailable,)g(to)g(our)g
(kno)o(wledge,)g(in)f(the)g(existing)f(literature.)39
b(T)l(o)23 b(mak)o(e)d(the)-5 1930 y(presen)o(t)15 b(pap)q(er)h(self)f
(con)o(tained)g(w)o(e)g(consider)g(therefore)g(essen)o(tial)f(to)i
(review)e(suc)o(h)h(a)h(construction)-5 1990 y(in)g(mo)q(dern)g(gear.)
68 2050 y(The)h(relev)m(an)o(t)e(homomorphism)e Fv(\023)714
2057 y Ft(\016)750 2050 y FH(\(see)j(eq.)f(2.33)p
 (#equation.2.33) [[294 275 315 287] [1 1 1 [3 3]] [0 0 1]] pdfm (\))i
(b)q(ecomes:)627 2175 y Fv(\023)644 2182 y Ft(\016)677
2175 y FH(:)k(Di\013)800 2115 y Fs(\022)841 2142 y FE(G)p
836 2164 43 2 v 836 2209 a(H)883 2115 y Fs(\023)936 2175
y FE(\000)-9 b(!)22 b Fv(S)s(p)p FH(\(2)p 1138 2149 30
2 v Fv(n)q(;)8 b FH(I)-9 b(R\))531 b(\(3.1\))-5 2300
y(In)24 b(particular,)g(fo)q(cusing)g(on)g(the)g(isometry)d(group)k(of)
f(the)f(canonical)g(metric)e(de\014ned)j(on)1820 2280
y FB(G)p 1817 2288 31 2 v 1817 2317 a(H)1852 2282 y FC(2)p
 (#Hfootnote.2) [[516 215 521 227] [1 1 1 [3 3]] [0 0 1]] pdfm 
1871 2300 a FH(:)-5 2371 y FE(I)34 2323 y Fs(\020)68
2351 y FB(G)p 64 2359 V 64 2388 a(H)99 2323 y Fs(\021)146
2371 y FH(=)e FE(G)d FH(w)o(e)d(m)o(ust)f(consider)h(the)g(em)o(b)q
(edding:)711 2478 y Fv(\023)728 2485 y Ft(\016)761 2478
y FH(:)22 b FE(G)i(\000)-8 b(!)22 b Fv(S)s(p)p FH(\(2)p
1054 2452 30 2 v Fv(n)q(;)8 b FH(I)-9 b(R)o(\))616 b(\(3.2\))-5
2579 y(That)19 b(in)f(eq.)f(3.1)p
 (#equation.3.1) [[134 148 149 160] [1 1 1 [3 3]] [0 0 1]] pdfm 
18 w(is)h(a)h(homomorphism)c(of)k(\014nite)e(dimensional)f(Lie)i
(groups)i(and)e(as)h(suc)o(h)f(it)g(con-)-5 2639 y(stitutes)i(a)h
(problem)e(that)i(can)g(b)q(e)f(solv)o(ed)g(in)g(explicit)e(form.)33
b(What)21 b(w)o(e)f(just)h(need)f(to)h(kno)o(w)f(is)p
-5 2671 756 2 v 51 2703 a Fq(2)70 2718 y Fx(Actually)m(,)13
b(in)g(order)i(to)f(b)q(e)g(true,)h(the)f(equation)g
Fl(I)s Fx(\()902 2702 y Fy(G)p 898 2709 29 2 v 898 2732
a(H)932 2718 y Fx(\))e(=)g Fl(G)k Fx(requires)f(that)f(that)g(the)h
(normaliser)d(of)h Fl(H)i Fx(in)e Fl(G)j Fx(b)q(e)-5
2768 y(the)f(iden)o(tit)o(y)e(group,)g(a)h(condition)f(that)h(is)g(v)o
(eri\014ed)g(in)g(all)e(the)j(relev)n(an)o(t)f(examples)928
2892 y FH(8)p eop
%%Page: 9 10
9 9 bop -5 15 a FH(the)15 b(dimension)e(of)j(the)e(symplectic)e(group,)
k(namely)d(the)h(n)o(um)o(b)q(er)p 1261 -11 30 2 v 14
w Fv(n)h FH(of)g(gauge)h(\014elds)e(app)q(earing)i(in)-5
76 y(the)f(theory)l(.)21 b(Without)15 b(sup)q(ersymmetry)e(the)i
(dimension)e Fv(m)i FH(of)h(the)f(scalar)g(manifold)f(\(namely)f(the)-5
136 y(p)q(ossible)j(c)o(hoices)f(of)406 116 y FB(G)p
402 124 31 2 v 402 153 a(H)437 136 y FH(\))h(and)h(the)f(n)o(um)o(b)q
(er)e(of)i(v)o(ectors)p 1048 109 30 2 v 15 w Fv(n)g FH(are)g(unrelated)
f(so)i(that)f(the)g(p)q(ossibilities)-5 196 y(co)o(v)o(ered)d(b)o(y)i
(eq.)e(3.2)p
 (#equation.3.2) [[146 720 161 732] [1 1 1 [3 3]] [0 0 1]] pdfm 
15 w(are)i(in\014nitely)e(man)o(y)l(.)19 b(In)14 b(sup)q(ersymmetric)e
(theories,)i(instead,)g(the)h(t)o(w)o(o)f(n)o(um-)-5
256 y(b)q(ers)f Fv(m)g FH(and)p 243 230 V 13 w Fv(n)g
FH(are)g(related,)f(so)h(that)g(there)f(are)h(\014nitely)f(man)o(y)f
(cases)i(to)g(b)q(e)g(studied)f(corresp)q(onding)-5 316
y(to)17 b(the)f(p)q(ossible)h(em)o(b)q(eddings)d(of)j(giv)o(en)f
(groups)h FE(G)i FH(in)o(to)d(a)h(symplectic)c(group)k
Fv(S)s(p)p FH(\(2)p 1596 290 V Fv(n)q(;)8 b FH(I)-9 b(R)o(\))17
b(of)f(\014xed)-5 377 y(dimension)p 231 350 V 20 w Fv(n)p
FH(.)37 b(Actually)20 b(taking)i(in)o(to)f(accoun)o(t)g(further)g
(conditions)h(on)g(the)f(holonom)o(y)g(of)g(the)-5 437
y(scalar)f(manifold)e(that)i(are)g(also)g(imp)q(osed)e(b)o(y)h(sup)q
(ersymmetry)l(,)e(the)i(solution)h(for)g(the)f(symplec-)-5
497 y(tic)e(em)o(b)q(edding)f(problem)h(is)g(unique)g(for)h(all)f
(extended)g(sup)q(ergra)o(vities)h(with)f Fv(N)22 b FE(\025)16
b FH(3)i(as)h(w)o(e)e(ha)o(v)o(e)-5 557 y(already)f(remark)o(ed)e
(\(see)i(for)h(instance)f([31)p
 (#cite.CaDFb) [[254 633 265 645] [1 1 1 [3 3]] [0 0 1]] pdfm (]\).)68
617 y(Apart)21 b(from)e(the)h(details)f(of)i(the)f(sp)q(eci\014c)f
(case)h(considered)g(once)g(a)h(symplectic)c(em)o(b)q(edding)-5
678 y(is)23 b(giv)o(en)f(there)h(is)f(a)i(general)e(form)o(ula)g(one)h
(can)g(write)g(do)o(wn)g(for)h(the)e Fu(p)n(erio)n(d)h(matrix)f
FE(N)31 b FH(that)-5 738 y(guaran)o(tees)21 b(symmetry)c(\()p
FE(N)541 720 y Ft(T)589 738 y FH(=)k FE(N)7 b FH(\))20
b(and)h(the)f(required)f(transformation)h(prop)q(ert)o(y)g(2.38)p
 (#equation.2.38) [[469 590 490 602] [1 1 1 [3 3]] [0 0 1]] pdfm (.)34
b(This)-5 798 y(is)19 b(the)g(result)f(w)o(e)g(w)o(an)o(t)h(to)g
(review.)28 b(It)19 b(will)f(b)q(e)h(useful)f(in)h(the)f(sequel)g(for)h
(comparison)g(with)f(the)-5 858 y(form)o(ulae)d(of)i(sp)q(ecial)f
(geometry)f(in)h(the)h(case)f(the)g(considered)g(sp)q(ecial)g(manifold)
g(is)g(homogeneous)-5 918 y(\(see)g(app)q(endix)g(C,)g(in)g
(particular\).)68 979 y(The)g(real)g(symplectic)d(group)k
Fv(S)s(p)p FH(\(2)p 741 952 V Fv(n)q(;)8 b FH(I)-9 b(R)o(\))16
b(is)g(de\014ned)g(as)h(the)f(set)g(of)g(all)f Fu(r)n(e)n(al)h
FH(2)p 1547 952 V Fv(n)11 b FE(\002)f FH(2)p 1660 952
V Fv(n)17 b FH(matrices)-5 1063 y(\003)22 b(=)111 1002
y Fs(\022)151 1033 y Fv(A)51 b(B)150 1093 y(C)h(D)288
1002 y Fs(\023)334 1063 y FH(satisfying)17 b(equation)32
b(2.25)p
 (#equation.2.25) [[256 512 277 524] [1 1 1 [3 3]] [0 0 1]] pdfm (,)17
b(namely)813 1196 y(\003)847 1175 y Ft(T)p 891 1196 2
33 v 878 1196 a FH(C)8 b(\003)22 b(=)p 1045 1196 V 17
w(C)718 b(\(3.3\))-5 1323 y(where)p 147 1323 V 14 w(C)26
b FE(\021)260 1263 y Fs(\022)320 1293 y FD(0)70 b FH(1)-17
b(1)299 1354 y FE(\000)p FH(1)g(1)51 b FD(0)458 1263
y Fs(\023)508 1323 y FH(If)18 b(w)o(e)g(relax)g(the)h(condition)f(that)
h(the)g(matrix)d(should)k(b)q(e)e(real)h(but)f(w)o(e)-5
1407 y(still)f(imp)q(ose)h(eq.)f(3.3)p
 (#equation.3.3) [[153 429 168 441] [1 1 1 [3 3]] [0 0 1]] pdfm 
19 w(w)o(e)g(obtain)i(the)f(de\014nition)g(of)h(the)f(complex)e
(symplectic)f(group)k Fv(S)s(p)p FH(\(2)p 1770 1381 30
2 v Fv(n)q(;)p 1830 1407 2 33 v 3 w FH(C)q(\).)-5 1468
y(It)d(is)g(a)h(w)o(ell)e(kno)o(wn)h(fact)g(that)h(the)f(follo)o(wing)g
(isomorphism)e(is)i(true:)458 1571 y Fv(S)s(p)p FH(\(2)p
558 1545 30 2 v Fv(n)q(;)8 b FH(I)-9 b(R)o(\))14 b FE(\030)f
Fv(U)5 b(sp)p FH(\()p 843 1545 V Fv(n)q(;)p 895 1545
V 8 w(n)p FH(\))14 b FE(\021)g Fv(S)s(p)p FH(\(2)p 1110
1545 V Fv(n)q(;)p 1170 1571 2 33 v 3 w FH(C\))d FE(\\)g
Fv(U)5 b FH(\()p 1323 1545 30 2 v Fv(n)q(;)p 1375 1545
V 8 w(n)p FH(\))362 b(\(3.4\))-5 1675 y(By)14 b(de\014nition)g(an)g
(elemen)o(t)d FE(S)26 b(2)d Fv(U)5 b(sp)p FH(\()p 744
1648 V Fv(n)q(;)p 796 1648 V 8 w(n)p FH(\))14 b(is)g(a)g(complex)e
(matrix)h(that)i(satis\014es)f(sim)o(ultaneously)-5 1735
y(eq.)i(3.3)p
 (#equation.3.3) [[90 351 104 363] [1 1 1 [3 3]] [0 0 1]] pdfm 
16 w(and)h(a)g(pseudo{unitarit)o(y)f(condition,)f(that)i(is:)518
1839 y FE(S)552 1818 y Ft(T)p 596 1839 2 33 v 583 1839
a FH(C)8 b FE(S)26 b FH(=)p 751 1839 V 18 w(C)146 b(;)154
b FE(S)1121 1818 y FB(y)1147 1839 y FH(I)-9 b(H)8 b FE(S)26
b FH(=)c(I)-9 b(H)422 b(\(3.5\))-5 1966 y(where)16 b(I)-9
b(H)22 b FE(\021)265 1905 y Fs(\022)303 1936 y FH(1)-17
b(1)71 b FD(0)305 1996 y(0)51 b FE(\000)p FH(1)-17 b(1)463
1905 y Fs(\023)493 1966 y FH(.)21 b(The)c(general)f(blo)q(c)o(k)f(form)
h(of)g(the)g(matrix)f FE(S)20 b FH(is:)766 2124 y FE(S)26
b FH(=)882 2063 y Fs(\022)922 2094 y Fv(T)58 b(V)1048
2075 y Ft(?)921 2154 y Fv(V)k(T)1047 2136 y Ft(?)1076
2063 y Fs(\023)1785 2124 y FH(\(3.6\))-5 2248 y(and)17
b(eq.s)f(3.5)p
 (#equation.3.5) [[117 227 132 239] [1 1 1 [3 3]] [0 0 1]] pdfm 
16 w(are)g(equiv)m(alen)o(t)f(to:)421 2352 y Fv(T)457
2331 y FB(y)482 2352 y Fv(T)26 b FE(\000)19 b Fv(V)635
2331 y FB(y)661 2352 y Fv(V)33 b FH(=)22 b(1)-17 b(1)98
b(;)106 b Fv(T)1067 2331 y FB(y)1092 2352 y Fv(V)1131
2331 y Ft(?)1171 2352 y FE(\000)19 b Fv(V)1268 2331 y
FB(y)1294 2352 y Fv(T)1330 2331 y Ft(?)1371 2352 y FH(=)j
FD(0)326 b FH(\(3.7\))-5 2455 y(The)17 b(isomorphism)d(of)i(eq.)f(3.4)p
 (#equation.3.4) [[195 178 210 190] [1 1 1 [3 3]] [0 0 1]] pdfm 
17 w(is)h(explicitly)d(realized)i(b)o(y)h(the)g(so)h(called)e(Ca)o
(yley)g(matrix:)713 2580 y FE(C)25 b(\021)850 2546 y
FH(1)p 830 2569 66 2 v 830 2578 a FE(p)p 871 2578 25
2 v 871 2619 a FH(2)917 2520 y Fs(\022)956 2550 y FH(1)-17
b(1)69 b(i1)-17 b(1)956 2610 y(1)g(1)50 b FE(\000)p FH(i1)-17
b(1)1129 2520 y Fs(\023)1785 2580 y FH(\(3.8\))-5 2707
y(via)16 b(the)g(relation:)804 2768 y FE(S)26 b FH(=)c
FE(C)12 b FH(\003)c FE(C)1029 2747 y FB(\000)p FC(1)1785
2768 y FH(\(3.9\))928 2892 y(9)p eop
%%Page: 10 11
10 10 bop -5 15 a FH(whic)o(h)16 b(yields:)125 127 y
Fv(T)29 b FH(=)248 93 y(1)p 248 115 25 2 v 248 161 a(2)294
127 y(\()p Fv(A)11 b FH(+)g Fv(D)q FH(\))g FE(\000)542
93 y FH(i)p 536 115 V 536 161 a(2)582 127 y(\()p Fv(B)j
FE(\000)d Fv(C)t FH(\))105 b(;)g Fv(V)34 b FH(=)1111
93 y(1)p 1111 115 V 1111 161 a(2)1157 127 y(\()p Fv(A)10
b FE(\000)h Fv(D)q FH(\))h FE(\000)1405 93 y FH(i)p 1400
115 V 1400 161 a(2)1446 127 y(\()p Fv(B)h FH(+)e Fv(C)t
FH(\))138 b(\(3.10\))-5 234 y(When)18 b(w)o(e)g(set)g
Fv(V)28 b FH(=)16 b(0)i(w)o(e)g(obtain)g(the)g(subgroup)h
Fv(U)5 b FH(\()p 1026 207 30 2 v Fv(n)q FH(\))16 b FE(\032)h
Fv(U)5 b(sp)p FH(\()p 1251 207 V Fv(n)q(;)p 1303 207
V 8 w(n)p FH(\),)18 b(that)g(in)g(the)f(real)h(basis)g(is)-5
318 y(giv)o(en)h(b)o(y)g(the)g(subset)h(of)g(symplectic)c(matrices)i
(of)i(the)f(form)1203 257 y Fs(\022)1262 288 y Fv(A)69
b(B)1241 348 y FE(\000)p Fv(B)53 b(A)1416 257 y Fs(\023)1447
318 y FH(.)31 b(The)20 b(basic)f(idea,)h(to)-5 399 y(obtain)15
b(the)g(general)f(form)o(ula)f(for)i(the)f(p)q(erio)q(d)h(matrix,)e(is)
h(that)h(the)f(symplectic)e(em)o(b)q(edding)g(of)j(the)-5
459 y(isometry)f(group)j FE(G)h FH(will)c(b)q(e)i(suc)o(h)f(that)h(the)
g(isotrop)o(y)f(subgroup)i FE(H)e(\032)e(G)18 b FH(gets)e(em)o(b)q
(edded)e(in)o(to)h(the)-5 520 y(maximal)e(compact)j(subgroup)h
Fv(U)5 b FH(\()p 658 493 V Fv(n)q FH(\),)15 b(namely:)358
611 y FE(G)424 582 y Ft(\023)436 588 y Fm(\016)399 611
y FE(\000)-9 b(!)8 b Fv(U)d(sp)p FH(\()p 591 584 V Fv(n)q(;)p
643 584 V 8 w(n)p FH(\))98 b(;)105 b FE(G)17 b(\033)c(H)1083
582 y Ft(\023)1095 588 y Fm(\016)1058 611 y FE(\000)-8
b(!)8 b Fv(U)d FH(\()p 1204 584 V Fv(n)p FH(\))14 b FE(\032)f
Fv(U)5 b(sp)p FH(\()p 1422 584 V Fv(n)q(;)p 1474 584
V 8 w(n)p FH(\))238 b(\(3.11\))-5 702 y(If)17 b(this)h(condition)f(is)h
(realized)e(let)h Fv(L)p FH(\()p Fv(\036)p FH(\))g(b)q(e)h(a)g
(parametrization)e(of)i(the)f(coset)h FE(G)s Fv(=)p FE(H)g
FH(b)o(y)f(means)g(of)-5 762 y(coset)f(represen)o(tativ)o(es.)j
(Relying)c(on)h(the)g(symplectic)c(em)o(b)q(edding)i(of)i(eq.)f(3.11)p
 (#equation.3.11) [[411 584 432 596] [1 1 1 [3 3]] [0 0 1]] pdfm 
17 w(w)o(e)g(obtain)h(a)g(map:)411 874 y Fv(L)p FH(\()p
Fv(\036)p FH(\))22 b FE(\000)-9 b(!)14 b(O)q FH(\()p
Fv(\036)p FH(\))22 b(=)817 814 y Fs(\022)856 844 y Fv(U)889
851 y FC(0)909 844 y FH(\()p Fv(\036)p FH(\))48 b Fv(U)1062
826 y Ft(?)1057 857 y FC(1)1082 844 y FH(\()p Fv(\036)p
FH(\))856 904 y Fv(U)889 911 y FC(1)909 904 y FH(\()p
Fv(\036)p FH(\))g Fv(U)1062 886 y Ft(?)1057 917 y FC(0)1082
904 y FH(\()p Fv(\036)p FH(\))1158 814 y Fs(\023)1210
874 y FE(2)23 b Fv(U)5 b(sp)p FH(\()p 1370 848 V Fv(n)q(;)p
1422 848 V 8 w(n)o FH(\))291 b(\(3.12\))-5 989 y(that)12
b(asso)q(ciates)h(to)f Fv(L)p FH(\()p Fv(\036)p FH(\))g(a)g(coset)f
(represen)o(tativ)o(e)f(of)i Fv(U)5 b(sp)p FH(\()p 1100
963 V Fv(n)q(;)p 1152 963 V 8 w(n)p FH(\))p Fv(=U)g FH(\()p
1281 963 V Fv(n)q FH(\).)19 b(By)11 b(construction)h(if)f
Fv(\036)1779 971 y FB(0)1804 989 y FE(6)p FH(=)j Fv(\036)-5
1050 y Fu(no)j FH(unitary)p 236 1023 V 16 w Fv(n)11 b
FE(\002)p 326 1023 V 11 w Fv(n)16 b FH(matrix)f Fv(W)23
b Fu(c)n(an)18 b(exist)f FH(suc)o(h)f(that:)659 1162
y FE(O)q FH(\()p Fv(\036)748 1141 y FB(0)760 1162 y FH(\))e(=)g
FE(O)q FH(\()p Fv(\036)p FH(\))969 1101 y Fs(\022)1008
1132 y Fv(W)78 b FD(0)1020 1192 y(0)61 b Fv(W)1162 1174
y Ft(?)1190 1101 y Fs(\023)1760 1162 y FH(\(3.13\))-5
1277 y(On)23 b(the)f(other)g(hand)h(let)f Fv(\030)27
b FE(2)d(G)h FH(b)q(e)e(an)g(elemen)o(t)c(of)k(the)f(isometry)e(group)k
(of)e FE(G)s Fv(=)p FE(H)q FH(.)39 b(Via)22 b(the)-5
1337 y(symplectic)13 b(em)o(b)q(edding)i(of)h(eq.)g(3.11)p
 (#equation.3.11) [[220 446 240 458] [1 1 1 [3 3]] [0 0 1]] pdfm 
17 w(w)o(e)f(obtain)i(a)g Fv(U)5 b(sp)p FH(\()p 1086
1311 V Fv(n)q(;)p 1138 1311 V 8 w(n)p FH(\))16 b(matrix)754
1452 y FE(S)784 1459 y Ft(\030)825 1452 y FH(=)885 1392
y Fs(\022)924 1422 y Fv(T)953 1429 y Ft(\030)1020 1422
y Fv(V)1060 1404 y Ft(?)1048 1435 y(\030)924 1482 y Fv(V)952
1489 y Ft(\030)1022 1482 y Fv(T)1058 1464 y Ft(?)1051
1495 y(\030)1088 1392 y Fs(\023)1760 1452 y FH(\(3.14\))-5
1565 y(suc)o(h)g(that)481 1636 y FE(S)511 1643 y Ft(\030)538
1636 y FE(O)q FH(\()p Fv(\036)p FH(\))22 b(=)g FE(O)q
FH(\()p Fv(\030)r FH(\()p Fv(\036)p FH(\)\))914 1576
y Fs(\022)953 1606 y Fv(W)7 b FH(\()p Fv(\030)r(;)h(\036)p
FH(\))128 b FD(0)1022 1666 y(0)117 b Fv(W)1220 1648 y
Ft(?)1240 1666 y FH(\()p Fv(\030)r(;)8 b(\036)p FH(\))1360
1576 y Fs(\023)1760 1636 y FH(\(3.15\))-5 1739 y(where)17
b Fv(\030)r FH(\()p Fv(\036)p FH(\))g(denotes)g(the)g(image)f(of)h(the)
g(p)q(oin)o(t)g Fv(\036)d FE(2)i(G)s Fv(=)p FE(H)h FH(through)h
Fv(\030)i FH(and)d Fv(W)7 b FH(\()p Fv(\030)r(;)h(\036)p
FH(\))17 b(is)g(a)g(suitable)-5 1799 y Fv(U)5 b FH(\()p
52 1773 V Fv(n)q FH(\))15 b(comp)q(ensator)h(dep)q(ending)g(b)q(oth)h
(on)f Fv(\030)j FH(and)d Fv(\036)p FH(.)21 b(Com)o(bining)14
b(eq.s)h(3.15)p
 (#equation.3.15) [[398 335 419 347] [1 1 1 [3 3]] [0 0 1]] pdfm (,)i
(3.12)p
 (#equation.3.12) [[426 335 447 347] [1 1 1 [3 3]] [0 0 1]] pdfm (,)f
(with)f(eq.s)g(3.10)p
 (#equation.3.10) [[504 335 524 347] [1 1 1 [3 3]] [0 0 1]] pdfm 
-5 1860 a(w)o(e)h(immedi)o(ately)d(obtain:)170 1951 y
Fv(U)208 1927 y FB(y)203 1962 y FC(0)234 1951 y FH(\()p
Fv(\030)r FH(\()p Fv(\036)p FH(\)\))f(+)f Fv(U)461 1927
y FB(y)456 1962 y FC(1)487 1951 y FH(\()p Fv(\030)r FH(\()p
Fv(\036)p FH(\)\))42 b(=)g Fv(W)798 1903 y Fs(h)817 1951
y Fv(U)855 1927 y FB(y)850 1962 y FC(0)882 1951 y FH(\()p
Fv(\036)p FH(\))957 1903 y Fs(\020)982 1951 y Fv(A)1019
1930 y Ft(T)1057 1951 y FH(+)11 b(i)p Fv(B)1160 1930
y Ft(T)1186 1903 y Fs(\021)1222 1951 y FH(+)g Fv(U)1309
1927 y FB(y)1304 1962 y FC(1)1336 1951 y FH(\()p Fv(\036)p
FH(\))1411 1903 y Fs(\020)1435 1951 y Fv(A)1472 1930
y Ft(T)1511 1951 y FE(\000)f FH(i)p Fv(B)1614 1930 y
Ft(T)1641 1903 y Fs(\021i)169 2042 y Fv(U)207 2018 y
FB(y)202 2053 y FC(0)233 2042 y FH(\()p Fv(\030)r FH(\()p
Fv(\036)p FH(\)\))i FE(\000)f Fv(U)461 2018 y FB(y)456
2053 y FC(1)487 2042 y FH(\()p Fv(\030)r FH(\()p Fv(\036)p
FH(\)\))42 b(=)g Fv(W)806 1994 y Fs(h)826 2042 y Fv(U)864
2018 y FB(y)859 2053 y FC(0)890 2042 y FH(\()p Fv(\036)p
FH(\))965 1994 y Fs(\020)990 2042 y Fv(D)1031 2022 y
Ft(T)1070 2042 y FE(\000)11 b FH(i)p Fv(C)1173 2022 y
Ft(T)1200 1994 y Fs(\021)1236 2042 y FE(\000)f Fv(U)1323
2018 y FB(y)1318 2053 y FC(1)1350 2042 y FH(\()p Fv(\036)p
FH(\))1425 1994 y Fs(\020)1450 2042 y Fv(D)1491 2022
y Ft(T)1530 2042 y FH(+)h(i)p Fv(C)1632 2022 y Ft(T)1659
1994 y Fs(\021)o(i)1760 2042 y FH(\(3.16\))-5 2133 y(Setting:)616
2205 y FE(N)29 b(\021)22 b FH(i)769 2157 y Fs(h)788 2205
y Fv(U)826 2182 y FB(y)821 2216 y FC(0)856 2205 y FH(+)11
b Fv(U)943 2182 y FB(y)938 2216 y FC(1)961 2157 y Fs(i)980
2169 y FB(\000)p FC(1)1044 2157 y Fs(h)1064 2205 y Fv(U)1102
2182 y FB(y)1097 2216 y FC(0)1131 2205 y FE(\000)g Fv(U)1219
2182 y FB(y)1214 2216 y FC(1)1237 2157 y Fs(i)1760 2205
y FH(\(3.17\))-5 2284 y(and)k(using)g(the)g(result)f(of)h(eq.)e(3.16)p
 (#equation.3.16) [[206 219 227 231] [1 1 1 [3 3]] [0 0 1]] pdfm 
15 w(one)i(c)o(hec)o(ks)e(that)i(the)f(transformation)h(rule)f(2.38)p
 (#equation.2.38) [[435 219 455 231] [1 1 1 [3 3]] [0 0 1]] pdfm 
15 w(is)g(v)o(eri\014ed.)19 b(It)-5 2344 y(is)e(also)g(an)h(imme)o
(diate)c(consequence)i(of)h(the)g(analogue)h(of)f(eq.s)f(3.7)p
 (#equation.3.7) [[366 204 381 216] [1 1 1 [3 3]] [0 0 1]] pdfm 
17 w(satis\014ed)h(b)o(y)g Fv(U)1594 2351 y FC(0)1630
2344 y FH(and)h Fv(U)1759 2351 y FC(1)1796 2344 y FH(that)-5
2405 y(the)e(matrix)f(in)h(eq.)f(3.17)p
 (#equation.3.17) [[161 190 182 202] [1 1 1 [3 3]] [0 0 1]] pdfm 
17 w(is)h(symmetri)o(c)837 2496 y FE(N)885 2475 y Ft(T)935
2496 y FH(=)22 b FE(N)724 b FH(\(3.18\))-5 2587 y(Eq.)17
b(3.17)p
 (#equation.3.17) [[92 146 113 158] [1 1 1 [3 3]] [0 0 1]] pdfm 
18 w(is)g(the)g(master)f(form)o(ula)g(deriv)o(ed)g(in)h(1981)h(b)o(y)f
(Gaillard)g(and)h(Zumino)e([46)p
 (#cite.gaizum) [[446 146 458 158] [1 1 1 [3 3]] [0 0 1]] pdfm (].)24
b(It)17 b(explains)-5 2647 y(the)e(structure)h(of)f(the)h(gauge)g
(\014eld)f(kinetic)f(terms)f(in)j(all)f Fv(N)k FE(\025)13
b FH(3)j(extended)f(sup)q(ergra)o(vit)o(y)f(theories)-5
2707 y(and)f(also)g(in)f(those)h Fv(N)19 b FH(=)14 b(2)e(theories)g
(where)g(the)g(Sp)q(ecial)g(K\177)-24 b(ahler)12 b(manifold)f
FE(S)t(M)h FH(is)g(a)h(homogeneous)-5 2768 y(manifold)i
FE(G)s Fv(=)p FE(H)p FH(.)916 2892 y(10)p eop
%%Page: 11 12
11 11 bop -5 15 a Fk(3.1)66 b(Symplectic)27 b(em)n(b)r(edding)f(of)e
(the)h Fj(S)t(T)g Fi([)p Fh(m;)10 b(n)p Fi(])26 b Fk(homogeneous)d
(mani-)148 90 y(folds)-5 183 y FH(Because)d(of)i(their)e(relev)m(ance)f
(in)i(sup)q(erstring)g(compacti\014cations)f(let)g(us)h(illustrate)f
(the)g(general)-5 243 y(pro)q(cedure)d(with)f(the)g(follo)o(wing)g
(class)g(of)g(homogeneous)h(manifolds:)483 367 y FE(S)t(T)k
FH([)o Fv(m;)8 b(n)p FH(])22 b FE(\021)774 333 y Fv(S)s(U)5
b FH(\(1)p Fv(;)j FH(1\))p 774 355 180 2 v 813 401 a
Fv(U)d FH(\(1\))978 367 y FE(\012)1115 333 y Fv(S)s(O)q
FH(\()p Fv(m;)j(n)p FH(\))p 1041 355 352 2 v 1041 401
a Fv(S)s(O)q FH(\()p Fv(m)p FH(\))j FE(\012)g Fv(S)s(O)q
FH(\()p Fv(n)p FH(\))1760 367 y(\(3.19\))-5 494 y(The)25
b(isometry)e(group)j(of)f(the)g FE(S)t(T)c FH([)o Fv(m;)8
b(n)p FH(])24 b(manifolds)g(de\014ned)h(in)f(eq.)g(3.19)p
 (#equation.3.19) [[408 648 429 660] [1 1 1 [3 3]] [0 0 1]] pdfm 
26 w(con)o(tains)g(a)i(factor)-5 554 y(\()p Fv(S)s(U)5
b FH(\(1)p Fv(;)j FH(1\)\))16 b(whose)f(transformations)g(act)g(as)g
(non{p)q(erturbativ)o(e)g Fv(S)s FH({dualities)f(and)h(another)h
(factor)-5 614 y(\()p Fv(S)s(O)q FH(\()p Fv(m;)8 b(n)p
FH(\)\))14 b(whose)h(transformations)g(act)f(as)h Fv(T)7
b FH({dualities,)12 b(holding)j(true)f(at)g(eac)o(h)g(order)g(in)g
(string)-5 674 y(p)q(erturbation)h(theory)l(.)20 b(The)14
b(\014eld)g Fv(S)j FH(is)c(obtained)i(b)o(y)e(com)o(bining)f(together)i
(the)g Fu(dilaton)h Fv(D)h FH(and)e(the)-5 734 y Fu(axion)j
FE(A)p FH(:)763 834 y Fv(S)45 b FH(=)d FE(A)11 b(\000)g
FH(iexp)o([)p Fv(D)q FH(])705 906 y Fv(@)734 886 y Ft(\026)756
906 y FE(A)42 b(\021)f Fv(")941 886 y Ft(\026\027)r(\032\033)1031
906 y Fv(@)1057 913 y Ft(\027)1087 906 y Fv(B)1124 913
y Ft(\032\033)1760 906 y FH(\(3.20\))-5 1005 y(while)17
b Fv(t)142 987 y Ft(i)174 1005 y FH(is)g(the)h(name)e(usually)i(giv)o
(en)f(to)h(the)f(mo)q(duli{\014elds)g(of)h(the)f(compacti\014ed)f
(target)i(space.)-5 1066 y(No)o(w)d(in)g(string)g(and)g(sup)q(ergra)o
(vit)o(y)f(applications)h Fv(S)j FH(will)c(b)q(e)h(iden)o(ti\014ed)e
(with)i(the)g(complex)d(co)q(ordi-)-5 1126 y(nate)g(on)h(the)e
(manifold)445 1103 y Ft(S)r(U)t FC(\(1)p Ft(;)p FC(1\))p
445 1114 124 2 v 470 1143 a Ft(U)t FC(\(1\))573 1126
y FH(,)h(while)f Fv(t)740 1108 y Ft(i)766 1126 y FH(will)g(b)q(e)h(the)
f(co)q(ordinates)i(of)f(the)g(coset)f(space)1677 1103
y Ft(S)r(O)q FC(\()p Ft(m;n)p FC(\))p 1629 1114 238 2
v 1629 1143 a Ft(S)r(O)q FC(\()p Ft(m)p FC(\))p FB(\012)p
Ft(S)r(O)q FC(\()p Ft(n)p FC(\))1871 1126 y FH(.)-5 1193
y(The)k(case)g FE(S)t(T)e FH([6)p Fv(;)8 b(n)p FH(])14
b(is)h(the)g(scalar)g(manifold)f(in)h Fv(N)k FH(=)14
b(4)h(sup)q(ergra)o(vit)o(y)l(,)f(while)g(the)h(case)g
FE(S)t(T)e FH([2)p Fv(;)8 b(n)p FH(])14 b(is)-5 1253
y(a)j(v)o(ery)f(in)o(teresting)f(instance)h(of)h(sp)q(ecial)f(K\177)-24
b(ahler)17 b(manifold)e(app)q(earing)i(in)g(sup)q(erstring)g(compact-)
-5 1313 y(i\014cations.)25 b(Although)17 b(as)h(di\013eren)o(tiable)e
(and)i(metric)d(manifolds)h(the)i(spaces)f FE(S)t(T)k
FH([)p Fv(m;)8 b(n)p FH(])16 b(are)i(just)-5 1373 y(direct)g(pro)q
(ducts)i(of)f(t)o(w)o(o)g(factors)g(\(corresp)q(onding)h(to)f(the)g(ab)
q(o)o(v)o(e)f(men)o(tioned)f(di\013eren)o(t)h(ph)o(ysical)-5
1434 y(in)o(terpretation)e(of)h(the)f(co)q(ordinates)h
Fv(S)j FH(and)d Fv(t)868 1415 y Ft(i)881 1434 y FH(\),)f(from)g(the)g
(p)q(oin)o(t)h(of)f(view)g(of)h(the)f(symplectic)d(em-)-5
1494 y(b)q(edding)19 b(and)h(dualit)o(y)e(rotations)h(they)g(ha)o(v)o
(e)f(to)h(b)q(e)g(regarded)g(as)g(a)g(single)g(en)o(tit)o(y)l(.)27
b(This)19 b(is)f(ev)o(en)-5 1554 y(more)h(eviden)o(t)g(in)i(the)f(case)
g Fv(m)h FH(=)g(2)p Fv(;)8 b(n)21 b FH(=)g(arbitrary,)g(where)g(the)f
(follo)o(wing)g(theorem)f(has)i(b)q(een)-5 1614 y(pro)o(v)o(en)16
b(b)o(y)g(F)l(errara)g(and)h(V)l(an)f(Pro)q(ey)o(en)g([48)p
 (#cite.ferratoine) [[262 380 273 392] [1 1 1 [3 3]] [0 0 1]] pdfm (]:)
21 b FE(S)t(T)g FH([2)p Fv(;)8 b(n)p FH(])16 b(are)g(the)g(only)g(sp)q
(ecial)g(K\177)-24 b(ahler)16 b(manifolds)-5 1674 y(with)k(a)h(direct)e
(pro)q(duct)i(structure.)33 b(The)20 b(de\014nition)g(of)g(sp)q(ecial)g
(K\177)-24 b(ahler)20 b(manifolds)f(is)h(giv)o(en)f(in)-5
1734 y(the)i(next)f(section,)i(y)o(et)e(the)h(an)o(ticipation)f(of)h
(this)g(result)g(should)g(mak)o(e)e(clear)h(that)i(the)f(sp)q(ecial)-5
1795 y(K\177)-24 b(ahler)17 b(structure)g(\(enco)q(ding)g(the)g(dualit)
o(y)f(rotations)i(in)e(the)h Fv(N)k FH(=)15 b(2)i(case\))g(is)g(not)g
(a)h(prop)q(ert)o(y)f(of)-5 1855 y(the)g(individual)f(factors)i(but)f
(of)g(the)g(pro)q(duct)h(as)g(a)f(whole.)24 b(Neither)16
b(factor)h(is)g(b)o(y)g(itself)f(a)i(sp)q(ecial)-5 1915
y(manifold)d(although)i(the)f(pro)q(duct)h(is.)68 1975
y(A)o(t)12 b(this)h(p)q(oin)o(t)g(comes)f(the)g(question)h(of)g(the)f
(correct)h(symplectic)c(em)o(b)q(edding.)19 b(Suc)o(h)12
b(a)h(question)-5 2035 y(has)k(t)o(w)o(o)f(asp)q(ects:)55
2128 y(1.)24 b(In)o(trinsically)14 b(inequiv)m(alen)o(t)g(em)o(b)q
(eddings)55 2226 y(2.)24 b(Symplecticall)o(y)13 b(equiv)m(alen)o(t)i
(em)o(b)q(eddings)g(that)i(b)q(ecome)d(inequiv)m(alen)o(t)h(after)h
(gauging)-5 2319 y(The)c(\014rst)h(issue)e(in)h(the)g(ab)q(o)o(v)o(e)g
(list)f(is)h(group{theoretical)g(in)f(nature.)20 b(When)12
b(w)o(e)g(sa)o(y)g(that)g(the)g(group)-5 2379 y FE(G)18
b FH(is)d(em)o(b)q(edded)e(in)o(to)i Fv(S)s(p)p FH(\(2)p
518 2353 30 2 v Fv(n)q(;)8 b FH(I)-9 b(R)o(\))15 b(w)o(e)g(m)o(ust)f
(sp)q(ecify)g(ho)o(w)i(this)f(is)g(done)g(from)f(the)h(p)q(oin)o(t)g
(of)g(view)g(of)-5 2439 y(irreducible)h(represen)o(tations.)27
b(Group{theoretically)18 b(the)f(matter)g(is)h(settled)g(b)o(y)f(sp)q
(ecifying)h(ho)o(w)-5 2499 y(the)e(fundamen)o(tal)f(represen)o(tation)h
(of)g Fv(S)s(p)p FH(\(2)p 835 2473 V Fv(n)q FH(\))g(splits)g(in)o(to)g
(irreducible)e(represen)o(tations)i(of)h FE(G)s FH(:)774
2608 y FD(2)p 802 2581 32 2 v(n)870 2582 y FB(G)841 2608
y FE(\000)-9 b(!)11 b(\010)971 2590 y Ft(`)971 2621 y(i)p
FC(=1)1050 2608 y FD(D)1093 2615 y Ft(i)1760 2608 y FH(\(3.21\))-5
2707 y(Once)19 b(eq.)g(3.21)p
 (#equation.3.21) [[121 117 142 129] [1 1 1 [3 3]] [0 0 1]] pdfm 
20 w(is)h(giv)o(en)e(\(in)i(sup)q(ersymmetric)c(theories)j(suc)o(h)g
(information)g(is)g(pro)o(vided)g(b)o(y)g(su-)-5 2768
y(p)q(ersymmetry)g(\))j(the)g(only)g(arbitrariness)g(whic)o(h)g(is)g
(left)f(is)h(that)h(of)f(conjugation)h(b)o(y)f(arbitrary)916
2892 y(11)p eop
%%Page: 12 13
12 12 bop -5 15 a Fv(S)s(p)p FH(\(2)p 95 -11 30 2 v Fv(n)q(;)8
b FH(I)-9 b(R\))15 b(matrices.)k(Supp)q(ose)e(w)o(e)e(ha)o(v)o(e)g
(determined)e(an)j(em)o(b)q(edding)e Fv(\023)1398 22
y Ft(\016)1433 15 y FH(that)i(ob)q(eys)h(the)e(la)o(w)g(in)-5
76 y(eq.)h(3.21)p
 (#equation.3.21) [[90 749 110 761] [1 1 1 [3 3]] [0 0 1]] pdfm (,)g
(then:)548 136 y FE(8)8 b(S)25 b(2)d Fv(S)s(p)p FH(\(2)p
795 109 V Fv(n)q(;)8 b FH(I)-9 b(R)o(\))23 b(:)e Fv(\023)985
115 y FB(0)985 148 y Ft(\016)1027 136 y FE(\021)g(S)15
b(\016)c Fv(\023)1185 143 y Ft(\016)1216 136 y FE(\016)g(S)1286
115 y FB(\000)p FC(1)1760 136 y FH(\(3.22\))-5 219 y(will)k(ob)q(ey)g
(the)h(same)e(la)o(w.)21 b(That)16 b(in)f(eq.)g(3.22)p
 (#equation.3.22) [[256 714 277 726] [1 1 1 [3 3]] [0 0 1]] pdfm 
16 w(is)g(a)h(symplectic)c(transformation)k(that)g(corresp)q(onds)-5
279 y(to)j(an)g(allo)o(w)o(ed)e(dualit)o
(y{rotation/\014eld{rede\014nition)h(in)g(the)g(ab)q(elian)g(theory)g
(of)h(t)o(yp)q(e)f(in)f(eq.)h(2.5)p
 (#equation.2.5) [[510 700 524 712] [1 1 1 [3 3]] [0 0 1]] pdfm 
-5 339 a(discussed)h(in)f(the)g(previous)h(subsection.)28
b(Therefore)18 b(all)h(ab)q(elian)f(Lagrangians)j(related)d(b)o(y)g
(suc)o(h)-5 399 y(transformations)f(are)f(ph)o(ysically)f(equiv)m(alen)
o(t.)68 459 y(The)k(matter)f(c)o(hanges)h(in)f(presence)g(of)h
Fu(gauging)p FH(.)31 b(When)19 b(w)o(e)f(switc)o(h)g(on)i(the)e(gauge)i
(coupling)-5 520 y(constan)o(t)i(and)h(the)e(electric)f(c)o(harges,)i
(symplectic)d(transformations)j(cease)f(to)h(yield)f(ph)o(ysically)-5
580 y(equiv)m(alen)o(t)14 b(theories.)21 b(This)16 b(is)g(the)f(second)
h(issue)g(in)f(the)h(ab)q(o)o(v)o(e)f(list.)21 b(The)15
b(c)o(hoice)g(of)h(a)g(symplectic)-5 640 y(gauge)h(b)q(ecomes)e(ph)o
(ysically)g(signi\014can)o(t.)21 b(The)16 b(construction)g(of)h(sup)q
(ergra)o(vit)o(y)e(theories)h(pro)q(ceeds)-5 700 y(in)24
b(t)o(w)o(o)g(steps.)45 b(In)24 b(the)g(\014rst)h(step,)g(one)g
(constructs)f(the)g(ab)q(elian)g(theory:)37 b(at)25 b(that)f(lev)o(el)e
(the)-5 760 y(only)17 b(relev)m(an)o(t)f(constrain)o(t)g(is)h(that)g
(enco)q(ded)g(in)f(eq.)g(3.21)p
 (#equation.3.21) [[311 585 332 597] [1 1 1 [3 3]] [0 0 1]] pdfm 
17 w(and)i(the)e(c)o(hoice)f(of)i(a)h(symplectic)13 b(gauge)-5
821 y(is)21 b(immateri)o(al.)32 b(Actually)19 b(one)i(can)g(write)f
(the)g(en)o(tire)f(theory)i(in)f(suc)o(h)h(a)g(w)o(a)o(y)f(that)h
Fu(symple)n(ctic)-5 881 y(c)n(ovarianc)n(e)d FH(is)e(manifest.)22
b(In)17 b(the)f(second)i(step)e(one)i Fu(gauges)g FH(the)e(theory)l(.)
24 b(This)17 b Fu(br)n(e)n(aks)g(symple)n(ctic)-5 941
y(c)n(ovarianc)n(e)f FH(and)h(the)e(c)o(hoice)g(of)h(the)f(correct)g
(symplectic)e(gauge)k(b)q(ecomes)d(a)i(ph)o(ysical)f(issue.)21
b(This)-5 1001 y(issue)e(has)h(b)q(een)f(recen)o(tly)e(emphasized)g(b)o
(y)h(the)h(results)g(in)f([29)p
 (#cite.FGP1) [[351 527 362 539] [1 1 1 [3 3]] [0 0 1]] pdfm 
1 w(])g(where)h(it)f(has)i(b)q(een)f(sho)o(wn)h(that)-5
1061 y(whether)14 b(N=2)f(sup)q(ersymmetry)e(can)j(b)q(e)g(sp)q(on)o
(taneously)h(brok)o(en)e(to)h(N=1)g(or)g(not)g(dep)q(ends)g(on)g(the)-5
1121 y(symplectic)f(gauge.)68 1182 y(These)24 b(facts)h(b)q(eing)f
(cleared)f(w)o(e)h(pro)q(ceed)g(to)g(discuss)h(the)f(symplectic)c(em)o
(b)q(edding)j(of)h(the)-5 1242 y FE(S)t(T)d FH([)p Fv(m;)8
b(n)p FH(])15 b(manifolds.)68 1302 y(Let)20 b Fv(\021)h
FH(b)q(e)e(the)g(symmetri)o(c)d(\015at)k(metric)c(with)j(signature)h
(\()p Fv(m;)8 b(n)p FH(\))18 b(that)i(de\014nes)f(the)g
Fv(S)s(O)q FH(\()p Fv(m;)8 b(n)p FH(\))-5 1362 y(group,)17
b(via)f(the)g(relation)597 1422 y Fv(L)23 b FE(2)f Fv(S)s(O)q
FH(\()p Fv(m;)8 b(n)p FH(\))22 b FE(\()-8 b(\))22 b Fv(L)1080
1402 y Ft(T)1116 1422 y Fv(\021)r(L)g FH(=)g Fv(\021)479
b FH(\(3.23\))-5 1505 y(Both)17 b(in)g(the)g Fv(N)k FH(=)15
b(4)j(and)f(in)g(the)g Fv(N)k FH(=)15 b(2)i(theory)l(,)g(the)g(n)o(um)o
(b)q(er)e(of)j(gauge)g(\014elds)f(in)f(the)h(theory)g(is)-5
1565 y(giv)o(en)f(b)o(y:)685 1626 y(#v)o(ector)f(\014elds)22
b(=)g Fv(m)10 b FE(\010)h Fv(n)565 b FH(\(3.24\))-5 1708
y Fv(m)20 b FH(b)q(eing)g(the)g(n)o(um)o(b)q(er)e(of)i
Fu(gr)n(aviphotons)g FH(and)g Fv(n)g FH(the)g(n)o(um)o(b)q(er)e(of)i
Fu(ve)n(ctor)h(multiplets)p FH(.)34 b(Hence)18 b(w)o(e)-5
1768 y(ha)o(v)o(e)c(to)h(em)o(b)q(ed)e Fv(S)s(O)q FH(\()p
Fv(m;)8 b(n)p FH(\))15 b(in)o(to)f Fv(S)s(p)p FH(\(2)p
Fv(m)8 b FH(+)g(2)p Fv(n;)g FH(I)-9 b(R)q(\))14 b(and)i(the)e(explicit)
f(form)g(of)i(the)g(decomp)q(osition)-5 1829 y(in)h(eq.)f(3.21)p
 (#equation.3.21) [[103 328 124 340] [1 1 1 [3 3]] [0 0 1]] pdfm 
17 w(required)g(b)o(y)h(sup)q(ersymmetry)d(is:)596 1942
y FD(2m)d FH(+)h FD(2n)798 1911 y Ft(S)r(O)q FC(\()p
Ft(m;n)p FC(\))829 1942 y FE(\000)-9 b(!)39 b FD(m)9
b FH(+)i FD(n)h FE(\010)e FD(m)g FH(+)h FD(n)476 b FH(\(3.25\))-5
2042 y(where)16 b FD(m)9 b FH(+)i FD(n)16 b FH(denotes)g(the)g
(fundamen)o(tal)e(represen)o(tation)h(of)h Fv(S)s(O)q
FH(\()p Fv(m;)8 b(n)p FH(\).)21 b(Eq.)16 b(3.25)p
 (#equation.3.25) [[439 277 460 289] [1 1 1 [3 3]] [0 0 1]] pdfm 
16 w(is)g(easily)f(un-)-5 2102 y(dersto)q(o)q(d)21 b(in)e(ph)o(ysical)g
(terms.)29 b Fv(S)s(O)q FH(\()p Fv(m;)8 b(n)p FH(\))19
b(m)o(ust)f(b)q(e)i(a)f(T{dualit)o(y)g(group,)i(namely)d(a)h(symmetry)
-5 2162 y(holding)f(true)g(order)g(b)o(y)g(order)g(in)f(p)q
(erturbation)i(theory)l(.)26 b(As)18 b(suc)o(h)g(it)f(m)o(ust)g(rotate)
h(electric)e(\014eld)-5 2222 y(strengths)f(in)o(to)e(electric)e
(\014eld)j(strengths)g(and)g(magnetic)e(\014eld)i(strengths)g(in)o(to)f
(magnetic)f(\014eld)i(\014eld)-5 2283 y(strengths.)21
b(The)12 b(t)o(w)o(o)h(irreducible)d(represen)o(tations)i(in)o(to)g
(whic)o(h)g(the)g(the)g(fundamen)o(tal)f(represen)o(ta-)-5
2343 y(tion)k(of)h(the)f(symplectic)d(group)k(decomp)q(oses)e(when)i
(reduced)e(to)i Fv(S)s(O)q FH(\()p Fv(m;)8 b(n)p FH(\))15
b(corresp)q(ond)h(precisely)-5 2403 y(to)j(electric)e(and)i(magnetic)e
(sectors,)i(resp)q(ectiv)o(ely)l(.)26 b(In)18 b(the)g
Fu(simplest)j(gauge)f FH(the)e(symplectic)d(em-)-5 2463
y(b)q(edding)i(satisfying)f(eq.)f(3.25)p
 (#equation.3.25) [[186 176 207 188] [1 1 1 [3 3]] [0 0 1]] pdfm 
17 w(is)h(blo)q(c)o(k{diagonal)h(and)g(tak)o(es)f(the)g(form:)322
2584 y FE(8)8 b Fv(L)21 b FE(2)i Fv(S)s(O)q FH(\()p Fv(m;)8
b(n)p FH(\))733 2551 y Ft(\023)745 2557 y Fm(\016)721
2584 y Fv(,)-8 b FE(!)833 2523 y Fs(\022)872 2554 y Fv(L)107
b FD(0)874 2614 y(0)52 b FH(\()p Fv(L)1006 2596 y Ft(T)1033
2614 y FH(\))1052 2596 y FB(\000)p FC(1)1108 2523 y Fs(\023)1160
2584 y FE(2)23 b Fv(S)s(p)p FH(\(2)p Fv(m)11 b FH(+)g(2)p
Fv(n;)d FH(I)-9 b(R\))202 b(\(3.26\))-5 2707 y(Consider)24
b(instead)f(the)f(group)i Fv(S)s(U)5 b FH(\(1)p Fv(;)j
FH(1\))27 b FE(\030)e Fv(S)s(L)p FH(\(2)p Fv(;)8 b FH(I)-9
b(R\).)41 b(This)23 b(is)g(the)g(factor)g(in)g(the)g(isometry)-5
2768 y(group)17 b(of)f FE(S)t(T)c FH([)p Fv(m;)c(n)p
FH(])15 b(that)h(is)f(going)i(to)f(act)g(b)o(y)f(means)f(of)i(S{dualit)
o(y)f(non)i(p)q(erturbativ)o(e)e(rotations.)916 2892
y(12)p eop
%%Page: 13 14
13 13 bop -5 15 a FH(T)o(ypically)22 b(it)h(will)f(rotate)i(eac)o(h)f
(electric)e(\014eld)i(strength)g(in)o(to)g(its)h(homologous)g(magnetic)
d(one.)-5 76 y(Corresp)q(ondingly)i(sup)q(ersymmetry)c(implies)g(that)j
(its)f(em)o(b)q(edding)g(in)o(to)g(the)h(symplectic)c(group)-5
136 y(m)o(ust)d(satisfy)h(the)g(follo)o(wing)g(condition:)679
236 y FD(2m)10 b FH(+)h FD(2n)881 205 y Ft(S)r(L)p FC(\(2)p
Ft(;)p FC(I)-9 b(R\))907 236 y FE(\000)h(!)45 b(\010)1072
216 y Ft(m)p FC(+)p Ft(n)1072 249 y(i)p FC(=1)1173 236
y FD(2)559 b FH(\(3.27\))-5 323 y(where)11 b FD(2)g FH(denotes)g(the)g
(fundamen)o(tal)f(represen)o(tation)g(of)i Fv(S)s(L)p
FH(\(2)p Fv(;)c FH(I)-9 b(R\).)19 b(In)11 b(addition)g(it)g(m)o(ust)e
(comm)o(ute)-5 383 y(with)16 b(the)g(em)o(b)q(edding)f(of)i
Fv(S)s(O)q FH(\()p Fv(m;)8 b(n)p FH(\))16 b(in)g(eq.)f(3.26)p
 (#equation.3.26) [[275 675 296 687] [1 1 1 [3 3]] [0 0 1]] pdfm 
17 w(.)21 b(Both)16 b(conditions)h(are)f(ful\014lled)f(b)o(y)h
(setting:)274 493 y FE(8)318 433 y Fs(\022)357 463 y
Fv(a)51 b(b)359 524 y(c)g(d)465 433 y Fs(\023)518 493
y FE(2)22 b Fv(S)s(L)p FH(\(2)p Fv(;)8 b FH(I)-9 b(R\))830
460 y Ft(\023)842 466 y Fm(\016)817 493 y Fv(,)h FE(!)929
433 y Fs(\022)968 463 y Fv(a)8 b FH(1)-17 b(1)54 b Fv(b)8
b(\021)973 524 y(c)g(\021)56 b(d)8 b FH(1)-17 b(1)1156
433 y Fs(\023)1209 493 y FE(2)22 b Fv(S)s(p)p FH(\(2)p
Fv(m)11 b FH(+)g(2)p Fv(n;)d FH(I)-9 b(R\))154 b(\(3.28\))-5
604 y(Utilizing)18 b(eq.s)g(3.9)p
 (#equation.3.9) [[143 622 158 634] [1 1 1 [3 3]] [0 0 1]] pdfm 
20 w(the)h(corresp)q(onding)i(em)o(b)q(eddings)d(in)o(to)h(the)g(group)
i Fv(U)5 b(sp)p FH(\()p Fv(m)13 b FH(+)g Fv(n;)8 b(m)13
b FH(+)g Fv(n)p FH(\))20 b(are)-5 664 y(immedi)o(ately)13
b(deriv)o(ed:)166 772 y FE(8)8 b Fv(L)21 b FE(2)i Fv(S)s(O)q
FH(\()p Fv(m;)8 b(n)p FH(\))570 739 y Ft(\023)582 745
y Fm(\016)557 772 y Fv(,)-8 b FE(!)654 711 y Fs(\022)698
722 y FC(1)p 698 730 18 2 v 698 759 a(2)729 742 y FH(\()p
Fv(L)11 b FH(+)g Fv(\021)r(L\021)r FH(\))999 722 y FC(1)p
999 730 V 999 759 a(2)1030 742 y FH(\()p Fv(L)g FE(\000)g
Fv(\021)r(L\021)r FH(\))698 782 y FC(1)p 698 790 V 698
819 a(2)728 802 y FH(\()p Fv(L)h FE(\000)e Fv(\021)r(L\021)r
FH(\))1000 782 y FC(1)p 1000 790 V 1000 819 a(2)1030
802 y FH(\()p Fv(L)i FH(+)f Fv(\021)r(L\021)r FH(\))1255
711 y Fs(\023)1316 772 y FE(2)23 b Fv(U)5 b(sp)p FH(\()p
Fv(m)11 b FH(+)g Fv(n;)d(m)j FH(+)g Fv(n)p FH(\))17 898
y FE(8)61 838 y Fs(\022)104 868 y Fv(t)52 b(v)200 850
y Ft(?)100 928 y Fv(v)i(t)196 910 y Ft(?)228 838 y Fs(\023)280
898 y FE(2)23 b Fv(S)s(U)5 b FH(\(1)p Fv(;)j FH(1\))570
865 y Ft(\023)582 871 y Fm(\016)557 898 y Fv(,)-8 b FE(!)654
838 y Fs(\022)700 868 y FH(Re)p Fv(t)p FH(1)-17 b(1)11
b(+)g(iIm)n Fv(t\021)58 b FH(Re)p Fv(v)r FH(1)-17 b(1)11
b FE(\000)g FH(iIm)m Fv(v)r(\021)693 928 y FH(Re)o Fv(v)r
FH(1)-17 b(1)11 b(+)g(iIm)n Fv(v)r(\021)58 b FH(Re)o
Fv(t)p FH(1)-17 b(1)12 b FE(\000)f FH(iIm)m Fv(t\021)1346
838 y Fs(\023)1399 898 y FE(2)22 b Fv(U)5 b(sp)p FH(\()p
Fv(m)11 b FH(+)g Fv(n;)d(m)j FH(+)g Fv(n)p FH(\))1760
995 y(\(3.29\))-5 1081 y(where)i(the)g(relation)f(b)q(et)o(w)o(een)g
(the)h(en)o(tries)e(of)j(the)e Fv(S)s(U)5 b FH(\(1)p
Fv(;)j FH(1\))14 b(matrix)d(and)j(those)f(of)g(the)g(corresp)q(ond-)-5
1142 y(ing)k Fv(S)s(L)p FH(\(2)p Fv(;)8 b FH(I)-9 b(R\))16
b(matrix)e(are)j(pro)o(vided)e(b)o(y)h(the)g(relation)g(in)g(eq.)f
(3.10)p
 (#equation.3.10) [[358 493 379 505] [1 1 1 [3 3]] [0 0 1]] pdfm (.)68
1202 y(Equipp)q(ed)g(with)g(these)f(relations)h(w)o(e)f(can)h(pro)q
(ceed)g(to)g(deriv)o(e)e(the)i(explicit)d(form)i(of)h(the)f
Fu(p)n(erio)n(d)-5 1262 y(matrix)i FE(N)7 b FH(.)68 1322
y(The)15 b(homogeneous)g(manifold)f Fv(S)s(U)5 b FH(\(1)p
Fv(;)j FH(1\))p Fv(=U)d FH(\(1\))16 b(can)f(b)q(e)g(con)o(v)o(enien)o
(tly)d(parametrized)h(in)i(terms)-5 1382 y(of)22 b(a)f(single)g
(complex)d(co)q(ordinate)k Fv(S)s FH(,)g(whose)f(ph)o(ysical)g(in)o
(terpretation)f(will)g(b)q(e)h(that)g(of)h Fu(axion{)-5
1443 y(dilaton)p FH(,)j(according)e(to)g(eq.)f(3.20)p
 (#equation.3.20) [[205 421 226 433] [1 1 1 [3 3]] [0 0 1]] pdfm (.)41
b(The)23 b(coset)g(parametrization)e(appropriate)j(for)f(comparison)-5
1503 y(with)16 b(other)f(constructions)h(\(sp)q(ecial)f(geometry)f(or)i
Fv(N)j FH(=)14 b(4)i(sup)q(ergra)o(vit)o(y\))f(is)g(giv)o(en)g(b)o(y)g
(the)g(family)-5 1563 y(of)i(matrices:)170 1672 y Fv(M)5
b FH(\()p Fv(S)s FH(\))22 b FE(\021)419 1639 y FH(1)p
381 1661 100 2 v 381 1706 a Fv(n)p FH(\()p Fv(S)s FH(\))503
1599 y Fs( )563 1632 y FH(1)-17 b(1)668 1612 y FC(i)p
FB(\000)p Ft(S)p 668 1620 61 2 v 668 1649 a FC(i+)p Ft(S)549
1687 y FC(i+)p 586 1660 24 2 v Ft(S)p 549 1695 61 2 v
549 1728 a FC(i)p FB(\000)p 586 1700 24 2 v Ft(S)682
1707 y FH(1)g(1)742 1599 y Fs(!)886 1672 y FH(:)111 b
Fv(n)p FH(\()p Fv(S)s FH(\))22 b FE(\021)1194 1597 y
Fs(s)p 1236 1597 351 2 v 1353 1639 a FH(4Im)o Fv(S)p
1241 1661 341 2 v 1241 1706 a FH(1)11 b(+)g FE(j)p Fv(S)s
FE(j)1386 1692 y FC(2)1416 1706 y FH(+)g(2Im)o Fv(S)1760
1672 y FH(\(3.30\))-5 1793 y(T)l(o)17 b(parametrize)d(the)h(coset)h
Fv(S)s(O)q FH(\()p Fv(m;)8 b(n)p FH(\))p Fv(=S)s(O)q
FH(\()p Fv(m)p FH(\))j FE(\002)g Fv(S)s(O)q FH(\()p Fv(n)p
FH(\))16 b(w)o(e)g(can)g(instead)g(tak)o(e)f(the)h(usual)g(coset)-5
1853 y(represen)o(tativ)o(es)f(\(see)h(for)g(instance)g([31)p
 (#cite.CaDFb) [[241 322 252 334] [1 1 1 [3 3]] [0 0 1]] pdfm (]\):)455
1991 y Fv(L)p FH(\()p Fv(X)t FH(\))23 b FE(\021)654 1906
y Fs(0)654 1980 y(@)698 1903 y(\020)723 1952 y FH(1)-17
b(1)12 b(+)f Fv(X)t(X)903 1934 y Ft(T)931 1903 y Fs(\021)956
1915 y FC(1)p Ft(=)p FC(2)1194 1952 y Fv(X)819 2042 y(X)863
2024 y Ft(T)1060 1994 y Fs(\020)1084 2042 y FH(1)-17
b(1)12 b(+)f Fv(X)1220 2024 y Ft(T)1248 2042 y Fv(X)1292
1994 y Fs(\021)1317 2006 y FC(1)p Ft(=)p FC(2)1381 1906
y Fs(1)1381 1980 y(A)1760 1991 y FH(\(3.31\))-5 2126
y(where)j(the)g Fv(m)7 b FE(\002)g Fv(n)15 b FH(real)f(matrix)e
Fv(X)19 b FH(pro)o(vides)14 b(a)h(set)f(of)h(indep)q(enden)o(t)e(co)q
(ordinates.)21 b(Inserting)14 b(these)-5 2186 y(matrices)h(in)o(to)h
(the)g(em)o(b)q(edding)e(form)o(ulae)h(of)h(eq.s)g(3.29)p
 (#equation.3.29) [[306 242 326 254] [1 1 1 [3 3]] [0 0 1]] pdfm 
17 w(w)o(e)f(obtain)i(a)g(matrix:)115 2294 y Fv(\023)132
2301 y Ft(\016)159 2294 y FH(\()p Fv(M)5 b FH(\()p Fv(S)s
FH(\)\))12 b FE(\016)f Fv(\023)385 2301 y Ft(\016)412
2294 y FH(\()p Fv(L)p FH(\()p Fv(X)t FH(\)\))23 b(=)648
2233 y Fs(\022)687 2264 y Fv(U)720 2271 y FC(0)740 2264
y FH(\()p Fv(S;)8 b(X)t FH(\))49 b Fv(U)961 2246 y Ft(?)956
2276 y FC(1)981 2264 y FH(\()p Fv(S;)8 b(X)t FH(\))687
2324 y Fv(U)720 2331 y FC(1)740 2324 y FH(\()p Fv(S;)g(X)t
FH(\))49 b Fv(U)961 2306 y Ft(?)956 2336 y FC(0)981 2324
y FH(\()p Fv(S;)8 b(X)t FH(\))1123 2233 y Fs(\023)1176
2294 y FE(2)22 b Fv(U)5 b(sp)p FH(\()p Fv(n)12 b FH(+)f
Fv(m;)d(n)j FH(+)g Fv(m)p FH(\))119 b(\(3.32\))-5 2402
y(that)17 b(inserted)e(in)o(to)h(the)g(master)g(form)o(ula)e(of)j(eq.)e
(3.17)p
 (#equation.3.17) [[298 191 318 203] [1 1 1 [3 3]] [0 0 1]] pdfm 
17 w(yields)g(the)h(follo)o(wing)g(result:)571 2488 y
FE(N)29 b FH(=)22 b(iIm)n Fv(S)11 b(\021)r(L)p FH(\()p
Fv(X)t FH(\))p Fv(L)988 2468 y Ft(T)1016 2488 y FH(\()p
Fv(X)t FH(\))p Fv(\021)j FH(+)d(Re)o Fv(S)g(\021)453
b FH(\(3.33\))-5 2575 y(Alternativ)o(ely)l(,)10 b(remarking)i(that)h
(if)f Fv(L)p FH(\()p Fv(X)t FH(\))h(is)g(an)g Fv(S)s(O)q
FH(\()p Fv(m;)8 b(n)p FH(\))13 b(matrix)e(also)j Fv(L)p
FH(\()p Fv(X)t FH(\))1488 2557 y FB(0)1514 2575 y FH(=)g
Fv(\021)r(L)p FH(\()p Fv(X)t FH(\))p Fv(\021)h FH(is)d(suc)o(h)-5
2635 y(a)19 b(matrix)e(and)i(represen)o(ts)f(the)g(same)f(equiv)m
(alence)g(class,)h(w)o(e)g(can)h(rewrite)36 b(3.33)p
 (#equation.3.33) [[427 135 448 147] [1 1 1 [3 3]] [0 0 1]] pdfm 
19 w(in)18 b(the)g(simpler)-5 2695 y(form:)586 2755 y
FE(N)30 b FH(=)22 b(iIm)m Fv(S)12 b(L)p FH(\()p Fv(X)t
FH(\))945 2735 y FB(0)957 2755 y Fv(L)990 2735 y Ft(T)5
b FB(0)1027 2755 y FH(\()p Fv(X)t FH(\))11 b(+)g(Re)p
Fv(S)g(\021)468 b FH(\(3.34\))916 2892 y(13)p eop
%%Page: 14 15
14 14 bop -5 15 a Fw(4)81 b(Sp)r(ecial)26 b(K)o(\177)-40
b(ahler)27 b(Geometry)-5 125 y FH(The)22 b(\014rst)g(disco)o(v)o(ery)d
(that)j(the)f(self-in)o(teraction)g(of)g(W)l(ess{Zumino)g(m)o
(ultiplets)d(is)k(go)o(v)o(erned)f(b)o(y)-5 185 y(K\177)-24
b(ahler)21 b(geometry)f(is)h(due)g(to)h(Zumino)e([49)p
 (#cite.sugkgeom_1) [[262 723 274 735] [1 1 1 [3 3]] [0 0 1]] pdfm (])h
(\(1979\).)38 b(Indep)q(enden)o(tly)l(,)21 b(the)g(parametrization)f
(of)-5 245 y(the)c(coupling)f(of)h(W)l(ess{Zumino)e(m)o(ultiplets)f(to)
j(sup)q(ergra)o(vit)o(y)f(in)g(terms)f(of)i(a)f(real)h(function,)e
(later)-5 306 y(iden)o(ti\014ed)f(with)g(the)h(K\177)-24
b(ahler)13 b(p)q(oten)o(tial,)h(w)o(as)g(obtained)h(in)e([50)p
 (#cite.sugkgeom_5) [[343 694 354 706] [1 1 1 [3 3]] [0 0 1]] pdfm (,)h
(51)p
 (#cite.sugkgeom_6) [[361 694 373 706] [1 1 1 [3 3]] [0 0 1]] pdfm 
1 w(])f(\(1978\),)j(shortly)d(after)h(that)g(su-)-5 366
y(p)q(ergra)o(vit)o(y)g(had)i(b)q(een)f(disco)o(v)o(ered)e(b)o(y)i(F)l
(reedman,)e(F)l(errara)i(and)g(v)m(an)h(Nieu)o(w)o(enh)o(uizen)c([52)p
 (#cite.sugraprimo) [[474 679 485 691] [1 1 1 [3 3]] [0 0 1]] pdfm (])j
(\(1976\))-5 426 y(and)i(recast)f(in)g(\014rst)h(order)f(formalism)e(b)
o(y)h(Deser)h(and)h(Zumino)e([53)p
 (#cite.sugrasecondo) [[368 665 379 677] [1 1 1 [3 3]] [0 0 1]] pdfm 
(])h(\(1976\).)68 486 y(The)g(complete)d(form)h(of)h(standard)i(N=1)e
(sup)q(ergra)o(vit)o(y)l(,)f(determined)f(b)o(y)i(means)f(of)h(the)g
(sup)q(er-)-5 546 y(conformal)g(calculus,)f(w)o(as)i(obtained)g(in)f
([54)p
 (#cite.sugkgeom_4) [[259 636 271 648] [1 1 1 [3 3]] [0 0 1]] pdfm (])g
(\(1983\),)h(while)f(the)g(geometric)e(in)o(terpretation)i(of)g(the)-5
607 y(coupling)h(structure)g(is)g(due)g(to)h(Bagger)g(and)g(Witten)e
([55)p
 (#cite.sugkgeom_2) [[322 621 333 633] [1 1 1 [3 3]] [0 0 1]] pdfm (,)h
(56)p
 (#cite.sugkgeom_3) [[340 621 352 633] [1 1 1 [3 3]] [0 0 1]] pdfm 
1 w(])g(\(1983\).)68 667 y(Sp)q(ecial)j(K\177)-24 b(ahler)20
b(geometry)e(in)h(sp)q(ecial)g(co)q(ordinates)i(w)o(as)f(in)o(tro)q
(duced)f(in)g(1984{85)j(b)o(y)e(B.)e(de)-5 727 y(Wit)g(et)g(al.)28
b(in)18 b([57)p
 (#cite.specspec1) [[146 593 157 605] [1 1 1 [3 3]] [0 0 1]] pdfm (,)g
(34)p  (#cite.BDW) [[165 593 177 605] [1 1 1 [3 3]] [0 0 1]] pdfm 
1 w(])g(and)h(E.)f(Cremmer)d(et)j(al.)28 b(in)18 b([58)p
 (#cite.skgsugra_2) [[326 593 338 605] [1 1 1 [3 3]] [0 0 1]] pdfm (],)
h(where)f(the)g(coupling)g(of)h(N=2)f(v)o(ector)-5 787
y(m)o(ultiplets)g(to)j(N=2)g(sup)q(ergra)o(vit)o(y)f(w)o(as)i(fully)d
(determined.)33 b(The)21 b(more)e(in)o(trinsic)g(de\014nition)i(of)-5
847 y(sp)q(ecial)16 b(K\177)-24 b(ahler)15 b(geometry)g(in)h(terms)e
(of)i(symplectic)d(bundles)j(is)g(due)g(to)g(Strominger)f([59)p
 (#cite.skgmat_1) [[470 564 481 576] [1 1 1 [3 3]] [0 0 1]] pdfm (])h
(\(1990\),)-5 907 y(who)k(obtained)f(it)f(in)g(connection)h(with)f(the)
h(mo)q(duli)e(spaces)i(of)g(Calabi{Y)l(au)h(compacti\014cations.)-5
968 y(The)15 b(co)q(ordinate-indep)q(enden)o(t)g(description)g(and)g
(deriv)m(ation)g(of)h(sp)q(ecial)e(K\177)-24 b(ahler)15
b(geometry)f(in)g(the)-5 1028 y(con)o(text)j(of)h(N=2)g(sup)q(ergra)o
(vit)o(y)f(is)g(due)h(to)g(Castellani,)f(D'Auria,)g(F)l(errara)g([27)p
 (#cite.CaDF) [[423 520 435 532] [1 1 1 [3 3]] [0 0 1]] pdfm 
1 w(])g(and)h(to)g(D'Auria,)-5 1088 y(F)l(errara,)g(F)l(re')e([24)p
 (#cite.DFF) [[143 506 154 518] [1 1 1 [3 3]] [0 0 1]] pdfm (])h
(\(1991\).)26 b(Recen)o(tly)15 b(Ceresole,)i(D'Auria,)f(F)l(errara)i
(and)g(V)l(an)f(Pro)q(ey)o(en)g([4)p
 (#cite.CDFVP) [[488 506 494 518] [1 1 1 [3 3]] [0 0 1]] pdfm (])g(ha)o
(v)o(e)-5 1148 y(sho)o(wn)c(ho)o(w)g(one)g(can)f(and)h(in)f(imp)q
(ortan)o(t)f(instances)i(m)o(ust)e(disp)q(ense)h(of)h(the)f(notion)h
(of)f(holomorphic)-5 1208 y(prep)q(oten)o(tial)18 b Fv(F)7
b FH(\()p Fv(X)t FH(\).)26 b(Let)18 b(us)g(b)q(egin)g(b)o(y)g
(reviewing)f(the)g(notions)i(of)f(K\177)-24 b(ahler)18
b(and)h(Ho)q(dge{K\177)-24 b(ahler)-5 1269 y(manifolds)16
b(that)g(are)h(the)f(prerequisites)f(to)h(in)o(tro)q(duce)g(the)g
(notion)h(of)g(Sp)q(ecial)f(K\177)-24 b(ahler)16 b(manifolds.)-5
1329 y(Once)g(again)h(w)o(e)f(do)h(this)f(in)g(order)g(to)h(\014x)f
(our)g(notations.)-5 1473 y Fk(4.1)66 b(Ho)r(dge{K\177)-33
b(ahler)21 b(manifolds)-5 1566 y FH(Consider)12 b(a)g
Fg(line)e(bundle)h FE(L)536 1539 y Ft(\031)506 1566 y
FE(\000)-8 b(!M)11 b FH(o)o(v)o(er)g(a)h(K\177)-24 b(ahler)11
b(manifold.)18 b(By)11 b(de\014nition)g(this)g(is)g(a)h(holomorphic)-5
1626 y(v)o(ector)k(bundle)f(of)i(rank)f Fv(r)g FH(=)d(1.)22
b(F)l(or)16 b(suc)o(h)g(bundles)h(the)f(only)g(a)o(v)m(ailable)f(Chern)
h(class)h(is)f(the)g(\014rst:)513 1756 y Fv(c)534 1763
y FC(1)554 1756 y FH(\()p FE(L)p FH(\))23 b(=)732 1722
y Fv(i)p 714 1744 54 2 v 714 1790 a FH(2)p Fv(\031)p
781 1716 29 2 v 781 1756 a(@)826 1708 y Fs(\020)859 1756
y Fv(h)887 1735 y FB(\000)p FC(1)942 1756 y Fv(@)11 b(h)1015
1708 y Fs(\021)1063 1756 y FH(=)1146 1722 y Fv(i)p 1128
1744 54 2 v 1128 1790 a FH(2)p Fv(\031)p 1195 1716 29
2 v 1195 1756 a(@)f(@)h FH(log)e Fv(h)418 b FH(\(4.1\))-5
1881 y(where)21 b(the)g(1-comp)q(onen)o(t)f(real)h(function)f
Fv(h)p FH(\()p Fv(z)r(;)p 913 1855 25 2 v 8 w(z)r FH(\))h(is)g(some)f
(hermitian)f(\014bre)h(metric)f(on)i FE(L)p FH(.)36 b(Let)-5
1941 y Fv(f)5 b FH(\()p Fv(z)r FH(\))18 b(b)q(e)g(a)g(holomorphic)e
(section)h(of)h(the)f(line)g(bundle)g FE(L)p FH(:)24
b(noting)18 b(that)g(under)g(the)f(action)g(of)h(the)-5
2008 y(op)q(erator)p 195 1968 29 2 v 21 w Fv(@)11 b(@)30
b FH(the)20 b(term)e(log)566 1960 y Fs(\020)p 591 1968
24 2 v 48 x Fv(\030)s FH(\()p 634 1981 25 2 v Fv(z)r
FH(\))8 b Fv(\030)r FH(\()p Fv(z)r FH(\))772 1960 y Fs(\021)817
2008 y FH(yields)19 b(a)h(v)m(anishing)g(con)o(tribution,)f(w)o(e)h
(conclude)f(that)-5 2068 y(the)d(form)o(ula)f(in)h(eq.)f(4.1)p
 (#equation.4.1) [[166 271 181 283] [1 1 1 [3 3]] [0 0 1]] pdfm 
17 w(for)h(the)g(\014rst)h(Chern)f(class)h(can)f(b)q(e)g(re-expressed)g
(as)h(follo)o(ws:)612 2198 y Fv(c)633 2205 y FC(1)653
2198 y FH(\()p FE(L)p FH(\))31 b(=)847 2164 y Fv(i)p
829 2186 54 2 v 829 2232 a FH(2)p Fv(\031)p 896 2159
29 2 v 896 2198 a(@)10 b(@)h FH(log)23 b FE(k)f Fv(\030)r
FH(\()p Fv(z)r FH(\))g FE(k)1234 2178 y FC(2)1785 2198
y FH(\(4.2\))-5 2329 y(where)16 b FE(k)22 b Fv(\030)r
FH(\()p Fv(z)r FH(\))h FE(k)317 2311 y FC(2)380 2329
y FH(=)30 b Fv(h)p FH(\()p Fv(z)r(;)p 542 2303 25 2 v
8 w(z)r FH(\))p 594 2290 24 2 v 8 w Fv(\030)s FH(\()p
637 2303 25 2 v Fv(z)r FH(\))8 b Fv(\030)r FH(\()p Fv(z)r
FH(\))17 b(denotes)f(the)g(norm)g(of)g(the)g(holomorphic)f(section)h
Fv(\030)r FH(\()p Fv(z)r FH(\).)68 2389 y(Eq.)f(4.2)p
 (#equation.4.2) [[109 194 124 206] [1 1 1 [3 3]] [0 0 1]] pdfm 
15 w(is)g(the)g(starting)h(p)q(oin)o(t)f(for)g(the)g(de\014nition)g(of)
g(Ho)q(dge)h(K\177)-24 b(ahler)15 b(manifolds,)e(an)j(essen)o(tial)-5
2450 y(notion)h(in)f(sup)q(ergra)o(vit)o(y)g(theory)l(.)68
2510 y(A)k(K\177)-24 b(ahler)19 b(manifold)f FE(M)i FH(is)g(a)g(Ho)q
(dge)g(manifold)e(if)h(and)i(only)e(if)g(there)h(exists)f(a)h(line)e
(bundle)-5 2570 y FE(L)23 b(\000)-9 b(!)22 b(M)13 b FH(suc)o(h)g(that)h
(its)f(\014rst)g(Chern)h(class)f(equals)g(the)g(cohomology)g(class)g
(of)h(the)f(K\177)-24 b(ahler)12 b(2-form)-5 2630 y(K:)782
2690 y Fv(c)803 2697 y FC(1)823 2690 y FH(\()p FE(L)p
FH(\))30 b(=)38 b([)8 b Fv(K)13 b FH(])694 b(\(4.3\))916
2892 y(14)p eop
%%Page: 15 16
15 15 bop 68 15 a FH(In)17 b(lo)q(cal)f(terms)f(this)i(means)f(that)h
(there)f(is)g(a)h(holomorphic)f(section)g Fv(W)7 b FH(\()p
Fv(z)r FH(\))16 b(suc)o(h)h(that)g(w)o(e)f(can)-5 76
y(write)411 146 y Fv(K)27 b FH(=)562 112 y Fv(i)p 544
135 54 2 v 544 180 a FH(2)p Fv(\031)611 146 y(g)634 153
y Ft(ij)662 144 y Fm(?)691 146 y Fv(dz)741 126 y Ft(i)774
146 y FE(^)20 b Fv(d)p 852 120 25 2 v(z)877 126 y Ft(j)893
114 y Fm(?)936 146 y FH(=)1019 112 y Fv(i)p 1001 135
54 2 v 1001 180 a FH(2)p Fv(\031)p 1068 107 29 2 v 1068
146 a(@)10 b(@)h FH(log)23 b FE(k)f Fv(W)7 b FH(\()p
Fv(z)r FH(\))22 b FE(k)1436 126 y FC(2)1785 146 y FH(\(4.4\))-5
246 y(Recalling)i(the)g(lo)q(cal)h(expression)f(of)i(the)e(K\177)-24
b(ahler)24 b(metric)f(in)h(terms)f(of)i(the)g(K\177)-24
b(ahler)24 b(p)q(oten)o(tial)-5 306 y Fv(g)18 313 y Ft(ij)46
304 y Fm(?)109 306 y FH(=)43 b Fv(@)216 313 y Ft(i)238
306 y Fv(@)264 313 y Ft(j)280 304 y Fm(?)300 306 y FE(K)q
FH(\()p Fv(z)r(;)p 405 280 25 2 v 8 w(z)q FH(\),)22 b(it)e(follo)o(ws)h
(from)e(eq.)h(4.4)p
 (#equation.4.4) [[289 694 304 706] [1 1 1 [3 3]] [0 0 1]] pdfm 
21 w(that)i(if)e(the)g(manifold)g FE(M)h FH(is)f(a)h(Ho)q(dge)h(man-)-5
366 y(ifold,)27 b(then)e(the)g(exp)q(onen)o(tial)f(of)i(the)f(K\177)-24
b(ahler)25 b(p)q(oten)o(tial)f(can)i(b)q(e)f(in)o(terpreted)f(as)i(the)
f(metric)-5 427 y Fv(h)p FH(\()p Fv(z)r(;)p 89 400 V
8 w(z)r FH(\))30 b(=)38 b(exp)8 b(\()p FE(K)q FH(\()p
Fv(z)r(;)p 446 400 V 8 w(z)q FH(\)\))17 b(on)f(an)h(appropriate)g(line)
e(bundle)h FE(L)p FH(.)68 487 y(This)f(structure)f(is)f(precisely)g
(that)h(adv)o(o)q(cated)h(b)o(y)f(the)g(Lagrangian)i(of)e
Fv(N)19 b FH(=)14 b(1)h(matter)d(coupled)-5 547 y(sup)q(ergra)o(vit)o
(y:)21 b(the)16 b(holomorphic)g(section)g Fv(W)7 b FH(\()p
Fv(z)r FH(\))16 b(of)g(the)g(line)g(bundle)g FE(L)g FH(is)g(what,)h(in)
f(N=1)g(sup)q(er-)-5 607 y(gra)o(vit)o(y)e(theory)l(,)h(is)g(named)e
(the)i(sup)q(erp)q(oten)o(tial)g(and)h(the)e(logarithm)g(of)h(its)g
(norm)f(log)23 b FE(k)f Fv(W)7 b FH(\()p Fv(z)r FH(\))21
b FE(k)1865 589 y FC(2)-5 667 y FH(=)h FE(K)q FH(\()p
Fv(z)r(;)p 160 641 V 8 w(z)r FH(\))c(+)g(log)9 b FE(j)f
Fv(W)f FH(\()p Fv(z)r FH(\))h FE(j)509 649 y FC(2)558
667 y FH(=)30 b Fv(G)p FH(\()p Fv(z)r(;)p 730 641 V 8
w(z)r FH(\))15 b(is)h(precisely)e(the)h(in)o(v)m(arian)o(t)g(function)h
(in)f(terms)g(of)h(whic)o(h)-5 728 y(one)i(writes)g(the)f(p)q(oten)o
(tial)h(and)g(Y)l(uk)m(a)o(w)o(a)g(coupling)g(terms)e(of)i(the)g(sup)q
(ergra)o(vit)o(y)f(action)h(\(see)f([54)p
 (#cite.sugkgeom_4) [[510 592 521 604] [1 1 1 [3 3]] [0 0 1]] pdfm (])
-5 788 y(and)g(for)g(a)f(review)f([31)p
 (#cite.CaDFb) [[161 578 173 590] [1 1 1 [3 3]] [0 0 1]] pdfm 
1 w(]\).)-5 932 y Fk(4.2)66 b(Sp)r(ecial)24 b(K\177)-33
b(ahler)22 b(Manifolds:)30 b(general)22 b(discussion)-5
1025 y FH(There)h(are)g(in)g(fact)g(t)o(w)o(o)g(kinds)g(of)g(sp)q
(ecial)g(K\177)-24 b(ahler)22 b(geometry:)33 b(the)23
b(lo)q(cal)g(and)h(the)f(rigid)f(one.)-5 1085 y(The)e(former)e(describ)
q(es)i(the)f(scalar)h(\014eld)f(sector)h(of)g(v)o(ector)f(m)o(ultiple)o
(ts)e(in)j Fv(N)25 b FH(=)19 b(2)i(sup)q(ergra)o(vit)o(y)-5
1145 y(while)h(the)g(latter)f(describ)q(es)h(the)g(same)f(sector)h(in)g
(rigid)g Fv(N)29 b FH(=)24 b(2)f(Y)l(ang{Mills)e(theories.)39
b(Since)-5 1205 y Fv(N)21 b FH(=)15 b(2)i(includes)f
Fv(N)21 b FH(=)15 b(1)i(sup)q(ersymmetry)l(,)d(lo)q(cal)j(and)h(rigid)e
(sp)q(ecial)h(K\177)-24 b(ahler)16 b(manifolds)g(m)o(ust)g(b)q(e)-5
1265 y(compatible)c(with)i(the)g(geometric)e(structures)i(that)g(are)g
(resp)q(ectiv)o(ely)e(enforced)h(b)o(y)h(lo)q(cal)g(and)g(rigid)-5
1326 y Fv(N)22 b FH(=)15 b(1)j(sup)q(ersymmetry)d(in)i(the)g(scalar)h
(sector.)25 b(The)17 b(distinction)g(b)q(et)o(w)o(een)g(the)g(t)o(w)o
(o)g(cases)h(deals)-5 1386 y(with)k(the)f(\014rst)g(Chern{class)h(of)g
(the)f(line{bundle)f FE(L)1059 1359 y Ft(\031)1029 1386
y FE(\000)-8 b(!M)p FH(,)22 b(whose)g(sections)f(are)h(the)f(p)q
(ossible)-5 1446 y(sup)q(erp)q(oten)o(tials.)33 b(In)20
b(the)g(lo)q(cal)g(theory)g Fv(c)816 1453 y FC(1)835
1446 y FH(\()p FE(L)p FH(\))h(=)f([)p Fv(K)t FH(])f(and)i(this)f
(restricts)f FE(M)h FH(to)h(b)q(e)f(a)g(Ho)q(dge{)-5
1506 y(K\177)-24 b(ahler)20 b(manifold.)33 b(In)21 b(the)f(rigid)g
(theory)l(,)h(instead,)g(w)o(e)f(ha)o(v)o(e)g Fv(c)1234
1513 y FC(1)1254 1506 y FH(\()p FE(L)p FH(\))h(=)g(0.)35
b(A)o(t)20 b(the)g(lev)o(el)e(of)j(the)-5 1566 y(Lagrangian)f(this)d
(re\015ects)f(in)o(to)h(a)h(di\013eren)o(t)f(b)q(eha)o(viour)g(of)g
(the)g(fermion)f(\014elds.)24 b(These)17 b(latter)g(are)-5
1626 y(sections)f(of)h FE(L)267 1608 y FC(1)p Ft(=)p
FC(2)339 1626 y FH(and)f(couple)g(to)h(the)f(canonical)g(hermitian)e
(connection)i(de\014ned)g(on)h FE(L)p FH(:)335 1736 y
Fv(\022)43 b FE(\021)e Fv(h)509 1718 y FB(\000)p FC(1)564
1736 y Fv(@)11 b(h)j FH(=)701 1717 y FC(1)p 700 1725
21 2 v 700 1754 a Ft(h)733 1736 y Fv(@)759 1743 y Ft(i)773
1736 y Fv(h)8 b(dz)859 1718 y Ft(i)915 1736 y FH(;)p
970 1697 25 2 v 41 w Fv(\022)43 b FE(\021)e Fv(h)1144
1718 y FB(\000)p FC(1)p 1200 1697 29 2 v 1200 1736 a
Fv(@)11 b(h)j FH(=)1337 1717 y FC(1)p 1335 1725 21 2
v 1335 1754 a Ft(h)1369 1736 y Fv(@)1395 1743 y Ft(i)1407
1734 y Fm(?)1427 1736 y Fv(h)8 b(d)p 1488 1710 25 2 v(z)1513
1718 y Ft(i)1525 1707 y Fm(?)1785 1736 y FH(\(4.5\))-5
1846 y(In)16 b(the)g(lo)q(cal)g(case)h(where)711 1859
y Fs(h)p 739 1867 29 2 v 739 1907 a Fv(@)11 b(\022)808
1859 y Fs(i)850 1907 y FH(=)22 b Fv(c)931 1914 y FC(1)951
1907 y FH(\()p FE(L)p FH(\))g(=)g([)p Fv(K)t FH(])607
b(\(4.6\))-5 1994 y(the)17 b(\014bre)h(metric)d Fv(h)i
FH(can)h(b)q(e)f(iden)o(ti\014ed)f(with)i(the)f(exp)q(onen)o(tial)f(of)
i(the)f(K\177)-24 b(ahler)17 b(p)q(oten)o(tial)g(and)h(w)o(e)-5
2054 y(obtain:)445 2114 y Fv(\022)43 b FH(=)e Fv(@)11
b FE(K)j FH(=)g Fv(@)757 2121 y Ft(i)771 2114 y FE(K)q
Fv(dz)860 2096 y Ft(i)915 2114 y FH(;)p 970 2075 25 2
v 41 w Fv(\022)43 b FH(=)p 1115 2075 29 2 v 41 w Fv(@)11
b FE(K)k FH(=)f Fv(@)1283 2121 y Ft(i)1295 2112 y Fm(?)1314
2114 y FE(K)q Fv(d)p 1378 2088 25 2 v(z)1403 2096 y Ft(i)1415
2084 y Fm(?)1785 2114 y FH(\(4.7\))-5 2201 y(In)22 b(the)f(rigid)g
(case,)h FE(L)g FH(is)g(instead)f(a)h(\015at)g(bundle)f(and)h(its)g
(metric)d(is)i(unrelated)g(to)h(the)f(K\177)-24 b(ahler)-5
2262 y(p)q(oten)o(tial.)21 b(Actually)15 b(one)h(can)h(c)o(ho)q(ose)g
(a)f(v)m(anishing)h(connection:)822 2372 y Fv(\022)23
b FH(=)p 928 2332 V 22 w Fv(\022)g FH(=)f(0)727 b(\(4.8\))-5
2482 y(The)22 b(distinction)f(b)q(et)o(w)o(een)f(rigid)i(and)g(lo)q
(cal)f(sp)q(ecial)g(manifolds)g(is)g(the)h Fv(N)28 b
FH(=)23 b(2)f(generalization)-5 2542 y(of)f(this)f(di\013erence)f(o)q
(ccurring)h(at)g(the)g Fv(N)26 b FH(=)20 b(1)h(lev)o(el.)30
b(In)20 b(the)g Fv(N)25 b FH(=)c(2)f(case,)h(in)f(addition)g(to)g(the)
-5 2602 y(line{bundle)c FE(L)i FH(w)o(e)e(need)h(a)g(\015at)h
(holomorphic)e(v)o(ector)g(bundle)h FE(S)t(V)27 b(\000)-9
b(!)23 b(M)17 b FH(whose)h(sections)f(can)-5 2662 y(b)q(e)f(iden)o
(ti\014ed)e(with)i(the)f(sup)q(erspace)h Fu(fermi{fermi)f
FH(comp)q(onen)o(ts)g(of)h(electric)e(and)i(magnetic)e(\014eld{)-5
2722 y(strengths)e(\(see)f(app)q(endix)g(B\).)f(In)h(this)g(w)o(a)o(y)l
(,)h(according)f(to)h(the)f(discussion)g(of)g(previous)g(sections)g
(the)916 2892 y(15)p eop
%%Page: 16 17
16 16 bop -5 15 a FH(di\013eomorphisms)14 b(of)h(the)g(scalar)h
(manifolds)e(will)g(b)q(e)h(lifted)f(to)i(pro)q(duce)g(an)g(action)f
(on)h(the)f(gauge{)-5 76 y(\014eld)g(strengths)h(as)h(w)o(ell.)i(In)c
(a)h(sup)q(ersymmetric)c(theory)k(where)f(scalars)h(and)g(gauge)g
(\014elds)f(b)q(elong)-5 136 y(to)22 b(the)f(same)g(m)o(ultiplet)d
(this)j(is)h(a)f(mandatory)h(condition.)36 b(Ho)o(w)o(ev)o(er)20
b(this)h(symplectic)d(bundle)-5 196 y(structure)f(m)o(ust)f(b)q(e)h
(made)e(compatible)g(with)i(the)g(line{bundle)f(structure)h(already)f
(requested)h(b)o(y)-5 256 y Fv(N)29 b FH(=)24 b(1)e(sup)q(ersymmetry)l
(.)35 b(This)22 b(leads)g(to)h(the)e(existence)g(of)h(t)o(w)o(o)g
(kinds)f(of)i(sp)q(ecial)e(geometry)l(.)-5 316 y(Another)15
b(essen)o(tial)f(distinction)g(b)q(et)o(w)o(een)g(the)g(t)o(w)o(o)h
(kind)f(of)i(geometries)d(arises)i(from)e(the)i(di\013eren)o(t)-5
377 y(n)o(um)o(b)q(er)j(of)j(v)o(ector)d(\014elds)i(in)g(the)f(theory)l
(.)32 b(In)20 b(the)f(rigid)h(case)f(this)h(n)o(um)o(b)q(er)e(equals)i
(that)g(of)g(the)-5 437 y(v)o(ector)c(m)o(ultiple)o(ts)e(so)j(that)625
547 y(#)8 b(v)o(ector)15 b(\014elds)22 b FE(\021)p 1012
520 30 2 v 22 w Fv(n)42 b FH(=)f Fv(n)537 619 y FH(#)8
b(v)o(ector)16 b(m)o(ultiple)o(ts)11 b FE(\021)j Fv(n)42
b FH(=)f(dim)1243 626 y Ff(C)1283 619 y FE(M)732 692
y FH(rank)8 b FE(S)t(V)26 b(\021)c FH(2)p 1012 666 V
Fv(n)42 b FH(=)f(2)p Fv(n)570 b FH(\(4.9\))-5 802 y(On)13
b(the)f(other)h(hand,)g(in)f(the)h(lo)q(cal)f(case,)h(in)f(addition)h
(to)g(the)f(v)o(ector)f(\014elds)i(arising)f(from)g(the)g(v)o(ector)-5
862 y(m)o(ultiplets)k(w)o(e)i(ha)o(v)o(e)g(also)h(the)g(gra)o(viphoton)
g(coming)f(from)f(the)i(gra)o(viton)g(m)o(ultiplet)o(.)26
b(Hence)17 b(w)o(e)-5 922 y(conclude:)625 1033 y(#)8
b(v)o(ector)15 b(\014elds)22 b FE(\021)p 1012 1006 V
22 w Fv(n)42 b FH(=)f Fv(n)11 b FH(+)g(1)537 1105 y(#)d(v)o(ector)16
b(m)o(ultiple)o(ts)11 b FE(\021)j Fv(n)42 b FH(=)f(dim)1243
1112 y Ff(C)1283 1105 y FE(M)732 1178 y FH(rank)8 b FE(S)t(V)26
b(\021)c FH(2)p 1012 1151 V Fv(n)42 b FH(=)f(2)p Fv(n)12
b FH(+)f(2)460 b(\(4.10\))-5 1288 y(In)15 b(the)f(sequel)g(w)o(e)g(mak)
o(e)f(extensiv)o(e)g(use)h(of)h(co)o(v)m(arian)o(t)g(deriv)m(ativ)o(es)
e(with)h(resp)q(ect)h(to)g(the)f(canonical)-5 1348 y(connection)20
b(of)h(the)e(line{bundle)h FE(L)p FH(.)33 b(Let)20 b(us)h(review)e(its)
h(normalization.)31 b(As)20 b(it)g(is)g(w)o(ell)f(kno)o(wn)-5
1408 y(there)g(exists)f(a)h(corresp)q(ondence)g(b)q(et)o(w)o(een)f
(line{bundles)g(and)h Fv(U)5 b FH(\(1\){bundles.)30 b(If)19
b(exp)o([)p Fv(f)1711 1415 y Ft(\013\014)1757 1408 y
FH(\()p Fv(z)r FH(\)])f(is)-5 1468 y(the)j(transition)f(function)h(b)q
(et)o(w)o(een)e(t)o(w)o(o)h(lo)q(cal)h(trivializations)e(of)i(the)f
(line{bundle)f FE(L)30 b(\000)-9 b(!)30 b(M)p FH(,)-5
1529 y(the)23 b(transition)h(function)e(in)h(the)g(corresp)q(onding)h
(principal)e Fv(U)5 b FH(\(1\){bundle)24 b FE(U)39 b(\000)-8
b(!)25 b(M)e FH(is)g(just)-5 1589 y(exp[iIm)m Fv(f)179
1596 y Ft(\013\014)225 1589 y FH(\()p Fv(z)r FH(\)])16
b(and)h(the)f(K\023)-24 b(ahler)16 b(p)q(oten)o(tials)g(in)g(t)o(w)o(o)
g(di\013eren)o(t)f(c)o(harts)i(are)f(related)f(b)o(y:)712
1699 y FE(K)750 1706 y Ft(\014)788 1699 y FH(=)e FE(K)877
1706 y Ft(\013)913 1699 y FH(+)e Fv(f)986 1706 y Ft(\013\014)1043
1699 y FH(+)p 1092 1659 V 11 w Fv(f)1122 1711 y Ft(\013\014)1760
1699 y FH(\(4.11\))-5 1809 y(.)22 b(A)o(t)15 b(the)h(lev)o(el)e(of)j
(connections)f(this)g(corresp)q(ondence)g(is)g(form)o(ulated)f(b)o(y)h
(setting:)479 1939 y Fv(U)5 b FH(\(1\){connection)15
b FE(\021)e(Q)22 b FH(=)g(Im)n Fv(\022)15 b FH(=)f FE(\000)1218
1905 y FH(i)p 1213 1928 25 2 v 1213 1973 a(2)1250 1891
y Fs(\020)1275 1939 y Fv(\022)e FE(\000)p 1360 1900 V
11 w Fv(\022)1384 1891 y Fs(\021)1760 1939 y FH(\(4.12\))-5
2065 y(If)k(w)o(e)g(apply)g(the)g(ab)q(o)o(v)o(e)g(form)o(ula)f(to)h
(the)g(case)g(of)h(the)f Fv(U)5 b FH(\(1\){bundle)16
b FE(U)28 b(\000)-9 b(!)22 b(M)16 b FH(asso)q(ciated)h(with)-5
2125 y(the)f(line{bundle)f FE(L)i FH(whose)g(\014rst)f(Chern)h(class)f
(equals)g(the)g(K\177)-24 b(ahler)16 b(class,)g(w)o(e)g(get:)626
2255 y FE(Q)e FH(=)f FE(\000)782 2222 y FH(i)p 776 2244
V 776 2289 a(2)814 2207 y Fs(\020)839 2255 y Fv(@)865
2262 y Ft(i)878 2255 y FE(K)q Fv(dz)967 2235 y Ft(i)992
2255 y FE(\000)e Fv(@)1068 2262 y Ft(i)1080 2253 y Fm(?)1100
2255 y FE(K)q Fv(d)p 1164 2229 V(z)1189 2235 y Ft(i)1201
2223 y Fm(?)1221 2207 y Fs(\021)1760 2255 y FH(\(4.13\))-5
2381 y(Let)17 b(no)o(w)f(\010\()p Fv(z)r(;)p 285 2354
V 8 w(z)r FH(\))g(b)q(e)h(a)f(section)g(of)h FE(U)707
2363 y Ft(p)727 2381 y FH(.)k(By)15 b(de\014nition)h(its)g(co)o(v)m
(arian)o(t)g(deriv)m(ativ)o(e)f(is)749 2491 y FE(r)p
FH(\010)e(=)h(\()p Fv(d)e FH(+)f Fv(ip)p FE(Q)p FH(\)\010)628
b(\(4.14\))-5 2601 y(or,)16 b(in)g(comp)q(onen)o(ts,)349
2711 y FE(r)391 2718 y Ft(i)405 2711 y FH(\010)41 b(=)h(\()p
Fv(@)606 2718 y Ft(i)631 2711 y FH(+)685 2691 y FC(1)p
685 2699 18 2 v 685 2728 a(2)707 2711 y Fv(p@)757 2718
y Ft(i)772 2711 y FE(K)q FH(\)\010)f(;)g FE(r)1003 2718
y Ft(i)1015 2708 y Fn(\003)1035 2711 y FH(\010)g(=)h(\()p
Fv(@)1236 2718 y Ft(i)1248 2708 y Fn(\003)1279 2711 y
FE(\000)1333 2691 y FC(1)p 1333 2699 V 1333 2728 a(2)1356
2711 y Fv(p@)1406 2718 y Ft(i)1418 2708 y Fn(\003)1438
2711 y FE(K)q FH(\)\010)229 b(\(4.15\))916 2892 y(16)p
eop
%%Page: 17 18
17 17 bop -5 15 a FH(A)19 b(co)o(v)m(arian)o(tly)g(holomorphic)f
(section)h(of)g FE(U)25 b FH(is)19 b(de\014ned)g(b)o(y)g(the)g
(equation:)27 b FE(r)1513 22 y Ft(i)1525 14 y Fn(\003)1545
15 y FH(\010)19 b(=)g(0.)31 b(W)l(e)19 b(can)-5 76 y(easily)d(map)f
(eac)o(h)h(section)g(\010\()p Fv(z)r(;)p 612 49 25 2
v 8 w(z)q FH(\))h(of)f FE(U)763 58 y Ft(p)799 76 y FH(in)o(to)g(a)h
(section)f(of)g(the)g(line{bundle)g FE(L)g FH(b)o(y)g(setting:)801
161 y Fs(e)795 178 y FH(\010)e(=)g Fv(e)919 157 y FB(\000)p
Ft(p)p FB(K)p Ft(=)p FC(2)1028 178 y FH(\010)8 b Fv(:)675
b FH(\(4.16\))-5 279 y(With)16 b(this)g(p)q(osition)h(w)o(e)f(obtain:)
487 383 y FE(r)529 390 y Ft(i)548 367 y Fs(e)542 383
y FH(\010)42 b(=)f(\()p Fv(@)743 390 y Ft(i)768 383 y
FH(+)11 b Fv(p@)867 390 y Ft(i)882 383 y FE(K)q FH(\))946
367 y Fs(e)940 383 y FH(\010)41 b(;)g FE(r)1113 390 y
Ft(i)1125 381 y Fn(\003)1151 367 y Fs(e)1145 383 y FH(\010)g(=)h
Fv(@)1327 390 y Ft(i)1339 381 y Fn(\003)1365 367 y Fs(e)1359
383 y FH(\010)1760 381 y(\(4.17\))-5 483 y(Under)18 b(the)h(map)f(of)h
(eq.)e(4.16)p
 (#equation.4.16) [[187 651 208 663] [1 1 1 [3 3]] [0 0 1]] pdfm 
20 w(co)o(v)m(arian)o(tly)h(holomorphic)f(sections)i(of)g
FE(U)24 b FH(\015o)o(w)19 b(in)o(to)f(holomorphic)-5
543 y(sections)e(of)h FE(L)g FH(and)f(vicev)o(ersa.)-5
686 y Fk(4.3)66 b(Sp)r(ecial)24 b(K\177)-33 b(ahler)22
b(manifolds:)30 b(the)23 b(lo)r(cal)g(case)-5 779 y FH(W)l(e)c(are)f
(no)o(w)h(ready)g(to)g(giv)o(e)e(the)i(de\014nition)f(of)h(lo)q(cal)f
(sp)q(ecial)g(K\177)-24 b(ahler)18 b(manifolds)g(and)h(illustrate)-5
839 y(their)e(prop)q(erties.)24 b(A)17 b(\014rst)g(de\014nition)g(that)
h(do)q(es)g(not)f(mak)o(e)f(direct)g(reference)g(to)h(the)g(symplectic)
-5 899 y(bundle)f(is)g(the)g(follo)o(wing:)-5 994 y FD(De\014nition)i
(4.1)24 b Fu(A)e(Ho)n(dge)g(K\177)-25 b(ahler)22 b(manifold)g(is)f
FD(Sp)r(ecial)i(K\177)-28 b(ahler)23 b(\(of)h(the)f(lo)r(cal)g(t)n(yp)r
(e\))d Fu(if)-5 1054 y(ther)n(e)i(exists)g(a)g(c)n(ompletely)h
(symmetric)e(holomorphic)h(3-index)h(se)n(ction)f Fv(W)1458
1061 y Ft(ij)r(k)1530 1054 y Fu(of)f FH(\()p Fv(T)1646
1036 y Ft(?)1665 1054 y FE(M)p FH(\))1744 1036 y FC(3)1778
1054 y FE(\012)14 b(L)1865 1036 y FC(2)-5 1114 y Fu(\(and)i(its)g
(antiholomorphic)g(c)n(onjugate)i Fv(W)796 1121 y Ft(i)808
1112 y Fn(\003)826 1121 y Ft(j)842 1112 y Fn(\003)860
1121 y Ft(k)879 1112 y Fn(\003)899 1114 y Fu(\))e(such)h(that)f(the)g
(fol)r(lowing)i(identity)f(is)f(satis\014e)n(d)g(by)-5
1174 y(the)i(R)o(iemann)g(tensor)g(of)f(the)h(L)n(evi{Civita)f(c)n
(onne)n(ction:)401 1276 y Fv(@)427 1283 y Ft(m)458 1274
y Fn(\003)478 1276 y Fv(W)524 1283 y Ft(ij)r(k)615 1276
y FH(=)41 b(0)50 b Fv(@)794 1283 y Ft(m)827 1276 y Fv(W)873
1283 y Ft(i)885 1274 y Fn(\003)903 1283 y Ft(j)919 1274
y Fn(\003)938 1283 y Ft(k)957 1274 y Fn(\003)991 1276
y FH(=)13 b(0)383 1349 y FE(r)425 1357 y FC([)p Ft(m)468
1349 y Fv(W)514 1357 y Ft(i)p FC(])p Ft(j)r(k)615 1349
y FH(=)41 b(0)50 b FE(r)810 1357 y FC([)p Ft(m)853 1349
y Fv(W)899 1357 y Ft(i)911 1347 y Fn(\003)929 1357 y
FC(])p Ft(j)955 1347 y Fn(\003)973 1357 y Ft(k)992 1347
y Fn(\003)1026 1349 y FH(=)14 b(0)431 1422 y FE(R)473
1429 y Ft(i)485 1420 y Fn(\003)503 1429 y Ft(j)r(`)533
1420 y Fn(\003)552 1429 y Ft(k)615 1422 y FH(=)41 b Fv(g)717
1429 y Ft(`)731 1420 y Fn(\003)750 1429 y Ft(j)768 1422
y Fv(g)791 1429 y Ft(k)q(i)822 1420 y Fn(\003)854 1422
y FH(+)11 b Fv(g)926 1429 y Ft(`)940 1420 y Fn(\003)959
1429 y Ft(k)980 1422 y Fv(g)1003 1429 y Ft(j)r(i)1031
1420 y Fn(\003)1063 1422 y FE(\000)f Fv(e)1135 1401 y
FC(2)p FB(K)1182 1422 y Fv(W)1228 1429 y Ft(i)1240 1420
y Fn(\003)1258 1429 y Ft(`)1272 1420 y Fn(\003)1290 1429
y Ft(s)1306 1420 y Fn(\003)1327 1422 y Fv(W)1373 1429
y Ft(tk)q(j)1423 1422 y Fv(g)1448 1401 y Ft(s)1464 1389
y Fn(\003)1482 1401 y Ft(t)1760 1422 y FH(\(4.18\))-5
1618 y(In)15 b(the)g(ab)q(o)o(v)o(e)g(equations)g FE(r)g
FH(denotes)g(the)g(co)o(v)m(arian)o(t)g(deriv)m(ativ)o(e)e(with)i(resp)
q(ect)g(to)g(b)q(oth)h(the)f(Levi{)-5 1678 y(Civita)k(and)h(the)f
Fv(U)5 b FH(\(1\))20 b(holomorphic)f(connection)g(of)g(eq.)g(4.13)p
 (#equation.4.13) [[341 364 361 376] [1 1 1 [3 3]] [0 0 1]] pdfm (.)31
b(In)20 b(the)f(case)g(of)h Fv(W)1614 1685 y Ft(ij)r(k)1663
1678 y FH(,)g(the)f Fv(U)5 b FH(\(1\))-5 1738 y(w)o(eigh)o(t)16
b(is)g Fv(p)e FH(=)g(2.)68 1799 y(The)j(holomorphic)e(sections)h
Fv(W)676 1806 y Ft(ij)r(k)742 1799 y FH(ha)o(v)o(e)g(t)o(w)o(o)g
(di\013eren)o(t)g(ph)o(ysical)f(in)o(terpretations)h(in)g(the)g(case)-5
1859 y(that)h(the)g(sp)q(ecial)f(manifold)f(is)h(utilized)f(as)i
(scalar)g(manifold)e(in)h(an)h(N=1)g(or)g(N=2)f(theory)l(.)22
b(In)16 b(the)-5 1919 y(\014rst)i(case)g(they)f(corresp)q(ond)h(to)g
(the)f(Y)l(uk)m(a)o(w)o(a)h(couplings)f(of)h(F)l(ermi)d(families)g([60)
p  (#cite.petropaolo) [[431 306 442 318] [1 1 1 [3 3]] [0 0 1]] pdfm 
1 w(].)24 b(In)18 b(the)f(second)-5 1979 y(case)h(they)f(pro)o(vide)g
(the)h(co)q(e\016cien)o(ts)e(for)i(the)g(anomalous)g(magnetic)e(momen)o
(ts)f(of)j(the)g(gauginos,)-5 2039 y(since)g(they)f(app)q(ear)i(in)f
(the)g(P)o(auli{terms)e(of)i(the)g Fv(N)k FH(=)17 b(2)i(e\013ectiv)o(e)
d(action.)27 b(Out)18 b(of)g(the)g Fv(W)1762 2046 y Ft(ij)r(k)1829
2039 y FH(w)o(e)-5 2100 y(can)f(construct)f(co)o(v)m(arian)o(tly)f
(holomorphic)g(sections)i(of)f(w)o(eigh)o(t)g(2)g(and)h(-)g(2)f(b)o(y)g
(setting:)504 2201 y Fv(C)539 2208 y Ft(ij)r(k)611 2201
y FH(=)22 b Fv(W)717 2208 y Ft(ij)r(k)775 2201 y Fv(e)798
2181 y FB(K)875 2201 y FH(;)57 b Fv(C)981 2208 y Ft(i)993
2199 y Fm(?)1011 2208 y Ft(j)1027 2199 y Fm(?)1045 2208
y Ft(k)1064 2199 y Fm(?)1106 2201 y FH(=)22 b Fv(W)1212
2208 y Ft(i)1224 2199 y Fm(?)1243 2208 y Ft(j)1259 2199
y Fm(?)1277 2208 y Ft(k)1296 2199 y Fm(?)1324 2201 y
Fv(e)1347 2181 y FB(K)1760 2201 y FH(\(4.19\))-5 2303
y(Next)f(w)o(e)g(can)h(giv)o(e)f(the)h(second)g(more)e(in)o(trinsic)g
(de\014nition)h(that)i(relies)d(on)i(the)g(notion)g(of)g(the)-5
2363 y(\015at)17 b(symplectic)c(bundle.)22 b(Let)16 b
FE(L)23 b(\000)-8 b(!)22 b(M)16 b FH(denote)g(the)h(complex)d(line)h
(bundle)h(whose)h(\014rst)g(Chern)-5 2424 y(class)22
b(equals)g(the)g(K\177)-24 b(ahler)22 b(form)f Fv(K)26
b FH(of)d(an)f Fv(n)p FH(-dimensional)f(Ho)q(dge{K\177)-24
b(ahler)23 b(manifold)d FE(M)p FH(.)39 b(Let)-5 2484
y FE(S)t(V)26 b(\000)-9 b(!)22 b(M)15 b FH(denote)f(a)h(holomorphic)e
(\015at)i(v)o(ector)e(bundle)h(of)h(rank)g(2)p Fv(n)7
b FH(+)g(2)16 b(with)e(structural)g(group)-5 2544 y Fv(S)s(p)p
FH(\(2)p Fv(n)8 b FH(+)g(2)p Fv(;)g FH(I)-9 b(R)r(\).)20
b(Consider)15 b(tensor)h(bundles)e(of)i(the)e(t)o(yp)q(e)h
FE(H)22 b FH(=)g FE(S)t(V)12 b(\012)c(L)p FH(.)21 b(A)15
b(t)o(ypical)e(holomorphic)-5 2604 y(section)j(of)h(suc)o(h)f(a)g
(bundle)g(will)f(b)q(e)i(denoted)f(b)o(y)g(\012)g(and)h(will)e(ha)o(v)o
(e)h(the)g(follo)o(wing)g(structure:)585 2734 y(\012)23
b(=)703 2661 y Fs( )756 2704 y Fv(X)800 2686 y FC(\003)762
2764 y Fv(F)794 2771 y FC(\006)848 2661 y Fs(!)930 2734
y FH(\003)p Fv(;)8 b FH(\006)13 b(=)h(0)p Fv(;)8 b FH(1)p
Fv(;)g(:)g(:)g(:)g(;)g(n)465 b FH(\(4.20\))916 2892 y(17)p
eop
%%Page: 18 19
18 18 bop -5 15 a FH(By)24 b(de\014nition)g(the)g(transition)g
(functions)h(b)q(et)o(w)o(een)e(t)o(w)o(o)h(lo)q(cal)g(trivializations)
f Fv(U)1614 22 y Ft(i)1656 15 y FE(\032)k(M)d FH(and)-5
76 y Fv(U)28 83 y Ft(j)60 76 y FE(\032)14 b(M)i FH(of)h(the)f(bundle)g
FE(H)g FH(ha)o(v)o(e)g(the)g(follo)o(wing)g(form:)666
144 y Fs( )720 187 y Fv(X)723 247 y(F)785 144 y Fs(!)818
269 y Ft(i)846 217 y FH(=)e Fv(e)921 197 y Ft(f)938 202
y Fm(ij)967 217 y Fv(M)1014 224 y Ft(ij)1044 144 y Fs( )1098
187 y Fv(X)1101 247 y(F)1163 144 y Fs(!)1196 269 y Ft(j)1760
217 y FH(\(4.21\))-5 366 y(where)21 b Fv(f)165 373 y
Ft(ij)217 366 y FH(are)g(holomorphic)g(maps)f Fv(U)753
373 y Ft(i)782 366 y FE(\\)15 b Fv(U)863 373 y Ft(j)912
366 y FE(!)p 1001 366 2 33 v 26 w FH(C)22 b(while)e Fv(M)1224
373 y Ft(ij)1276 366 y FH(is)i(a)f(constan)o(t)h Fv(S)s(p)p
FH(\(2)p Fv(n)16 b FH(+)e(2)p Fv(;)8 b FH(I)-9 b(R\))-5
426 y(matrix.)29 b(F)l(or)20 b(a)f(consisten)o(t)g(de\014nition)g(of)h
(the)f(bundle)g(the)g(transition)h(functions)f(are)h(ob)o(viously)-5
486 y(sub)s(ject)c(to)h(the)f(co)q(cycle)f(condition)h(on)g(a)h(triple)
e(o)o(v)o(erlap:)760 595 y Fv(e)783 575 y Ft(f)800 580
y Fm(ij)826 575 y FC(+)p Ft(f)870 581 y Fm(j)q(k)904
575 y FC(+)p Ft(f)948 581 y Fm(k)q(i)1022 595 y FH(=)42
b(1)738 668 y Fv(M)785 675 y Ft(ij)815 668 y Fv(M)862
675 y Ft(j)r(k)900 668 y Fv(M)947 675 y Ft(k)q(i)1022
668 y FH(=)g(1)634 b(\(4.22\))-5 777 y(Let)17 b Fv(i)p
FE(h)f(j)g(i)h FH(b)q(e)f(the)g(compatible)e(hermitian)h(metric)e(on)k
FE(H)610 917 y Fv(i)p FE(h)p FH(\012)8 b FE(j)p 711 878
36 2 v 8 w FH(\012)q FE(i)22 b(\021)g(\000)p Fv(i)p FH(\012)940
897 y Ft(T)976 844 y Fs( )1052 887 y FH(0)65 b(1)-17
b(1)1029 947 y FE(\000)p FH(1)g(1)46 b(0)1194 844 y Fs(!)p
1235 878 V 1235 917 a FH(\012)490 b(\(4.23\))-5 1127
y FD(De\014nition)18 b(4.2)24 b Fu(We)f(say)f(that)h(a)f(Ho)n
(dge{K\177)-25 b(ahler)24 b(manifold)f FE(M)f Fu(is)h
FD(sp)r(ecial)h(K\177)-28 b(ahler)24 b(of)i(the)-5 1187
y(lo)r(cal)f(t)n(yp)r(e)e Fu(if)g(ther)n(e)h(exists)g(a)f(bund)r(le)j
FE(H)e Fu(of)f(the)h(typ)n(e)f(describ)n(e)n(d)h(ab)n(ove)g(such)f
(that)h(for)f(some)-5 1248 y(se)n(ction)18 b FH(\012)23
b FE(2)f FH(\000\()p FE(H)p Fv(;)8 b FE(M)p FH(\))18
b Fu(the)g(K\177)-25 b(ahler)18 b(two)g(form)f(is)g(given)i(by:)669
1379 y Fv(K)e FH(=)803 1346 y Fv(i)p 784 1368 54 2 v
784 1414 a FH(2)p Fv(\031)843 1379 y(@)p 872 1340 29
2 v 3 w(@)10 b FH(log)987 1331 y Fs(\020)1012 1379 y
FH(i)p FE(h)p FH(\012)e FE(j)p 1110 1340 36 2 v 8 w FH(\012)q
FE(i)1165 1331 y Fs(\021)1198 1379 y Fv(:)548 b FH(\(4.24\))-5
1501 y(F)l(rom)14 b(the)g(p)q(oin)o(t)g(of)h(view)f(of)h(lo)q(cal)f
(prop)q(erties,)g(eq.)g(4.24)p
 (#equation.4.24) [[307 407 327 419] [1 1 1 [3 3]] [0 0 1]] pdfm 
15 w(implies)e(that)j(w)o(e)f(ha)o(v)o(e)g(an)h(expression)f(for)-5
1561 y(the)i(K\177)-24 b(ahler)16 b(p)q(oten)o(tial)g(in)g(terms)f(of)h
(the)g(holomorphic)f(section)h(\012:)404 1676 y FE(K)23
b FH(=)f FE(\000)p FH(log)635 1628 y Fs(\020)660 1676
y FH(i)p FE(h)p FH(\012)8 b FE(j)p 758 1637 V 8 w FH(\012)p
FE(i)812 1628 y Fs(\021)860 1676 y FH(=)22 b FE(\000)p
FH(log)1029 1628 y Fs(h)1049 1676 y FH(i)1071 1628 y
Fs(\020)p 1095 1637 45 2 v 1095 1676 a Fv(X)1140 1647
y FC(\003)1166 1676 y Fv(F)1198 1683 y FC(\003)1235 1676
y FE(\000)p 1285 1637 39 2 v 11 w Fv(F)1324 1683 y FC(\006)1351
1676 y Fv(X)1395 1655 y FC(\006)1423 1628 y Fs(\021i)1760
1676 y FH(\(4.25\))-5 1785 y(The)c(relation)f(b)q(et)o(w)o(een)f(the)h
(t)o(w)o(o)g(de\014nitions)h(of)f(sp)q(ecial)g(manifolds)f(is)i
(obtained)f(b)o(y)g(in)o(tro)q(ducing)-5 1845 y(a)g(non{holomorphic)f
(section)g(of)g(the)g(bundle)g FE(H)h FH(according)g(to:)504
1983 y Fv(V)33 b FH(=)625 1910 y Fs( )686 1952 y Fv(L)719
1934 y FC(\003)679 2012 y Fv(M)726 2019 y FC(\006)774
1910 y Fs(!)829 1983 y FE(\021)22 b Fv(e)913 1962 y FB(K)p
Ft(=)p FC(2)977 1983 y FH(\012)h(=)f Fv(e)1118 1962 y
FB(K)p Ft(=)p FC(2)1190 1910 y Fs( )1244 1952 y Fv(X)1288
1934 y FC(\003)1250 2012 y Fv(F)1282 2019 y FC(\006)1335
1910 y Fs(!)1760 1983 y FH(\(4.26\))-5 2120 y(so)17 b(that)g(eq.)e
(4.25)p
 (#equation.4.25) [[129 258 150 270] [1 1 1 [3 3]] [0 0 1]] pdfm 
17 w(b)q(ecomes:)558 2235 y(1)22 b(=)g(i)p FE(h)p Fv(V)e
FE(j)p 767 2196 40 2 v 8 w Fv(V)11 b FE(i)23 b FH(=)f(i)930
2186 y Fs(\020)p 954 2196 34 2 v 954 2235 a Fv(L)988
2205 y FC(\003)1014 2235 y Fv(M)1061 2242 y FC(\003)1099
2235 y FE(\000)p 1149 2196 53 2 v 11 w Fv(M)1201 2242
y FC(\006)1229 2235 y Fv(L)1262 2214 y FC(\006)1289 2186
y Fs(\021)1760 2235 y FH(\(4.27\))-5 2344 y(Since)16
b Fv(V)27 b FH(is)16 b(related)g(to)g(a)h(holomorphic)e(section)h(b)o
(y)g(eq.)f(4.26)p
 (#equation.4.26) [[330 204 351 216] [1 1 1 [3 3]] [0 0 1]] pdfm 
17 w(it)h(imme)o(diatel)o(y)d(follo)o(ws)k(that:)606
2472 y FE(r)648 2479 y Ft(i)660 2470 y Fm(?)680 2472
y Fv(V)33 b FH(=)801 2411 y Fs(\022)832 2472 y Fv(@)858
2479 y Ft(i)870 2470 y Fm(?)901 2472 y FE(\000)955 2438
y FH(1)p 955 2460 25 2 v 955 2506 a(2)985 2472 y Fv(@)1011
2479 y Ft(i)1023 2470 y Fm(?)1043 2472 y FE(K)1082 2411
y Fs(\023)1128 2472 y Fv(V)h FH(=)22 b(0)486 b(\(4.28\))-5
2597 y(On)17 b(the)f(other)g(hand,)g(from)g(eq.)f(4.27)p
 (#equation.4.27) [[220 144 240 156] [1 1 1 [3 3]] [0 0 1]] pdfm (,)h
(de\014ning:)509 2734 y Fv(U)542 2741 y Ft(i)570 2734
y FH(=)e FE(r)664 2741 y Ft(i)677 2734 y Fv(V)25 b FH(=)782
2674 y Fs(\022)813 2734 y Fv(@)839 2741 y Ft(i)864 2734
y FH(+)918 2701 y(1)p 918 2723 V 918 2769 a(2)947 2734
y Fv(@)973 2741 y Ft(i)987 2734 y FE(K)1026 2674 y Fs(\023)1073
2734 y Fv(V)g FE(\021)1178 2661 y Fs( )1243 2704 y Fv(f)1272
2686 y FC(\003)1267 2716 y Ft(i)1232 2764 y Fv(h)1260
2772 y FC(\006)p FB(j)p Ft(i)1330 2661 y Fs(!)1760 2734
y FH(\(4.29\))916 2892 y(18)p eop
%%Page: 19 20
19 19 bop -5 15 a FH(it)16 b(follo)o(ws)g(that:)721 76
y FE(r)763 83 y Ft(i)776 76 y Fv(U)809 83 y Ft(j)842
76 y FH(=)d(i)p Fv(C)942 83 y Ft(ij)r(k)1000 76 y Fv(g)1025
55 y Ft(k)q(`)1058 43 y Fm(?)p 1087 37 39 2 v 1087 76
a Fv(U)1125 83 y Ft(`)1139 74 y Fm(?)1760 76 y FH(\(4.30\))-5
163 y(where)22 b FE(r)184 170 y Ft(i)219 163 y FH(denotes)g(the)g(co)o
(v)m(arian)o(t)f(deriv)m(ativ)o(e)f(con)o(taining)i(b)q(oth)h(the)e
(Levi{Civita)g(connection)-5 223 y(on)h(the)f(bundle)f
FE(T)13 b(M)21 b FH(and)h(the)f(canonical)f(connection)h
Fv(\022)h FH(on)g(the)f(line)f(bundle)g FE(L)p FH(.)36
b(In)21 b(eq.)f(4.30)p
 (#equation.4.30) [[504 713 524 725] [1 1 1 [3 3]] [0 0 1]] pdfm 
-5 283 a(the)e(sym)o(b)q(ol)f Fv(C)285 290 y Ft(ij)r(k)352
283 y FH(denotes)h(a)g(co)o(v)m(arian)o(tly)f(holomorphic)g(\()h
FE(r)1183 290 y Ft(`)1197 281 y Fm(?)1217 283 y Fv(C)1252
290 y Ft(ij)r(k)1318 283 y FH(=)f(0\))h(section)g(of)g(the)f(bundle)-5
343 y FE(T)c(M)95 322 y FC(3)124 343 y FE(\012)8 b(L)205
325 y FC(2)241 343 y FH(that)15 b(is)g(totally)g(symmetri)o(c)d(in)j
(its)g(indices.)20 b(This)15 b(tensor)h(can)f(b)q(e)h(iden)o(ti\014ed)d
(with)i(the)-5 403 y(tensor)i(of)f(eq.)g(4.19)p
 (#equation.4.19) [[138 670 159 682] [1 1 1 [3 3]] [0 0 1]] pdfm 
17 w(app)q(earing)h(in)f(eq.)f(4.18)p
 (#equation.4.18) [[249 670 270 682] [1 1 1 [3 3]] [0 0 1]] pdfm (.)22
b(Alternativ)o(ely)l(,)13 b(the)j(set)g(of)g(di\013eren)o(tial)f
(equations:)773 513 y FE(r)815 520 y Ft(i)829 513 y Fv(V)25
b FH(=)14 b Fv(U)967 520 y Ft(i)1760 513 y FH(\(4.31\))773
585 y FE(r)815 592 y Ft(i)829 585 y Fv(U)862 592 y Ft(j)894
585 y FH(=)g(i)p Fv(C)995 592 y Ft(ij)r(k)1044 585 y
Fv(g)1069 565 y Ft(k)q(`)1102 553 y Fm(?)1123 585 y Fv(U)1156
592 y Ft(`)1170 583 y Fm(?)1760 585 y FH(\(4.32\))773
658 y FE(r)815 665 y Ft(i)827 656 y Fm(?)847 658 y Fv(U)880
665 y Ft(j)912 658 y FH(=)g Fv(g)987 665 y Ft(i)999 656
y Fm(?)1017 665 y Ft(j)1035 658 y Fv(V)697 b FH(\(4.33\))773
731 y FE(r)815 738 y Ft(i)827 729 y Fm(?)847 731 y Fv(V)25
b FH(=)14 b(0)784 b(\(4.34\))-5 840 y(with)18 b(V)g(satisfying)g(eq.s)f
(4.26)p
 (#equation.4.26) [[187 565 208 577] [1 1 1 [3 3]] [0 0 1]] pdfm (,)i
(4.27)p
 (#equation.4.27) [[216 565 236 577] [1 1 1 [3 3]] [0 0 1]] pdfm 
19 w(giv)o(e)e(y)o(et)g(another)i(de\014nition)e(of)h(sp)q(ecial)g
(geometry)l(.)25 b(This)18 b(is)-5 900 y(actually)h(what)i(one)e
(obtains)i(from)d(the)i Fv(N)25 b FH(=)19 b(2)h(solution)g(of)g(Bianc)o
(hi)e(iden)o(tities)g(\(see)h(app)q(endix)-5 961 y(A\).)e(In)g
(particular)g(it)h(is)f(easy)h(to)g(\014nd)f(eq.)g(4.18)p
 (#equation.4.18) [[268 536 289 548] [1 1 1 [3 3]] [0 0 1]] pdfm 
18 w(as)i(in)o(tegrabilit)o(y)c(conditions)j(of)f(4.34)p
 (#equation.4.31) [[444 536 465 548] [1 1 1 [3 3]] [0 0 1]] pdfm 
19 w(The)g Fu(p)n(erio)n(d)-5 1021 y(matrix)f FH(is)g(no)o(w)h(in)o
(tro)q(duced)f(via)g(the)g(relations:)p 578 1091 53 2
v 578 1130 a Fv(M)630 1137 y FC(\003)670 1130 y FH(=)p
722 1091 49 2 v 14 w FE(N)770 1137 y FC(\003\006)p 822
1091 34 2 v 822 1130 a Fv(L)856 1101 y FC(\006)932 1130
y FH(;)57 b Fv(h)1031 1138 y FC(\006)p FB(j)p Ft(i)1094
1130 y FH(=)p 1146 1091 49 2 v 14 w FE(N)1194 1137 y
FC(\003\006)1246 1130 y Fv(f)1275 1110 y FC(\006)1270
1143 y Ft(i)1760 1130 y FH(\(4.35\))-5 1240 y(whic)o(h)16
b(can)g(b)q(e)h(solv)o(ed)e(in)o(tro)q(ducing)h(the)g(t)o(w)o(o)g(\()p
Fv(n)c FH(+)f(1\))g FE(\002)g FH(\()p Fv(n)g FH(+)g(1\))17
b(v)o(ectors)561 1383 y Fv(f)590 1363 y FC(\003)585 1395
y Ft(I)631 1383 y FH(=)682 1310 y Fs( )738 1348 y Fv(f)767
1330 y FC(\003)762 1360 y Ft(i)p 736 1379 34 2 v 736
1418 a Fv(L)769 1388 y FC(\003)816 1310 y Fs(!)906 1383
y FH(;)57 b Fv(h)1005 1391 y FC(\003)p FB(j)p Ft(I)1073
1383 y FH(=)1125 1310 y Fs( )1180 1352 y Fv(h)1208 1360
y FC(\003)p FB(j)p Ft(i)p 1179 1374 53 2 v 1179 1413
a Fv(M)1231 1420 y FC(\003)1278 1310 y Fs(!)1760 1383
y FH(\(4.36\))-5 1524 y(and)17 b(setting:)p 703 1558
49 2 v 703 1597 a FE(N)751 1604 y FC(\003\006)817 1597
y FH(=)c Fv(h)896 1605 y FC(\003)p FB(j)p Ft(I)962 1597
y FE(\016)998 1549 y Fs(\020)1023 1597 y Fv(f)1052 1576
y FB(\000)p FC(1)1099 1549 y Fs(\021)1124 1560 y Ft(I)1142
1624 y FC(\006)1760 1597 y FH(\(4.37\))-5 1689 y(As)h(a)h(consequence)e
(of)i(its)f(de\014nition)f(the)h(matrix)f FE(N)21 b FH(transforms,)14
b(under)h(di\013eomorphisms)d(of)i(the)-5 1750 y(base)j(K\177)-24
b(ahler)16 b(manifold)f(exactly)g(as)h(it)g(is)g(requested)g(b)o(y)f
(the)h(rule)g(in)g(eq.)f(2.38)p
 (#equation.2.38) [[406 347 427 359] [1 1 1 [3 3]] [0 0 1]] pdfm (.)22
b(Indeed)15 b(this)h(is)g(the)-5 1810 y(v)o(ery)f(reason)i(wh)o(y)e
(the)h(structure)f(of)i(sp)q(ecial)e(geometry)f(has)j(b)q(een)f(in)o
(tro)q(duced.)21 b(The)16 b(existence)e(of)-5 1870 y(the)j(symplectic)d
(bundle)j FE(H)24 b(\000)-8 b(!)23 b(M)17 b FH(is)g(required)f(in)h
(order)g(to)h(b)q(e)f(able)g(to)h(pull{bac)o(k)e(the)h(action)-5
1930 y(of)g(the)f(di\013eomorphisms)e(on)j(the)f(\014eld)g(strengths)g
(and)h(to)g(construct)f(the)g(kinetic)f(matrix)f FE(N)7
b FH(.)68 1990 y(F)l(rom)16 b(the)h(previous)g(form)o(ulae)e(it)h(is)h
(easy)g(to)h(deriv)o(e)d(a)i(set)g(of)g(useful)g(relations)g(among)g
(whic)o(h)-5 2051 y(w)o(e)f(quote)g(the)g(follo)o(wing)g([20)p
 (#cite.CDFp) [[193 275 205 287] [1 1 1 [3 3]] [0 0 1]] pdfm (]:)278
2182 y(Im)n FE(N)377 2189 y FC(\003\006)429 2182 y Fv(L)462
2162 y FC(\003)p 489 2143 34 2 v 489 2182 a Fv(L)522
2153 y FC(\006)591 2182 y FH(=)42 b FE(\000)715 2148
y FH(1)p 715 2171 25 2 v 715 2216 a(2)1760 2182 y(\(4.38\))411
2270 y FE(h)p Fv(V)s(;)8 b(U)516 2277 y Ft(i)530 2270
y FE(i)42 b FH(=)g FE(h)p Fv(V)s(;)8 b(U)776 2277 y Ft(i)788
2268 y Fm(?)808 2270 y FE(i)14 b FH(=)g(0)843 b(\(4.39\))170
2365 y Fv(U)208 2345 y FC(\003\006)283 2365 y FE(\021)21
b Fv(f)372 2345 y FC(\003)367 2377 y Ft(i)408 2365 y
Fv(f)437 2345 y FC(\006)432 2377 y Ft(j)448 2368 y Fm(?)476
2365 y Fv(g)501 2345 y Ft(ij)529 2333 y Fm(?)591 2365
y FH(=)42 b FE(\000)715 2331 y FH(1)p 715 2354 V 715
2399 a(2)760 2365 y(\(Im)o FE(N)7 b FH(\))905 2341 y
FB(\000)p FC(1)p FB(j)p FC(\003\006)1031 2365 y FE(\000)p
1089 2326 34 2 v 19 w Fv(L)1122 2336 y FC(\003)1149 2365
y Fv(L)1182 2345 y FC(\006)1760 2365 y FH(\(4.40\))478
2459 y Fv(g)501 2466 y Ft(ij)529 2457 y Fm(?)591 2459
y FH(=)42 b FE(\000)p FH(i)p FE(h)8 b Fv(U)784 2466 y
Ft(i)806 2459 y FE(j)p 828 2420 39 2 v 8 w Fv(U)867 2466
y Ft(j)883 2457 y Fm(?)911 2459 y FE(i)14 b FH(=)g FE(\000)p
FH(2)p Fv(f)1088 2439 y FC(\003)1083 2472 y Ft(i)1115
2459 y FH(Im)h FE(N)1231 2466 y FC(\003\006)1283 2459
y Fv(f)1312 2439 y FC(\006)1307 2472 y Ft(j)1323 2462
y Fm(?)1359 2459 y FH(;)387 b(\(4.41\))465 2538 y Fv(C)500
2545 y Ft(ij)r(k)591 2538 y FH(=)42 b FE(h)8 b(r)740
2545 y Ft(i)754 2538 y Fv(U)787 2545 y Ft(j)814 2538
y FE(j)g Fv(U)869 2545 y Ft(k)898 2538 y FE(i)15 b FH(=)e
Fv(f)1012 2517 y FC(\003)1007 2550 y Ft(i)1039 2538 y
Fv(@)1065 2545 y Ft(j)p 1083 2499 49 2 v 1083 2538 a
FE(N)1132 2545 y FC(\003\006)1184 2538 y Fv(f)1213 2517
y FC(\006)1208 2550 y Ft(k)1254 2538 y FH(=)h(\()p FE(N)k(\000)p
1434 2499 V 11 w(N)7 b FH(\))1501 2545 y FC(\003\006)1553
2538 y Fv(f)1582 2517 y FC(\003)1577 2550 y Ft(i)1609
2538 y Fv(@)1635 2545 y Ft(j)1653 2538 y Fv(f)1682 2517
y FC(\006)1677 2550 y Ft(k)1760 2538 y FH(\(4.42\))-5
2647 y(In)18 b(particular)f(eq.s)g(4.42)p
 (#equation.4.38) [[164 132 184 144] [1 1 1 [3 3]] [0 0 1]] pdfm 
19 w(express)g(the)h(K\177)-24 b(ahler)17 b(metric)f(and)i(the)g
(anomalous)g(magnetic)e(momen)o(ts)-5 2707 y(in)j(terms)f(of)h
(symplectic)d(in)o(v)m(arian)o(ts.)29 b(It)19 b(is)g(clear)f(from)g
(our)i(discussion)f(that)g(no)o(where)g(w)o(e)g(ha)o(v)o(e)-5
2768 y(assumed)h(the)g(base)h(K\177)-24 b(ahler)20 b(manifold)f(to)h(b)
q(e)h(a)g(homogeneous)f(space.)33 b(So,)22 b(in)e(general,)h(sp)q
(ecial)916 2892 y(19)p eop
%%Page: 20 21
20 20 bop -5 15 a FH(manifolds)11 b(are)g(not)h(homogeneous)g(spaces.)
20 b(Y)l(et)10 b(there)h(is)h(a)f(sub)q(class)i(of)f(homogenous)g(sp)q
(ecial)f(man-)-5 76 y(ifolds.)28 b(The)19 b(homogeneous)g(symmetri)o(c)
d(ones)j(w)o(ere)f(classi\014ed)g(b)o(y)g(Cremmer)d(and)20
b(V)l(an)e(Pro)q(ey)o(en)-5 136 y(in)e([61)p
 (#cite.cremvanp) [[88 734 99 746] [1 1 1 [3 3]] [0 0 1]] pdfm 
1 w(])f(and)i(are)g(displa)o(y)o(ed)e(in)h(table)g(1)p
 (#table.1) [[243 734 249 746] [1 1 1 [3 3]] [0 0 1]] pdfm (.)22
b(It)15 b(go)q(es)j(without)e(sa)o(ying)h(that)g(for)f(homogeneous)h
(sp)q(ecial)-5 196 y(manifolds)11 b(the)i(t)o(w)o(o)f(constructions)g
(of)h(the)f(p)q(erio)q(d)h(matrix,)e(that)i(pro)o(vided)e(b)o(y)h(the)g
(master)f(form)o(ula)-5 256 y(in)18 b(eq.)f(3.17)p
 (#equation.3.17) [[104 706 125 718] [1 1 1 [3 3]] [0 0 1]] pdfm 
18 w(and)i(that)f(giv)o(en)f(b)o(y)g(eq.)g(4.37)p
 (#equation.4.37) [[244 706 265 718] [1 1 1 [3 3]] [0 0 1]] pdfm 
19 w(m)o(ust)f(agree.In)i(App)q(endix)f(C)h(w)o(e)f(shall)h(shortly)g
(v)o(erify)-5 316 y(it)g(in)h(the)f(case)h(of)f(the)h(manifolds)e
FE(S)t(T)c FH([2)p Fv(;)8 b(n)p FH(])18 b(that)h(corresp)q(ond)h(to)f
(the)f(second)h(in\014nite)e(family)g(of)-5 377 y(homogeneous)g(sp)q
(ecial)e(manifolds)h(displa)o(y)o(ed)f(in)g(table)33
b(1)p  (#table.1) [[332 677 337 689] [1 1 1 [3 3]] [0 0 1]] pdfm (.)68
437 y(An)o(yho)o(w,)20 b(since)f(sp)q(ecial)g(geometry)g(guaran)o(tees)
h(the)f(existence)f(of)i(a)h(kinetic)d(p)q(erio)q(d)i(matrix)-5
497 y(with)g(the)f(correct)g(co)o(v)m(ariance)g(prop)q(ert)o(y)h(it)f
(is)h(eviden)o(t)e(that)i(to)g(eac)o(h)f(sp)q(ecial)g(manifold)g(w)o(e)
g(can)-5 557 y(asso)q(ciate)12 b(a)g(dualit)o(y)e(co)o(v)m(arian)o(t)h
(b)q(osonic)h(Lagrangian)i(of)d(the)g(t)o(yp)q(e)g(considered)g(in)g
(eq.)f(2.5)p
 (#equation.2.5) [[458 633 473 645] [1 1 1 [3 3]] [0 0 1]] pdfm (.)20
b(Ho)o(w)o(ev)o(er)-5 617 y(sp)q(ecial)d(geometry)e(con)o(tains)i(more)
e(structures)i(than)g(just)g(the)g(p)q(erio)q(d)g(matrix)e
FE(N)24 b FH(and)17 b(the)g(scalar)-5 678 y(metric)d
Fv(g)170 685 y Ft(ij)198 676 y Fm(?)219 678 y FH(.)21
b(All)15 b(the)h(other)g(items)e(of)j(the)e(construction)i(do)f(ha)o(v)
o(e)g(a)g(place)g(and)h(pla)o(y)e(an)i(essen)o(tial)-5
738 y(role)f(in)g(the)g(sup)q(ergra)o(vit)o(y)g(Lagrangian)i(and)f(the)
f(sup)q(ersymmetry)d(transformation)k(rules.)-5 881 y
Fk(4.4)66 b(Sp)r(ecial)24 b(K\177)-33 b(ahler)22 b(manifolds:)30
b(the)23 b(rigid)h(case)-5 973 y FH(Let)17 b FE(M)f FH(b)q(e)g(a)g
(K\177)-24 b(ahler)16 b(manifold)f(with)h(dim)819 980
y Ff(C)859 973 y FE(M)22 b FH(=)g Fv(n)16 b FH(and)h(let)e
FE(L)23 b(\000)-9 b(!)22 b(M)16 b FH(b)q(e)h(a)f FD(\015at)g
FH(line)f(bundle)-5 1034 y Fv(c)16 1041 y FC(1)36 1034
y FH(\()p FE(L)p FH(\))k(=)g(0)208 1016 y FC(3)p
 (#Hfootnote.3) [[122 519 127 531] [1 1 1 [3 3]] [0 0 1]] pdfm 
228 1034 a FH(.)31 b(Let)19 b FE(S)t(V)31 b(\000)-9 b(!)27
b(M)20 b FH(denote)f(a)g(holomorphic)g FD(\015at)g FH(v)o(ector)f
(bundle)h(of)h(rank)f(2)p Fv(n)h FH(with)-5 1094 y(structural)13
b(group)h Fv(I)t(S)s(p)p FH(\(2)p Fv(n;)8 b FH(I)-9 b(R)o(\).)20
b(Consider)13 b(tensor)h(bundles)e(of)h(the)g(t)o(yp)q(e)f
FE(H)23 b FH(=)f FE(S)t(V)7 b(\012)t(L)p FH(.)20 b(A)12
b(t)o(ypical)-5 1154 y(holomorphic)18 b(section)h(of)h(suc)o(h)f(a)h
(bundle)f(will)f(b)q(e)i(denoted)f(b)o(y)g(\012)h(and)f(will)g(ha)o(v)o
(e)f(the)h(follo)o(wing)-5 1214 y(structure:)620 1293
y(\012)k(=)738 1220 y Fs( )791 1263 y Fv(Y)830 1245 y
Ft(I)793 1323 y Fv(F)825 1330 y Ft(J)871 1220 y Fs(!)953
1293 y Fv(I)t(;)8 b(J)18 b FH(=)13 b(1)p Fv(;)8 b(:)g(:)g(:)g(;)g(n)500
b FH(\(4.43\))-5 1406 y(By)24 b(de\014nition)g(the)g(transition)g
(functions)h(b)q(et)o(w)o(een)e(t)o(w)o(o)h(lo)q(cal)g(trivializations)
f Fv(U)1614 1413 y Ft(i)1656 1406 y FE(\032)k(M)d FH(and)-5
1466 y Fv(U)28 1473 y Ft(j)60 1466 y FE(\032)14 b(M)i
FH(of)h(the)f(bundle)g FE(H)g FH(ha)o(v)o(e)g(the)g(follo)o(wing)g
(form:)672 1528 y Fs( )725 1571 y Fv(Y)726 1631 y(F)785
1528 y Fs(!)818 1653 y Ft(i)846 1601 y FH(=)e Fv(e)926
1575 y Fs(b)921 1580 y Ft(f)938 1585 y Fm(ij)g Fs(c)967
1601 y Fv(M)1014 1608 y Ft(ij)1044 1528 y Fs( )1098 1571
y Fv(Y)1098 1631 y(F)1158 1528 y Fs(!)1190 1653 y Ft(j)1760
1601 y FH(\(4.44\))-5 1753 y(where)148 1737 y Fs(b)136
1753 y Fv(f)160 1760 y Ft(ij)205 1753 y FE(2)p 261 1753
2 33 v 10 w FH(C)i(are)h(purely)e(imaginary)h(complex)e(n)o(um)o(b)q
(ers)h(while)1286 1737 y Fs(c)1276 1753 y Fv(M)1323 1760
y Ft(ij)1370 1753 y FH(denotes)i(the)f(action)h(of)g(an)-5
1819 y(elemen)o(t)d(\()205 1803 y Fs(c)195 1819 y Fv(M)5
b(;)j(c)p FH(\))15 b FE(2)g Fv(I)t(S)s(p)p FH(\(2)p Fv(n;)8
b FH(I)-9 b(R\))17 b(on)g(\012.)780 1803 y Fs(c)770 1819
y Fv(M)23 b FH(is)16 b(a)h(symplectic)d(matrix)1340 1803
y Fs(c)1330 1819 y Fv(M)20 b FE(2)c Fv(S)s(p)p FH(\(2)p
Fv(n;)8 b FH(I)-9 b(R\))17 b(and)g Fv(c)g FH(is)g(a)-5
1879 y Fv(n)p FH(-v)o(ector:)572 1951 y(\()608 1934 y
Fs(c)599 1951 y Fv(M)54 b(c)8 b FH(\))757 1890 y Fs(\022)795
1921 y Fv(Y)796 1981 y(F)843 1890 y Fs(\023)887 1951
y FH(=)949 1934 y Fs(c)939 1951 y Fv(M)1000 1890 y Fs(\022)1039
1921 y Fv(V)1039 1981 y(F)1086 1890 y Fs(\023)1128 1951
y FH(+)1177 1890 y Fs(\022)1216 1921 y FH(0)1217 1981
y Fv(c)1248 1890 y Fs(\023)1303 1951 y Fv(:)443 b FH(\(4.45\))-5
2056 y(F)l(or)16 b(a)g(consisten)o(t)f(de\014nition)g(of)h(the)g
(bundle)f(the)g(transition)h(functions)g(are)g(ob)o(viously)f(sub)s
(ject)g(to)-5 2116 y(the)h(co)q(cycle)f(condition)h(on)h(a)g(triple)e
(o)o(v)o(erlap:)760 2228 y Fv(e)788 2202 y Fs(b)783 2207
y Ft(f)800 2212 y Fm(ij)826 2208 y FC(+)858 2203 y Fs(b)853
2208 y Ft(f)870 2214 y Fm(j)q(k)904 2208 y FC(+)936 2203
y Fs(b)931 2208 y Ft(f)948 2214 y Fm(k)q(i)1022 2228
y FH(=)42 b(1)748 2285 y Fs(c)738 2301 y Fv(M)785 2308
y Ft(ij)825 2285 y Fs(c)815 2301 y Fv(M)862 2308 y Ft(j)r(k)910
2285 y Fs(c)900 2301 y Fv(M)947 2308 y Ft(k)q(i)1022
2301 y FH(=)g(1)-17 b(1)627 b(\(4.46\))-5 2404 y(Let)17
b Fv(i)p FE(h)f(j)g(i)h FH(b)q(e)f(the)g(compatible)e(hermitian)h
(metric)e(on)k FE(H)613 2537 y FH(i)p FE(h)p FH(\012)8
b FE(j)p 711 2498 36 2 v 8 w FH(\012)q FE(i)22 b(\021)g(\000)p
FH(i\012)937 2517 y Ft(T)973 2464 y Fs( )1049 2507 y
FH(0)65 b(1)-17 b(1)1026 2567 y FE(\000)p FH(1)g(1)46
b(0)1191 2464 y Fs(!)p 1232 2498 V 1232 2537 a FH(\012)493
b(\(4.47\))p -5 2672 756 2 v 51 2703 a Fq(3)70 2718 y
Fx(the)11 b(holomorphic)d(sections)k(of)e Fl(L)g Fx(w)o(ould)g(b)q(e)h
(the)g(p)q(ossible)g(sup)q(erp)q(oten)o(tials)h(if)d
Fl(M)i Fx(w)o(ere)g(used)h(as)e(scalar)h(manifold)-5
2768 y(in)j(an)f Fp(N)k Fx(=)12 b(1)h(globally)f(sup)q(ersymmetric)h
(theory)m(.)916 2892 y FH(20)p eop
%%Page: 21 22
21 21 bop -5 15 a FD(De\014nition)18 b(4.3)24 b Fu(We)f(say)f(that)h(a)
f(Ho)n(dge{K\177)-25 b(ahler)24 b(manifold)f FE(M)f Fu(is)h
FD(sp)r(ecial)h(K\177)-28 b(ahler)24 b(of)i(the)-5 76
y(rigid)g(t)n(yp)r(e)c Fu(if)h(ther)n(e)h(exists)g(a)f(bund)r(le)j
FE(H)e Fu(of)f(the)h(typ)n(e)f(describ)n(e)n(d)h(ab)n(ove)g(such)g
(that)f(for)g(some)-5 136 y(se)n(ction)164 120 y Fs(b)158
136 y FH(\012)g FE(2)f FH(\000\()p FE(H)p Fv(;)8 b FE(M)p
FH(\))18 b Fu(the)g(K\177)-25 b(ahler)18 b(two)g(form)f(is)g(given)i
(by:)675 269 y Fv(K)e FH(=)23 b FE(\000)864 235 y Fv(i)p
846 257 54 2 v 846 303 a FH(2)p Fv(\031)904 269 y(@)p
933 229 29 2 v 3 w(@)970 208 y Fs(\022)1000 269 y FH(i)p
FE(h)1039 252 y Fs(b)1033 269 y FH(\012)9 b FE(j)1105
244 y Fs(b)p 1099 230 36 2 v 1099 269 a FH(\012)p FE(i)1153
208 y Fs(\023)1192 269 y Fv(:)554 b FH(\(4.48\))-5 395
y(Just)16 b(as)g(in)g(the)f(lo)q(cal)g(case)h(eq.)e(4.48)p
 (#equation.4.48) [[214 672 235 684] [1 1 1 [3 3]] [0 0 1]] pdfm 
16 w(yields)h(an)h(expression)f(for)h(the)f(K\177)-24
b(ahler)15 b(p)q(oten)o(tial)h(in)f(terms)f(of)-5 455
y(the)i(holomorphic)f(section)527 439 y Fs(b)521 455
y FH(\012:)488 581 y FE(K)43 b FH(=)648 520 y Fs(\022)679
581 y FH(i)p FE(h)718 564 y Fs(b)712 581 y FH(\012)8
b FE(j)783 556 y Fs(b)p 777 542 V 777 581 a FH(\012)p
FE(i)831 520 y Fs(\023)904 581 y FH(=)983 533 y Fs(h)1003
581 y FH(i)1025 533 y Fs(\020)p 1050 542 40 2 v 48 x
Fv(Y)1089 551 y Ft(I)1109 581 y Fv(F)1141 588 y Ft(I)1171
581 y FE(\000)p 1221 542 39 2 v 11 w Fv(F)1259 588 y
Ft(J)1284 581 y Fv(Y)1323 563 y Ft(J)1348 533 y Fs(\021)o(i)1760
581 y FH(\(4.49\))-5 707 y(Similarly)14 b(de\014ning)727
779 y Fs(b)718 795 y Fv(U)751 802 y Ft(i)779 795 y FH(=)g
Fv(@)857 802 y Ft(i)877 779 y Fs(b)871 795 y FH(\012)g
FE(\021)972 722 y Fs( )1038 765 y Fv(f)1067 747 y Ft(I)1062
777 y(i)1026 825 y Fv(h)1054 833 y Ft(J)s FB(j)p Ft(i)1121
722 y Fs(!)1760 795 y FH(\(4.50\))-5 911 y(one)j(\014nds:)721
971 y Fv(D)761 978 y Ft(i)785 955 y Fs(b)776 971 y Fv(U)809
978 y Ft(j)841 971 y FH(=)d(i)p Fv(C)942 978 y Ft(ij)r(k)999
971 y Fv(g)1024 950 y Ft(k)q(`)1057 939 y Fm(?)1094 946
y Fs(b)p 1086 932 V 1086 971 a Fv(U)1125 978 y Ft(`)1139
969 y Fm(?)1760 971 y FH(\(4.51\))-5 1058 y(where)j Fv(D)177
1065 y Ft(i)209 1058 y FH(is)h(the)f(co)o(v)m(arian)o(t)g(deriv)m(ativ)
o(e)f(with)h(resp)q(ect)g(to)h(the)f(Levi{Civita)f(connection)i(on)f
FE(T)c(M)-5 1118 y FH(and)23 b(where)f Fv(C)278 1125
y Ft(ij)r(k)350 1118 y FH(is)g(a)h(totally)f(symmetri)o(c)d
(holomorphic)i(section)h(of)h(the)f(bundle)g FE(T)13
b(M)1729 1097 y FC(3)1763 1118 y FE(\012)i(L)1851 1100
y FC(2)1871 1118 y FH(:)-5 1178 y Fv(@)21 1185 y Ft(`)35
1176 y Fm(?)56 1178 y Fv(C)91 1185 y Ft(ij)r(k)154 1178
y FH(=)f(0.)20 b(Just)12 b(as)g(in)f(the)h(lo)q(cal)g(case)f(w)o(e)g
(ma)o(y)g(alternativ)o(ely)e(de\014ne)j(the)f(rigid)g(sp)q(ecial)h
(geometry)-5 1239 y(b)o(y)k(the)g(follo)o(wing)g(set)g(of)h(di\013eren)
o(tial)e(equations:)935 1349 y Fv(@)961 1356 y Ft(i)973
1347 y Fm(?)998 1332 y Fs(b)992 1349 y FH(\012)f(=)g(0)643
b(\(4.52\))939 1405 y Fs(b)930 1421 y Fv(U)963 1428 y
Ft(i)991 1421 y FH(=)14 b Fv(@)1069 1428 y Ft(i)1088
1405 y Fs(b)1082 1421 y FH(\012)643 b(\(4.53\))680 1505
y Fv(D)720 1512 y Ft(i)743 1489 y Fs(b)734 1505 y Fv(U)767
1512 y Ft(j)800 1505 y FH(=)13 b(i)p Fv(C)900 1512 y
Ft(ij)r(k)958 1505 y Fv(g)983 1484 y Ft(k)q(`)1016 1472
y Fm(?)1052 1480 y Fs(b)p 1045 1466 V 1045 1505 a Fv(U)1083
1512 y Ft(`)1097 1503 y Fm(?)1760 1505 y FH(\(4.54\))-5
1615 y(.)25 b(The)18 b(in)o(tegrabilit)o(y)d(condition)j(of)g(eq.)e
(4.54)p
 (#equation.4.52) [[255 379 276 391] [1 1 1 [3 3]] [0 0 1]] pdfm 
18 w(is)i(similar)d(but)j(di\013eren)o(t)f(from)f(eq.)h(4.18)p
 (#equation.4.18) [[446 379 467 391] [1 1 1 [3 3]] [0 0 1]] pdfm 
18 w(due)g(to)h(the)-5 1675 y(replacemen)o(t)c(of)i(the)g(co)o(v)m
(arian)o(t)h(deriv)m(ativ)o(e)d(on)j FE(T)c(M)e(\002)g(L)16
b FH(b)o(y)g(that)h(on)g FE(T)c(M)o FH(,)j(due)h(to)f(the)g(\015atness)
-5 1735 y(of)h FE(L)p FH(.)k(W)l(e)16 b(get)610 1845
y Fv(@)636 1852 y Ft(m)667 1843 y Fn(\003)687 1845 y
Fv(C)722 1852 y Ft(ij)r(k)813 1845 y FH(=)41 b(0)49 b
Fv(@)991 1852 y Ft(m)1024 1845 y Fv(C)1059 1852 y Ft(i)1071
1843 y Fn(\003)1089 1852 y Ft(j)1105 1843 y Fn(\003)1123
1852 y Ft(k)1142 1843 y Fn(\003)1176 1845 y FH(=)14 b(0)592
1918 y FE(r)634 1926 y FC([)p Ft(m)677 1918 y Fv(C)712
1926 y Ft(i)p FC(])p Ft(j)r(k)813 1918 y FH(=)41 b(0)49
b FE(r)1007 1926 y FC([)p Ft(m)1050 1918 y Fv(C)1085
1926 y Ft(i)1097 1916 y Fn(\003)1115 1926 y FC(])p Ft(j)1141
1916 y Fn(\003)1159 1926 y Ft(k)1178 1916 y Fn(\003)1212
1918 y FH(=)14 b(0)629 1990 y FE(R)671 1997 y Ft(i)683
1988 y Fn(\003)701 1997 y Ft(j)r(`)731 1988 y Fn(\003)750
1997 y Ft(k)813 1990 y FH(=)41 b FE(\000)p Fv(C)966 1997
y Ft(i)978 1988 y Fn(\003)996 1997 y Ft(`)1010 1988 y
Fn(\003)1028 1997 y Ft(s)1044 1988 y Fn(\003)1064 1990
y Fv(C)1099 1997 y Ft(tk)q(j)1150 1990 y Fv(g)1175 1970
y Ft(s)1191 1958 y Fn(\003)1209 1970 y Ft(t)1760 1990
y FH(\(4.55\))-5 2100 y(whic)o(h)15 b(are)g(the)f(rigid)h(coun)o
(terpart)g(of)g(4.18)p
 (#equation.4.18) [[246 263 267 275] [1 1 1 [3 3]] [0 0 1]] pdfm (.)22
b(The)15 b(de\014nition)f(of)i(the)e Fu(p)n(erio)n(d)h(matrix)g
FH(is)g(obtained)g(in)-5 2161 y(full)h(analogy)h(to)f(eq.)g(4.35)p
 (#equation.4.35) [[168 248 188 260] [1 1 1 [3 3]] [0 0 1]] pdfm (:)800
2221 y Fv(h)828 2229 y Ft(I)s FB(j)p Ft(i)884 2221 y
FH(=)p 936 2182 49 2 v 14 w FE(N)984 2228 y Ft(I)s(J)1026
2221 y Fv(f)1055 2200 y Ft(J)1050 2233 y(i)1760 2221
y FH(\(4.56\))-5 2308 y(that)h(yields:)p 718 2341 V 718
2380 a FE(N)766 2387 y Ft(I)s(J)823 2380 y FH(=)c Fv(h)902
2388 y Ft(I)s FB(j)p Ft(i)955 2380 y FE(\016)991 2332
y Fs(\020)1016 2380 y Fv(f)1045 2360 y FB(\000)p FC(1)1093
2332 y Fs(\021)1117 2344 y Ft(i)1129 2407 y(J)1760 2380
y FH(\(4.57\))-5 2473 y(Finally)e(w)o(e)h(observ)o(e)g(that,)h(exactly)
e(as)j(in)e(the)g(lo)q(cal)g(case,)h(the)f(metric)e(and)j(the)f
(magnetic)f(momen)o(ts)-5 2533 y(can)17 b(b)q(e)f(expressed)g(in)g
(terms)e(of)j(the)f(symplectic)d(sections:)447 2649 y
Fv(g)470 2656 y Ft(ij)498 2647 y Fm(?)560 2649 y FH(=)42
b FE(\000)p FH(i)p FE(h)729 2633 y Fs(b)720 2649 y Fv(U)753
2656 y Ft(i)775 2649 y FE(j)805 2625 y Fs(b)p 797 2610
39 2 v 797 2649 a Fv(U)836 2656 y Ft(j)852 2647 y Fm(?)880
2649 y FE(i)g FH(;)f Fv(C)1031 2656 y Ft(ij)r(k)1122
2649 y FH(=)h FE(h)8 b Fv(@)1255 2656 y Ft(i)1278 2633
y Fs(b)1269 2649 y Fv(U)1302 2656 y Ft(j)1329 2649 y
FE(j)1360 2633 y Fs(b)1351 2649 y Fv(U)1384 2656 y Ft(k)1414
2649 y FE(i)1760 2643 y FH(\(4.58\))916 2892 y(21)p eop
%%Page: 22 23
22 22 bop -5 15 a Fk(4.5)66 b(Sp)r(ecial)24 b(K\177)-33
b(ahler)22 b(manifolds:)30 b(the)23 b(issue)f(of)f(sp)r(ecial)i(co)r
(ordinates)-5 108 y FH(So)18 b(far)g(no)f(privileged)f(co)q(ordinate)i
(system)e(has)i(b)q(een)f(c)o(hosen)g(on)h(the)f(base)g(K\177)-24
b(ahler)17 b(manifold)f FE(M)-5 168 y FH(and)h(no)g(men)o(tion)d(has)j
(b)q(een)f(made)f(of)h(the)g(holomorphic)f(prep)q(oten)o(tial)h
Fv(F)7 b FH(\()p Fv(X)t FH(\))16 b(that)g(is)g(ubiquitous)-5
228 y(in)g(the)f Fv(N)k FH(=)14 b(2)i(literature.)k(The)15
b(sim)o(ultaneous)g(a)o(v)o(oidance)g(of)h(privileged)e(co)q(ordinates)
i(and)g(of)g(the)-5 288 y(prep)q(oten)o(tial)g(is)h(not)g(acciden)o
(tal.)j(Indeed,)c(when)g(the)h(de\014nition)f(of)h(sp)q(ecial)f(K\177)
-24 b(ahler)16 b(manifolds)f(is)-5 349 y(giv)o(en)c(in)h(in)o(trinsic)e
(terms,)h(as)i(w)o(e)f(did)f(in)h(the)g(previous)g(subsection,)g(the)g
(holomorphic)f(prep)q(oten)o(tial)-5 409 y Fv(F)c FH(\()p
Fv(X)t FH(\))19 b(can)g(b)q(e)g(disp)q(ensed)g(of.)30
b(Whether)18 b(a)i(prep)q(oten)o(tial)e Fv(F)7 b FH(\()p
Fv(X)t FH(\))19 b(exists)f(or)h(not)h(dep)q(ends)f(on)g(the)-5
469 y(c)o(hoice)h(of)h(a)h(symplectic)17 b(gauge)22 b(whic)o(h)f(is)f
(immaterial)e(in)i(the)h(ab)q(elian)g(theory)g(but)g(not)h(in)e(the)-5
529 y(gauged)e(one.)23 b(Actually)l(,)14 b(in)j(the)f(lo)q(cal)g(case,)
h(it)f(app)q(ears)i(that)f(some)e(ph)o(ysically)g(in)o(teresting)h
(cases)-5 589 y(are)d(precisely)d(instances)j(where)f
Fv(F)7 b FH(\()p Fv(X)t FH(\))12 b(do)q(es)h(not)g(exist.)19
b(On)12 b(the)g(con)o(trary)g(the)h(prep)q(oten)o(tial)e
Fv(F)c FH(\()p Fv(X)t FH(\))-5 650 y(seems)15 b(to)h(b)q(e)g(a)h
(necessary)f(ingredien)o(t)e(in)i(the)g(tensor)g(calculus)f
(constructions)i(of)f Fv(N)j FH(=)14 b(2)i(theories)-5
710 y(that)e(for)f(this)g(reason)h(are)f(not)g(completely)e(general.)19
b(This)14 b(happ)q(ens)g(b)q(ecause)f(tensor)g(calculus)g(uses)-5
770 y(sp)q(ecial)j(co)q(ordinates)g(from)f(the)g(v)o(ery)f(start.)22
b(Let)16 b(us)g(then)f(see)h(ho)o(w)g(the)f(notion)h(of)g
Fv(F)7 b FH(\()p Fv(X)t FH(\))16 b(emerges)-5 830 y(if)g(w)o(e)g
(resort)g(to)h(sp)q(ecial)f(co)q(ordinate)g(systems.)68
890 y(Note)22 b(that)h(under)f(a)g(K\177)-24 b(ahler)22
b(transformation)g FE(K)33 b(!)f(K)16 b FH(+)f Fv(f)5
b FH(\()p Fv(z)r FH(\))15 b(+)p 1418 851 30 2 v 15 w
Fv(f)5 b FH(\()p 1466 864 25 2 v Fv(z)r FH(\))22 b(the)g(holomorphic)-5
951 y(section)e(transforms,)h(in)f(the)g(lo)q(cal)h(case,)g(as)g(\012)
29 b FE(!)g FH(\012)8 b Fv(e)1088 932 y FB(\000)p Ft(f)1139
951 y FH(,)21 b(so)g(that)g(w)o(e)f(ha)o(v)o(e)f Fv(X)1584
932 y FC(\003)1640 951 y FE(!)30 b Fv(X)1764 932 y FC(\003)1799
951 y Fv(e)1822 932 y FB(\000)p Ft(f)1871 951 y FH(.)-5
1011 y(This)19 b(means)f(that,)i(at)f(least)g(lo)q(cally)l(,)f(the)h
(upp)q(er)g(half)g(of)g(\012)h(\(asso)q(ciated)f(with)g(the)g(electric)
e(\014eld)-5 1071 y(strengths\))f(can)e(b)q(e)h(regarded)g(as)h(a)f
(set)f Fv(X)792 1053 y FC(\003)834 1071 y FH(of)h(homogeneous)g(co)q
(ordinates)g(on)g FE(M)p FH(,)g(pro)o(vided)f(that)-5
1131 y(the)i(jacobian)h(matrix)570 1220 y Fv(e)593 1199
y Ft(I)593 1232 y(i)612 1220 y FH(\()p Fv(z)r FH(\))d(=)g
Fv(@)767 1227 y Ft(i)789 1147 y Fs( )827 1186 y Fv(X)871
1168 y Ft(I)p 827 1208 65 2 v 827 1254 a Fv(X)871 1239
y FC(0)896 1147 y Fs(!)986 1220 y FH(;)57 b Fv(a)13 b
FH(=)h(1)p Fv(;)8 b(:)g(:)g(:)g(;)g(n)449 b FH(\(4.59\))-5
1334 y(is)24 b(in)o(v)o(ertible.)43 b(In)24 b(this)h(case,)h(for)e(the)
h(lo)o(w)o(er)e(part)i(of)g(the)f(symplectic)d(section)j(\012)h(w)o(e)f
(obtain)-5 1394 y Fv(F)27 1401 y FC(\003)67 1394 y FH(=)14
b Fv(F)151 1401 y FC(\003)177 1394 y FH(\()p Fv(X)t FH(\).)22
b(Recalling)15 b(eq.s)g(4.39)p
 (#equation.4.38) [[217 432 237 444] [1 1 1 [3 3]] [0 0 1]] pdfm (,)i
(in)f(particular:)552 1515 y(0)22 b(=)h FE(h)8 b Fv(V)20
b FE(j)8 b Fv(U)789 1522 y Ft(i)811 1515 y FE(i)23 b
FH(=)f Fv(X)957 1494 y FC(\003)992 1515 y Fv(@)1018 1522
y Ft(i)1032 1515 y Fv(F)1064 1522 y FC(\003)1101 1515
y FE(\000)11 b Fv(@)1177 1522 y Ft(i)1191 1515 y Fv(X)1235
1494 y FC(\003)1270 1515 y Fv(F)1302 1522 y FC(\003)1760
1515 y FH(\(4.60\))-5 1601 y(w)o(e)16 b(obtain:)700 1661
y Fv(X)744 1640 y FC(\006)780 1661 y Fv(@)806 1668 y
FC(\006)834 1661 y Fv(F)866 1668 y FC(\003)892 1661 y
FH(\()p Fv(x)p FH(\))22 b(=)g Fv(F)1072 1668 y FC(\003)1098
1661 y FH(\()p Fv(X)t FH(\))580 b(\(4.61\))-5 1747 y(so)17
b(that)g(w)o(e)f(can)g(conclude:)714 1819 y Fv(F)746
1826 y FC(\003)772 1819 y FH(\()p Fv(X)t FH(\))22 b(=)977
1785 y Fv(@)p 941 1808 100 2 v 941 1853 a(@)s(X)1014
1839 y FC(\003)1046 1819 y Fv(F)7 b FH(\()p Fv(X)t FH(\))593
b(\(4.62\))-5 1924 y(where)16 b Fv(F)7 b FH(\()p Fv(X)t
FH(\))17 b(is)f(a)h(homogeneous)f(function)h(of)g(degree)f(2)h(of)f
(the)h(homogeneous)f(co)q(ordinates)i Fv(X)1845 1906
y FC(\003)1871 1924 y FH(.)-5 1984 y(Therefore,when)g(the)h(determinan)
o(t)d(of)k(the)e(Jacobian)38 b(4.59)p
 (#equation.4.59) [[330 291 351 303] [1 1 1 [3 3]] [0 0 1]] pdfm 
20 w(is)18 b(non)i(v)m(anishing,)f(w)o(e)g(can)f(use)h(the)-5
2044 y Fu(sp)n(e)n(cial)f(c)n(o)n(or)n(dinates)p FH(:)843
2133 y Fv(t)861 2112 y Ft(I)902 2133 y FE(\021)968 2099
y Fv(X)1012 2081 y Ft(I)p 968 2121 65 2 v 968 2167 a
Fv(X)1012 2153 y FC(0)1760 2133 y FH(\(4.63\))-5 2231
y(and)f(the)f(whole)g(geometric)f(structure)g(can)i(b)q(e)f(deriv)o(ed)
f(b)o(y)h(a)g(single)g(holomorphic)f(prep)q(oten)o(tial:)716
2339 y FE(F)5 b FH(\()p Fv(t)p FH(\))21 b FE(\021)h FH(\()p
Fv(X)958 2318 y FC(0)978 2339 y FH(\))997 2318 y FB(\000)p
FC(2)1044 2339 y Fv(F)7 b FH(\()p Fv(X)t FH(\))595 b(\(4.64\))-5
2446 y(In)16 b(particular,)g(eq.)f(4.25)p
 (#equation.4.25) [[161 180 182 192] [1 1 1 [3 3]] [0 0 1]] pdfm 
17 w(for)h(the)g(K\177)-24 b(ahler)16 b(p)q(oten)o(tial)g(b)q(ecomes)
356 2553 y FE(K)q FH(\()p Fv(t;)p 454 2518 18 2 v 8 w(t)o
FH(\))e(=)g FE(\000)p FH(log)i(i)687 2505 y Fs(h)706
2553 y FH(2)738 2505 y Fs(\020)764 2553 y FE(F)g(\000)p
866 2514 41 2 v 11 w(F)906 2505 y Fs(\021)942 2553 y
FE(\000)992 2505 y Fs(\020)1017 2553 y Fv(@)1043 2560
y Ft(I)1062 2553 y FE(F)g FH(+)11 b Fv(@)1189 2560 y
Ft(I)1207 2551 y Fm(?)p 1227 2514 V 1227 2553 a FE(F)1268
2505 y Fs(\021)d(\020)1326 2553 y Fv(t)1344 2533 y Ft(I)1374
2553 y FE(\000)p 1424 2518 18 2 v 11 w Fv(t)1442 2527
y Ft(I)1460 2516 y Fm(?)1480 2505 y Fs(\021)o(i)1760
2553 y FH(\(4.65\))-5 2660 y(while)16 b(eq.)f(4.42)p
 (#equation.4.38) [[120 129 141 141] [1 1 1 [3 3]] [0 0 1]] pdfm 
17 w(for)h(the)g(magnetic)f(momen)o(ts)f(simpli\014es)f(in)o(to)721
2768 y Fv(W)767 2775 y Ft(I)s(J)s(K)855 2768 y FH(=)h
Fv(@)933 2775 y Ft(I)953 2768 y Fv(@)979 2775 y Ft(J)1003
2768 y Fv(@)1029 2775 y Ft(K)1063 2768 y FE(F)5 b FH(\()p
Fv(t)p FH(\))600 b(\(4.66\))916 2892 y(22)p eop
%%Page: 23 24
23 23 bop -5 15 a FH(Finally)21 b(w)o(e)g(note)h(that)g(in)f(the)g
(rigid)g(case)h(the)f(Jacobian)i(from)d(a)i(generic)f(parametrisation)g
(to)-5 76 y(sp)q(ecial)16 b(co)q(ordinates)636 164 y
Fv(e)659 144 y Ft(I)659 177 y(i)678 164 y FH(\()p Fv(z)r
FH(\))e(=)g Fv(@)833 171 y Ft(i)855 91 y Fs( )893 131
y Fv(X)937 112 y Ft(I)p 893 153 65 2 v 893 198 a Fv(X)937
184 y FC(0)962 91 y Fs(!)1009 164 y FH(=)f Fv(A)e FH(+)g
Fv(B)p 1197 125 49 2 v 3 w FE(N)522 b FH(\(4.67\))-5
274 y(cannot)15 b(ha)o(v)o(e)f(zero)g(eingen)o(v)m(alues,)f(and)i
(therefore)f(the)g(function)g Fv(F)21 b FH(alw)o(a)o(ys)14
b(exist.)20 b(In)14 b(this)g(case)g(the)-5 334 y(matrix)p
154 295 V 15 w FE(N)23 b FH(coincides)15 b(with)580 314
y Ft(@)601 303 y Fr(2)618 314 y Ft(F)p 541 322 144 2
v 541 351 a(@)r(X)594 342 y Fm(I)610 351 y Ft(@)r(X)663
342 y Fm(J)689 334 y FH(.)-5 498 y Fw(5)81 b(Hyp)r(ergeometry)-5
608 y FH(Next)20 b(w)o(e)g(turn)h(to)g(the)g(h)o(yp)q(erm)o(ultiple)o
(t)d(sector)j(of)g(an)g Fv(N)27 b FH(=)22 b(2)f(theory)l(.)35
b(Here)19 b(there)h(are)h(4)g(real)-5 668 y(scalar)h(\014elds)f(for)g
(eac)o(h)g(h)o(yp)q(erm)o(ultipl)o(et)d(and,)23 b(at)e(least)g(lo)q
(cally)l(,)h(they)e(can)i(b)q(e)f(regarded)g(as)h(the)-5
728 y(four)f(comp)q(onen)o(ts)f(of)h(a)g(quaternion.)34
b(The)20 b(lo)q(calit)o(y)f(ca)o(v)o(eat)h(is,)h(in)f(this)g(case,)i(v)
o(ery)d(substan)o(tial)-5 788 y(b)q(ecause)k(global)h(quaternionic)e
(co)q(ordinates)h(can)g(b)q(e)h(constructed)e(only)h(o)q(ccasionally)g
(ev)o(en)f(on)-5 849 y(those)e(manifolds)f(that)h(are)f(denominated)f
(quaternionic)h(in)g(the)h(mathematical)c(literature)j([62)p
 (#cite.alekseev) [[506 563 518 575] [1 1 1 [3 3]] [0 0 1]] pdfm (],)-5
909 y([23)p  (#cite.gal) [[74 549 86 561] [1 1 1 [3 3]] [0 0 1]] pdfm 
1 w(].)h(An)o(yho)o(w,)13 b(what)h(is)g(imp)q(ortan)o(t)f(is)h(that,)g
(in)f(the)h(h)o(yp)q(erm)o(ultiple)o(t)d(sector,)j(the)f(scalar)h
(manifold)-5 969 y FE(HM)j FH(has)g(dimension)d(m)o(ultiple)g(of)i
(four:)472 1065 y(dim)554 1072 y Ff(R)594 1065 y FE(HM)23
b FH(=)f(4)8 b Fv(m)22 b FE(\021)g FH(4)8 b(#)g(of)17
b(h)o(yp)q(erm)o(ultiplets)374 b(\(5.1\))-5 1161 y(and,)17
b(in)f(some)f(appropriate)i(sense,)e(it)h(has)h(a)g(quaternionic)e
(structure.)68 1221 y(As)e Fu(Sp)n(e)n(cial)i(K\177)-25
b(ahler)14 b FH(is)e(the)h(collectiv)o(e)d(name)i(giv)o(en)g(to)h(the)g
(v)o(ector)f(m)o(ultiple)o(t)e(geometry)i(b)q(oth)h(in)-5
1282 y(the)k(rigid)f(and)h(in)g(the)f(lo)q(cal)h(case,)f(in)h(the)f
(same)g(w)o(a)o(y)g(w)o(e)h(name)e Fu(Hyp)n(er)n(ge)n(ometry)h
FH(that)h(p)q(ertaining)-5 1342 y(to)23 b(the)f(h)o(yp)q(erm)o(ultipl)o
(et)d(sector,)k(irresp)q(ectiv)o(ely)d(whether)h(w)o(e)h(deal)g(with)g
(global)h(or)f(lo)q(cal)g(N=2)-5 1402 y(theories.)f(Y)l(et)14
b(in)h(the)g(v)o(ery)f(same)g(w)o(a)o(y)h(as)h(there)f(are)g(t)o(w)o(o)
g(kinds)g(of)g(sp)q(ecial)g(geometries,)e(there)i(are)-5
1462 y(also)h(t)o(w)o(o)f(kinds)g(of)g(h)o(yp)q(ergeometries)e(and)j
(for)f(a)h(v)o(ery)d(similar)g(reason.)22 b(Sup)q(ersymmetry)12
b(requires)-5 1522 y(the)k(existence)f(of)h(a)h(principal)e
Fv(S)s(U)5 b FH(\(2\){bundle)792 1619 y FE(S)t(U)27 b(\000)-9
b(!)22 b(HM)697 b FH(\(5.2\))-5 1715 y(that)19 b(pla)o(ys)f(for)h(h)o
(yp)q(erm)o(ultipl)o(ets)d(the)i(same)f(role)h(pla)o(y)o(ed)f(b)o(y)h
(the)g(the)g(line{bundle)f FE(L)26 b(\000)-8 b(!)25 b(S)t(M)-5
1775 y FH(in)19 b(the)f(case)g(of)h(v)o(ector)f(m)o(ultiplets.)25
b(As)19 b(it)f(happ)q(ens)h(there)f(the)h(bundle)f FE(S)t(U)24
b FH(is)18 b FD(\015at)h FH(in)f(the)g Fu(rigid)-5 1835
y(c)n(ase)f FH(while)e(its)h(curv)m(ature)g(is)g(prop)q(ortional)i(to)e
(the)g(K\177)-24 b(ahler)16 b(forms)g(in)f(the)h Fu(lo)n(c)n(al)i(c)n
(ase)p FH(.)68 1895 y(The)12 b(di\013erence)f(with)h(the)g(case)g(of)g
(v)o(ector)f(m)o(ultiplets)e(is)j(that)g(rigid)g(and)g(lo)q(cal)g(h)o
(yp)q(ergeometries)-5 1955 y(w)o(ere)21 b(already)h(kno)o(wn)g(in)f
(mathematics)e(prior)j(to)g(their)f(use)g([26)p
 (#cite.dWLVP) [[365 298 377 310] [1 1 1 [3 3]] [0 0 1]] pdfm 
1 w(],)h([63)p
 (#cite.skgsugra_13) [[392 298 404 310] [1 1 1 [3 3]] [0 0 1]] pdfm 
(],)g([24)p  (#cite.DFF) [[419 298 431 310] [1 1 1 [3 3]] [0 0 1]] pdfm 
1 w(],)g([64)p
 (#cite.sabarwhal) [[446 298 458 310] [1 1 1 [3 3]] [0 0 1]] pdfm (],)g
([65)p
 (#cite.vanderseypen) [[473 298 485 310] [1 1 1 [3 3]] [0 0 1]] pdfm 
1 w(])f(in)g(the)-5 2016 y(con)o(text)16 b(of)g Fv(N)j
FH(=)14 b(2)j(sup)q(ersymmetry)c(and)k(had)g(the)f(follo)o(wing)g
(names:)456 2112 y(rigid)g(h)o(yp)q(ergeometry)39 b FE(\021)i
FH(Hyp)q(erK\177)-24 b(ahler)16 b(geom.)455 2184 y(lo)q(cal)g(h)o(yp)q
(ergeometry)39 b FE(\021)i FH(Quaternionic)16 b(geom.)358
b(\(5.3\))-5 2327 y Fk(5.1)66 b(Quaternionic,)24 b(v)n(ersus)f(Hyp)r
(erK\177)-33 b(ahler)22 b(manifolds)-5 2419 y FH(Both)c(a)f
(quaternionic)g(or)h(a)f(Hyp)q(erK\177)-24 b(ahler)17
b(manifold)f FE(HM)i FH(is)f(a)h(4)p Fv(m)p FH(-dimensional)d(real)i
(manifold)-5 2479 y(endo)o(w)o(ed)f(with)g(a)h(metric)d
Fv(h)p FH(:)477 2575 y Fv(ds)525 2555 y FC(2)559 2575
y FH(=)g Fv(h)639 2582 y Ft(uv)680 2575 y FH(\()p Fv(q)r
FH(\))p Fv(dq)791 2555 y Ft(u)823 2575 y FE(\012)d Fv(dq)922
2555 y Ft(v)991 2575 y FH(;)57 b Fv(u;)8 b(v)15 b FH(=)e(1)p
Fv(;)8 b(:)g(:)g(:)g(;)g FH(4)p Fv(m)382 b FH(\(5.4\))-5
2672 y(and)17 b(three)f(complex)e(structures)418 2768
y(\()p Fv(J)469 2747 y Ft(x)491 2768 y FH(\))22 b(:)46
b Fv(T)7 b FH(\()p FE(HM)o FH(\))23 b FE(\000)-9 b(!)22
b Fv(T)7 b FH(\()p FE(HM)p FH(\))146 b(\()p Fv(x)13 b
FH(=)h(1)p Fv(;)8 b FH(2)p Fv(;)g FH(3\))324 b(\(5.5\))916
2892 y(23)p eop
%%Page: 24 25
24 24 bop -5 15 a FH(that)17 b(satisfy)f(the)g(quaternionic)g(algebra)
680 122 y Fv(J)712 101 y Ft(x)733 122 y Fv(J)765 101
y Ft(y)800 122 y FH(=)d FE(\000)p Fv(\016)914 101 y Ft(xy)962
122 y FH(1)-17 b(1)21 b(+)e Fv(\017)1091 101 y Ft(xy)q(z)1149
122 y Fv(J)1181 101 y Ft(z)1785 122 y FH(\(5.6\))-5 228
y(and)e(resp)q(ect)f(to)h(whic)o(h)e(the)h(metric)e(is)i(hermitian:)281
335 y FE(8)p FD(X)o Fv(;)8 b FD(Y)14 b FE(2)g Fv(T)7
b FE(HM)21 b FH(:)63 b Fv(h)8 b FH(\()p Fv(J)799 314
y Ft(x)820 335 y FD(X)q Fv(;)g(J)917 314 y Ft(x)938 335
y FD(Y)p FH(\))14 b(=)g Fv(h)8 b FH(\()p FD(X)q Fv(;)g
FD(Y)p FH(\))106 b(\()p Fv(x)13 b FH(=)h(1)p Fv(;)8 b
FH(2)p Fv(;)g FH(3\))186 b(\(5.7\))-5 441 y(F)l(rom)15
b(eq.)h(5.7)p
 (#equation.5.7) [[120 661 135 673] [1 1 1 [3 3]] [0 0 1]] pdfm 
16 w(it)g(follo)o(ws)g(that)h(one)f(can)h(in)o(tro)q(duce)e(a)i
(triplet)e(of)i(2-forms)459 548 y Fv(K)504 529 y Ft(x)567
548 y FH(=)42 b Fv(K)692 529 y Ft(x)688 559 y(uv)729
548 y Fv(dq)778 529 y Ft(u)812 548 y FE(^)11 b Fv(dq)905
529 y Ft(v)967 548 y FH(;)41 b Fv(K)1067 529 y Ft(x)1063
559 y(uv)1145 548 y FH(=)h Fv(h)1253 555 y Ft(uw)1302
548 y FH(\()p Fv(J)1353 529 y Ft(x)1374 548 y FH(\))1393
529 y Ft(w)1393 559 y(v)1785 548 y FH(\(5.8\))-5 654
y(that)18 b(pro)o(vides)f(the)g(generalization)g(of)h(the)f(concept)g
(of)h(K\177)-24 b(ahler)17 b(form)f(o)q(ccurring)i(in)f(the)g(complex)
-5 714 y(case.)23 b(The)17 b(triplet)e Fv(K)414 696 y
Ft(x)453 714 y FH(is)i(named)e(the)i Fu(Hyp)n(erK\177)-25
b(ahler)17 b FH(form.)k(It)c(is)f(an)i Fv(S)s(U)5 b FH(\(2\))17
b(Lie{algebra)g(v)m(alued)-5 774 y(2{form)g(in)g(the)f(same)g(w)o(a)o
(y)h(as)g(the)g(K\177)-24 b(ahler)17 b(form)f(is)g(a)i
Fv(U)5 b FH(\(1\))17 b(Lie{algebra)h(v)m(alued)f(2{form.)23
b(In)16 b(the)-5 834 y(complex)d(case)i(the)g(de\014nition)g(of)g
(K\177)-24 b(ahler)15 b(manifold)f(in)o(v)o(olv)o(es)f(the)i(statemen)o
(t)e(that)j(the)f(K\177)-24 b(ahler)14 b(2{)-5 895 y(form)i(is)h
(closed.)22 b(A)o(t)16 b(the)h(same)f(time)f(in)h(Ho)q(dge{K\177)-24
b(ahler)17 b(manifolds)f(\(those)h(appropriate)h(to)f(lo)q(cal)-5
955 y(sup)q(ersymmetry\))c(the)j(K\177)-24 b(ahler)16
b(2{form)g(can)g(b)q(e)g(iden)o(ti\014ed)f(with)h(the)f(curv)m(ature)h
(of)h(a)f(line{bundle)-5 1015 y(whic)o(h)e(in)h(the)f(case)h(of)g
(rigid)g(sup)q(ersymmetry)c(is)k(\015at.)21 b(Similar)13
b(steps)i(can)g(b)q(e)g(tak)o(en)f(also)h(here)f(and)-5
1075 y(lead)i(to)h(t)o(w)o(o)f(p)q(ossibilities:)k(either)15
b(Hyp)q(erK\177)-24 b(ahler)16 b(or)g(Quaternionic)g(manifolds.)68
1135 y(Let)h(us)g(in)o(tro)q(duce)f(a)h(principal)e Fv(S)s(U)5
b FH(\(2\){bundle)17 b FE(S)t(U)k FH(as)c(de\014ned)g(in)f(eq.)f(5.2)p
 (#equation.5.2) [[419 495 434 507] [1 1 1 [3 3]] [0 0 1]] pdfm (.)22
b(Let)17 b Fv(!)1665 1117 y Ft(x)1703 1135 y FH(denote)g(a)-5
1196 y(connection)e(on)h(suc)o(h)f(a)h(bundle.)k(T)l(o)c(obtain)g
(either)e(a)i(Hyp)q(erK\177)-24 b(ahler)14 b(or)i(a)g(quaternionic)e
(manifold)-5 1256 y(w)o(e)20 b(m)o(ust)g(imp)q(ose)f(the)i(condition)f
(that)h(the)g(Hyp)q(erK\177)-24 b(ahler)19 b(2{form)i(is)f(co)o(v)m
(arian)o(tly)g(closed)g(with)-5 1316 y(resp)q(ect)c(to)h(the)f
(connection)g Fv(!)582 1298 y Ft(x)604 1316 y FH(:)598
1422 y FE(r)p Fv(K)685 1402 y Ft(x)720 1422 y FE(\021)d
Fv(dK)842 1402 y Ft(x)876 1422 y FH(+)e Fv(\017)945 1402
y Ft(xy)q(z)1003 1422 y Fv(!)1035 1402 y Ft(y)1067 1422
y FE(^)g Fv(K)1156 1402 y Ft(z)1198 1422 y FH(=)22 b(0)503
b(\(5.9\))-5 1529 y(The)20 b(only)f(di\013erence)f(b)q(et)o(w)o(een)g
(the)h(t)o(w)o(o)h(kinds)f(of)g(geometries)f(resides)h(in)g(the)g
(structure)g(of)g(the)-5 1589 y FE(S)t(U)5 b FH({bundle.)-5
1688 y FD(De\014nition)18 b(5.1)24 b Fu(A)13 b(Hyp)n(erK\177)-25
b(ahler)12 b(manifold)h(is)g(a)f FH(4)p Fv(m)p Fu({dimensional)i
(manifold)f(with)g(the)g(structur)n(e)-5 1748 y(describ)n(e)n(d)18
b(ab)n(ove)g(and)f(such)h(that)g(the)g FE(S)t(U)5 b Fu({bund)r(le)19
b(is)f FD(\015at)-5 1846 y FH(De\014ning)f(the)f FE(S)t(U)5
b FH({curv)m(ature)16 b(b)o(y:)664 1972 y(\012)699 1952
y Ft(x)743 1972 y FE(\021)22 b Fv(d!)861 1952 y Ft(x)895
1972 y FH(+)949 1939 y(1)p 949 1961 25 2 v 949 2006 a(2)978
1972 y Fv(\017)998 1952 y Ft(xy)q(z)1056 1972 y Fv(!)1088
1952 y Ft(y)1120 1972 y FE(^)11 b Fv(!)1196 1952 y Ft(z)1760
1972 y FH(\(5.10\))-5 2091 y(in)16 b(the)g(Hyp)q(erK\177)-24
b(ahler)15 b(case)i(w)o(e)e(ha)o(v)o(e:)858 2152 y(\012)893
2131 y Ft(x)938 2152 y FH(=)22 b(0)738 b(\(5.11\))-5
2237 y(Vicev)o(ersa)-5 2336 y FD(De\014nition)18 b(5.2)24
b Fu(A)c(quaternionic)i(manifold)f(is)f(a)g FH(4)p Fv(m)p
Fu({dimensional)h(manifold)g(with)g(the)f(struc-)-5 2396
y(tur)n(e)e(describ)n(e)n(d)g(ab)n(ove)h(and)f(such)h(that)f(the)h
(curvatur)n(e)f(of)h(the)f FE(S)t(U)5 b Fu({bund)r(le)21
b(is)d(pr)n(op)n(ortional)e(to)j(the)-5 2456 y(Hyp)n(erK\177)-25
b(ahler)18 b(2{form)-5 2555 y FH(Hence,)d(in)h(the)g(quaternionic)f
(case)h(w)o(e)g(can)h(write:)819 2661 y(\012)854 2641
y Ft(x)898 2661 y FH(=)22 b Fv(\025)8 b(K)1039 2641 y
Ft(x)1760 2661 y FH(\(5.12\))-5 2768 y(where)16 b Fv(\025)h
FH(is)f(a)h(non)f(v)m(anishing)h(real)f(n)o(um)o(b)q(er.)916
2892 y(24)p eop
%%Page: 25 26
25 25 bop 68 15 a FH(As)17 b(a)h(consequence)e(of)h(the)g(ab)q(o)o(v)o
(e)g(structure)f(the)h(manifold)e FE(HM)j FH(has)g(a)f(holonom)o(y)f
(group)i(of)-5 76 y(the)e(follo)o(wing)g(t)o(yp)q(e:)478
180 y(Hol)o(\()p FE(HM)q FH(\))42 b(=)f Fv(S)s(U)5 b
FH(\(2\))12 b FE(\012)f(H)49 b FH(\(quaternionic)o(\))478
253 y(Hol)o(\()p FE(HM)q FH(\))42 b(=)f(1)-17 b(1)12
b FE(\012)f(H)49 b FH(\(Hyp)q(erK\177)-24 b(ahler)o(\))650
325 y FE(H)42 b(\032)f Fv(S)s(p)p FH(\(2)p Fv(m;)8 b
FH(I)-9 b(R\))717 b(\(5.13\))-5 430 y(In)23 b(b)q(oth)i(cases,)f(in)o
(tro)q(ducing)g(\015at)f(indices)g FE(f)p Fv(A;)8 b(B)s(;)g(C)28
b FH(=)e(1)p Fv(;)8 b FH(2)p FE(gf)p Fv(\013;)g(\014)s(;)g(\015)28
b FH(=)e(1)p Fv(;)8 b(::;)g FH(2)p Fv(m)p FE(g)23 b FH(that)g(run,)-5
490 y(resp)q(ectiv)o(ely)l(,)15 b(in)i(the)g(fundamen)o(tal)e(represen)
o(tations)i(of)h Fv(S)s(U)5 b FH(\(2\))17 b(and)h Fv(S)s(p)p
FH(\(2)p Fv(m;)8 b FH(I)-9 b(R\),)17 b(w)o(e)g(can)g(\014nd)h(a)-5
550 y(vielb)q(ein)d(1-form)754 610 y FE(U)790 590 y Ft(A\013)855
610 y FH(=)f FE(U)943 590 y Ft(A\013)938 623 y(u)994
610 y FH(\()p Fv(q)r FH(\))p Fv(dq)1105 590 y Ft(u)1760
610 y FH(\(5.14\))-5 695 y(suc)o(h)i(that)709 755 y Fv(h)737
762 y Ft(uv)791 755 y FH(=)e FE(U)879 735 y Ft(A\013)874
767 y(u)930 755 y FE(U)966 735 y Ft(B)r(\014)961 767
y(v)p 1027 755 2 33 v 1014 755 a FH(C)1049 762 y Ft(\013\014)1095
755 y Fv(\017)1115 762 y Ft(AB)1760 755 y FH(\(5.15\))-5
840 y(where)p 142 840 V 9 w(C)164 847 y Ft(\013\014)224
840 y FH(=)g FE(\000)p 323 840 V -5 w FH(C)345 847 y
Ft(\014)r(\013)405 840 y FH(and)g Fv(\017)517 847 y Ft(AB)587
840 y FH(=)g FE(\000)p Fv(\017)698 847 y Ft(B)r(A)767
840 y FH(are,)g(resp)q(ectiv)o(ely)l(,)d(the)i(\015at)h
Fv(S)s(p)p FH(\(2)p Fv(m)p FH(\))f(and)h Fv(S)s(p)p FH(\(2\))h
FE(\030)e Fv(S)s(U)5 b FH(\(2\))-5 900 y(in)o(v)m(arian)o(t)23
b(metrics.)39 b(The)23 b(vielb)q(ein)f FE(U)749 882 y
Ft(A\013)823 900 y FH(is)h(co)o(v)m(arian)o(tly)f(closed)h(with)g(resp)
q(ect)g(to)g(the)g Fv(S)s(U)5 b FH(\(2\)-)-5 960 y(connection)16
b Fv(!)271 942 y Ft(z)307 960 y FH(and)h(to)g(some)e
Fv(S)s(p)p FH(\(2)p Fv(m;)8 b FH(I)-9 b(R\)-Lie)16 b(Algebra)g(v)m
(alued)g(connection)g(\001)1532 942 y Ft(\013\014)1592
960 y FH(=)e(\001)1685 942 y Ft(\014)r(\013)1731 960
y FH(:)497 1087 y FE(rU)575 1067 y Ft(A\013)667 1087
y FE(\021)41 b Fv(d)p FE(U)808 1067 y Ft(A\013)871 1087
y FH(+)929 1054 y Fv(i)p 925 1076 25 2 v 925 1122 a FH(2)954
1087 y Fv(!)986 1067 y Ft(x)1008 1087 y FH(\()p Fv(\017\033)1075
1094 y Ft(x)1097 1087 y Fv(\017)1117 1067 y FB(\000)p
FC(1)1164 1087 y FH(\))1183 1067 y Ft(A)1209 1100 y(B)1250
1087 y FE(^)12 b(U)1331 1067 y Ft(B)r(\013)667 1182 y
FH(+)42 b(\001)788 1161 y Ft(\013\014)845 1182 y FE(^)11
b(U)925 1161 y Ft(A\015)p 982 1182 2 33 v 21 x FH(C)1005
1189 y Ft(\014)r(\015)1062 1182 y FH(=)j(0)622 b(\(5.16\))-5
1286 y(where)23 b(\()p Fv(\033)192 1268 y Ft(x)214 1286
y FH(\))259 1268 y Ft(B)233 1298 y(A)313 1286 y FH(are)g(the)g
(standard)i(P)o(auli)d(matrices.)41 b(F)l(urthermore)21
b FE(U)1397 1268 y Ft(A\013)1472 1286 y FH(satis\014es)j(the)f(realit)o
(y)-5 1346 y(condition:)640 1406 y FE(U)671 1413 y Ft(A\013)736
1406 y FE(\021)14 b FH(\()p FE(U)844 1386 y Ft(A\013)895
1406 y FH(\))914 1386 y FB(\003)947 1406 y FH(=)g Fv(\017)1019
1413 y Ft(AB)p 1084 1406 V 1071 1406 a FH(C)1106 1413
y Ft(\013\014)1152 1406 y FE(U)1188 1386 y Ft(B)r(\014)1760
1406 y FH(\(5.17\))-5 1491 y(Eq.5.17)p
 (#equation.5.17) [[88 409 109 421] [1 1 1 [3 3]] [0 0 1]] pdfm 
19 w(de\014nes)19 b(the)f(rule)g(to)h(lo)o(w)o(er)f(the)h(symplectic)c
(indices)j(b)o(y)g(means)g(of)h(the)f(\015at)h(symplectic)-5
1551 y(metrics)14 b Fv(\017)186 1558 y Ft(AB)259 1551
y FH(and)p 362 1551 V 12 w(C)384 1558 y Ft(\013\014)431
1551 y FH(.)21 b(More)16 b(sp)q(eci\014cally)f(w)o(e)g(can)i(write)f(a)
g(stronger)h(v)o(ersion)f(of)g(eq.)f(5.15)p
 (#equation.5.15) [[469 395 489 407] [1 1 1 [3 3]] [0 0 1]] pdfm ([56)p
 (#cite.sugkgeom_3) [[493 395 504 407] [1 1 1 [3 3]] [0 0 1]] pdfm 
2 w(]:)518 1656 y(\()p FE(U)573 1635 y Ft(A\013)568 1668
y(u)624 1656 y FE(U)660 1635 y Ft(B)r(\014)655 1668 y(v)723
1656 y FH(+)c FE(U)808 1635 y Ft(A\013)803 1668 y(v)859
1656 y FE(U)895 1635 y Ft(B)r(\014)890 1668 y(u)947 1656
y FH(\))p 974 1656 V -5 w(C)997 1663 y Ft(\013\014)1085
1656 y FH(=)41 b Fv(h)1192 1663 y Ft(uv)1233 1656 y Fv(\017)1253
1635 y Ft(AB)518 1752 y FH(\()p FE(U)573 1732 y Ft(A\013)568
1764 y(u)624 1752 y FE(U)660 1732 y Ft(B)r(\014)655 1764
y(v)723 1752 y FH(+)11 b FE(U)808 1732 y Ft(A\013)803
1764 y(v)860 1752 y FE(U)896 1732 y Ft(B)r(\014)891 1764
y(u)948 1752 y FH(\))p Fv(\017)987 1759 y Ft(AB)1085
1752 y FH(=)41 b Fv(h)1192 1759 y Ft(uv)1247 1718 y FH(1)p
1238 1740 43 2 v 1238 1786 a Fv(m)p 1294 1752 2 33 v
-34 x FH(C)1316 1731 y Ft(\013\014)1760 1752 y FH(\(5.18\))-5
1869 y(W)l(e)16 b(ha)o(v)o(e)g(also)h(the)f(in)o(v)o(erse)e(vielb)q
(ein)h FE(U)753 1851 y Ft(u)748 1881 y(A\013)815 1869
y FH(de\014ned)h(b)o(y)g(the)g(equation)800 1973 y FE(U)836
1953 y Ft(u)831 1986 y(A\013)882 1973 y FE(U)918 1953
y Ft(A\013)913 1986 y(v)983 1973 y FH(=)e Fv(\016)1059
1953 y Ft(u)1057 1986 y(v)1760 1973 y FH(\(5.19\))-5
2078 y(Flattening)i(a)h(pair)f(of)g(indices)g(of)g(the)g(Riemann)f
(tensor)h FE(R)1124 2060 y Ft(uv)1163 2090 y(ts)1211
2078 y FH(w)o(e)g(obtain)427 2205 y FE(R)469 2185 y Ft(uv)508
2217 y(ts)539 2205 y FE(U)575 2185 y Ft(\013A)570 2217
y(u)627 2205 y FE(U)663 2185 y Ft(\014)r(B)658 2217 y(v)728
2205 y FH(=)e FE(\000)838 2171 y FH(i)p 832 2194 25 2
v 832 2239 a(2)861 2205 y(\012)896 2185 y Ft(x)896 2217
y(ts)928 2205 y Fv(\017)948 2185 y Ft(AC)1004 2205 y
FH(\()p Fv(\033)1051 2212 y Ft(x)1072 2205 y FH(\))1119
2185 y Ft(B)1091 2217 y(C)p 1157 2205 2 33 v 1144 2205
a FH(C)1180 2184 y Ft(\013\014)1237 2205 y FH(+)d(I)-9
b(R)1331 2182 y Ft(\013\014)1331 2215 y(ts)1377 2205
y Fv(\017)1397 2185 y Ft(AB)1760 2205 y FH(\(5.20\))-5
2334 y(where)16 b(I)-9 b(R)181 2311 y Ft(\013\014)181
2344 y(ts)243 2334 y FH(is)16 b(the)g(\014eld)g(strength)h(of)f(the)g
Fv(S)s(p)p FH(\(2)p Fv(m)p FH(\))h(connection:)458 2439
y Fv(d)p FH(\001)524 2418 y Ft(\013\014)582 2439 y FH(+)11
b(\001)672 2418 y Ft(\013\015)727 2439 y FE(^)g FH(\001)812
2418 y Ft(\016)q(\014)p 861 2439 V 848 2439 a FH(C)883
2446 y Ft(\015)r(\016)936 2439 y FE(\021)j FH(I)-9 b(R)1033
2418 y Ft(\013\014)1093 2439 y FH(=)14 b(I)-9 b(R)1190
2415 y Ft(\013\014)1190 2449 y(ts)1236 2439 y Fv(dq)1285
2418 y Ft(t)1311 2439 y FE(^)11 b Fv(dq)1404 2418 y Ft(s)1760
2439 y FH(\(5.21\))-5 2543 y(Eq.)49 b(5.20)p
 (#equation.5.20) [[100 157 121 169] [1 1 1 [3 3]] [0 0 1]] pdfm 
20 w(is)18 b(the)h(explicit)e(statemen)o(t)g(that)j(the)f(Levi)f
(Civita)h(connection)f(asso)q(ciated)i(with)f(the)-5
2603 y(metric)13 b Fv(h)i FH(has)h(a)f(holonom)o(y)f(group)i(con)o
(tained)f(in)f Fv(S)s(U)5 b FH(\(2\))k FE(\012)g Fv(S)s(p)p
FH(\(2)p Fv(m)p FH(\).)21 b(Consider)15 b(no)o(w)g(eq.s)g(5.6)p
 (#equation.5.6) [[488 142 503 154] [1 1 1 [3 3]] [0 0 1]] pdfm (,)g
(5.8)p  (#equation.5.8) [[510 142 524 154] [1 1 1 [3 3]] [0 0 1]] pdfm 
-5 2663 a(and)i(5.12)p
 (#equation.5.12) [[94 128 114 140] [1 1 1 [3 3]] [0 0 1]] pdfm (.)22
b(W)l(e)16 b(easily)f(deduce)h(the)g(follo)o(wing)g(relation:)592
2768 y Fv(h)620 2747 y Ft(st)652 2768 y Fv(K)697 2747
y Ft(x)693 2780 y(us)732 2768 y Fv(K)777 2744 y Ft(y)773
2778 y(tw)828 2768 y FH(=)e FE(\000)p Fv(\016)943 2747
y Ft(xy)983 2768 y Fv(h)1011 2775 y Ft(uw)1071 2768 y
FH(+)d Fv(\017)1140 2747 y Ft(xy)q(z)1198 2768 y Fv(K)1243
2747 y Ft(z)1239 2780 y(uw)1760 2768 y FH(\(5.22\))916
2892 y(25)p eop
%%Page: 26 27
26 26 bop -5 15 a FH(that)15 b(holds)g(true)g(b)q(oth)g(in)g(the)f(Hyp)
q(erK\177)-24 b(ahler)14 b(and)h(in)f(the)h(Quaternionic)f(case.)21
b(In)14 b(the)g(latter)h(case,)-5 76 y(using)i(eq.)k(5.12)p
 (#equation.5.12) [[121 749 142 761] [1 1 1 [3 3]] [0 0 1]] pdfm (,)16
b(eq.)f(5.22)p
 (#equation.5.22) [[168 749 188 761] [1 1 1 [3 3]] [0 0 1]] pdfm 
17 w(can)i(b)q(e)f(rewritten)f(as)i(follo)o(ws:)563 183
y Fv(h)591 162 y Ft(st)623 183 y FH(\012)658 162 y Ft(x)658
195 y(us)697 183 y FH(\012)732 159 y Ft(y)732 193 y(tw)787
183 y FH(=)d FE(\000)p Fv(\025)906 162 y FC(2)925 183
y Fv(\016)949 162 y Ft(xy)990 183 y Fv(h)1018 190 y Ft(uw)1077
183 y FH(+)d Fv(\025\017)1174 162 y Ft(xy)q(z)1233 183
y FH(\012)1268 162 y Ft(z)1268 195 y(uw)1760 183 y FH(\(5.23\))-5
290 y(Eq.)20 b(5.23)p
 (#equation.5.23) [[93 697 114 709] [1 1 1 [3 3]] [0 0 1]] pdfm 
21 w(implies)e(that)i(the)g(in)o(trinsic)f(comp)q(onen)o(ts)g(of)i(the)
f(curv)m(ature)g(2-form)g(\012)1592 272 y Ft(x)1634 290
y FH(yield)f(a)i(rep-)-5 350 y(resen)o(tation)d(of)g(the)g(quaternion)f
(algebra.)27 b(In)18 b(the)f(Hyp)q(erK\177)-24 b(ahler)17
b(case)h(suc)o(h)g(a)g(represen)o(tation)f(is)-5 410
y(pro)o(vided)f(only)g(b)o(y)g(the)g(Hyp)q(erK\177)-24
b(ahler)15 b(form.)20 b(In)c(the)g(quaternionic)f(case)i(w)o(e)e(can)i
(write:)490 517 y(\012)525 497 y Ft(x)525 529 y(A\013;B)r(\014)649
517 y FE(\021)d FH(\012)737 497 y Ft(x)737 529 y(uv)778
517 y FE(U)814 497 y Ft(u)809 529 y(A\013)860 517 y FE(U)896
497 y Ft(v)891 529 y(B)r(\014)957 517 y FH(=)g FE(\000)p
Fv(i\025)p 1101 517 2 33 v -5 w FH(C)1123 524 y Ft(\013\014)1170
517 y FH(\()p Fv(\033)1217 524 y Ft(x)1238 517 y FH(\))1284
497 y Ft(C)1257 529 y(A)1313 517 y Fv(\017)1333 524 y
Ft(C)r(B)1760 517 y FH(\(5.24\))-5 624 y(Alternativ)o(ely)g(eq.5.24)p
 (#equation.5.24) [[157 617 177 629] [1 1 1 [3 3]] [0 0 1]] pdfm 
16 w(can)i(b)q(e)g(rewritten)g(in)g(an)g(in)o(trinsic)f(form)g(as)566
731 y(\012)601 711 y Ft(x)637 731 y FH(=)22 b FE(\000)p
FH(i)8 b Fv(\025)p 794 731 V -5 w FH(C)817 738 y Ft(\013\014)863
731 y FH(\()p Fv(\033)910 738 y Ft(x)931 731 y FH(\))977
711 y Ft(C)950 744 y(A)1006 731 y Fv(\017)1026 738 y
Ft(C)r(B)1084 731 y FE(U)1120 711 y Ft(\013A)1182 731
y FE(^)k(U)1263 711 y Ft(\014)r(B)1760 731 y FH(\(5.25\))-5
838 y(whence)k(w)o(e)g(also)h(get:)671 885 y Fv(i)p 667
907 25 2 v 667 953 a FH(2)696 918 y(\012)731 898 y Ft(x)753
918 y FH(\()p Fv(\033)800 925 y Ft(x)822 918 y FH(\))867
898 y Ft(B)841 931 y(A)911 918 y FH(=)d Fv(\025)p FE(U)1022
925 y Ft(A\013)1085 918 y FE(^)d(U)1165 898 y Ft(B)r(\013)1760
918 y FH(\(5.26\))-5 1017 y(Homogeneous)16 b(symmetric)c(quaternionic)k
(spaces)g(are)h(displa)o(y)o(ed)e(in)h(T)l(able)32 b(2)p
 (#table.2) [[425 523 431 535] [1 1 1 [3 3]] [0 0 1]] pdfm (.)-5
1183 y Fw(6)81 b(The)27 b(Gauging)-5 1293 y FH(With)12
b(the)g(ab)q(o)o(v)o(e)h(discussion)f(of)h(Hyp)q(erK\177)-24
b(ahler)11 b(and)i(Quaternionic)f(manifolds)f(w)o(e)h(ha)o(v)o(e)f
(completed)-5 1353 y(the)i(review)e(of)i(the)g(geometric)d(structures)j
(in)o(v)o(olv)o(ed)d(in)j(the)f(construction)h(of)g(an)g
Fu(ab)n(elian,)j(ungauge)n(d)-5 1413 y Fv(N)24 b FH(=)17
b(2)j(sup)q(ergra)o(vit)o(y)e(or)h(of)g(an)g(ab)q(elian)g
Fv(N)k FH(=)18 b(2)h(rigid)f(gauge)i(theory)l(.)28 b(As)19
b(w)o(e)f(are)h(going)g(to)g(see)-5 1473 y(in)f(the)f(next)g(section,)h
(the)f(b)q(osonic)i(Lagrangian)g(of)f Fv(N)k FH(=)16
b(2)i(sup)q(ergra)o(vit)o(y)g(coupled)f(to)h Fv(n)g FH(ab)q(elian)-5
1533 y(v)o(ector)e(m)o(ultiple)o(ts)e(and)j Fv(m)f FH(h)o(yp)q(erm)o
(ultipl)o(ets)d(is)j(the)g(follo)o(wing:)177 1640 y FE(L)211
1615 y Ft(S)r(U)t(GRA)p FB(j)p Ft(B)r(ose)211 1653 y(ung)q(aug)q(ed)474
1640 y FH(=)553 1603 y FE(p)p 595 1603 64 2 v 37 x(\000)p
Fv(g)659 1592 y Fs(h)687 1640 y Fv(R)p FH([)p Fv(g)r
FH(])j(+)g Fv(g)876 1647 y Ft(ij)904 1638 y Fm(?)925
1640 y FH(\()p Fv(z)r(;)p 991 1614 25 2 v 8 w(z)q FH(\))8
b Fv(@)1071 1620 y Ft(\026)1094 1640 y Fv(z)1119 1620
y Ft(i)1142 1640 y Fv(@)1168 1647 y Ft(\026)p 1191 1614
V 1191 1640 a Fv(z)1216 1620 y Ft(j)1232 1608 y Fm(?)1271
1640 y FE(\000)19 b Fv(\025)8 b(h)1393 1647 y Ft(uv)1435
1640 y FH(\()p Fv(q)r FH(\))g Fv(@)1534 1620 y Ft(\026)1556
1640 y Fv(q)1580 1620 y Ft(u)1611 1640 y Fv(@)1637 1647
y Ft(\026)1660 1640 y Fv(q)1684 1620 y Ft(v)553 1732
y FH(+)g(i)630 1684 y Fs(\020)p 655 1693 49 2 v 48 x
FE(N)703 1739 y FC(\003\006)755 1732 y FE(F)796 1711
y FB(\000)p FC(\003)791 1744 y Ft(\026\027)850 1732 y
FE(F)891 1711 y FB(\000)p FC(\006)p FB(j)p Ft(\026\027)1015
1732 y FE(\000)19 b(N)1114 1739 y FC(\003\006)1166 1732
y FE(F)1207 1711 y FC(+\003)1202 1744 y Ft(\026\027)1261
1732 y FE(F)1302 1711 y FC(+\006)p FB(j)p Ft(\026\027)1407
1684 y Fs(\021)8 b(i)1785 1732 y FH(\(6.1\))-5 1848 y(where)14
b(the)f Fv(n)h FH(complex)d(\014elds)i Fv(z)593 1830
y Ft(i)621 1848 y FH(span)h(some)f Fu(sp)n(e)n(cial)i(K\177)-25
b(ahler)15 b(manifold)g(of)g(the)h(lo)n(c)n(al)f(typ)n(e)e
FE(S)t(M)g FH(and)-5 1908 y(the)h(4)p Fv(m)h FH(real)e(\014elds)h
Fv(q)398 1890 y Ft(u)434 1908 y FH(span)i(a)e(quaternionic)g(manifold)e
FE(HM)q FH(.)20 b(By)14 b Fv(g)1298 1915 y Ft(ij)1326
1906 y Fm(?)1361 1908 y FH(and)h Fv(h)1482 1915 y Ft(uv)1537
1908 y FH(w)o(e)f(ha)o(v)o(e)f(denoted)-5 1968 y(the)22
b(metrics)d(on)j(these)f(t)o(w)o(o)h(manifolds.)36 b(The)22
b(prop)q(ortionalit)o(y)f(constan)o(t)h(b)q(et)o(w)o(een)f(the)g
Fv(S)s(U)5 b FH(\(2\))-5 2028 y(curv)m(ature)20 b(and)g(the)f(Hyp)q
(erK\177)-24 b(ahler)19 b(form)f(app)q(earing)j(in)e(the)h(Lagrangian)h
(is)f(\014xed)f(to)h(the)f(v)m(alue)-5 2088 y Fv(\025)i
FH(=)g FE(\000)p FH(1)g(if)e(w)o(e)h(w)o(an)o(t)h(canonical)f(kinetic)e
(terms)h(for)i(the)f(h)o(yp)q(erm)o(ultipl)o(et)d(scalars.)34
b(The)21 b(p)q(erio)q(d)-5 2149 y(matrix)16 b FE(N)196
2156 y FC(\003\006)266 2149 y FH(dep)q(ends)j(only)e(on)i(the)e(sp)q
(ecial)h(manifold)e(co)q(ordinates)j Fv(z)1370 2130 y
Ft(i)1384 2149 y Fv(;)p 1406 2122 25 2 v 8 w(z)1431 2130
y Ft(j)1447 2119 y Fm(?)1485 2149 y FH(and)f(it)g(is)g(expressed)-5
2209 y(in)c(terms)e(of)j(the)f(symplectic)c(sections)k(of)h(the)e
(\015at)i(symplectic)c(bundle)i(b)o(y)h(eq.)f(4.37)p
 (#equation.4.37) [[430 237 451 249] [1 1 1 [3 3]] [0 0 1]] pdfm (.)21
b(On)14 b(the)g(other)-5 2269 y(hand)k(the)g(b)q(osonic)g(Lagrangian)h
(of)f(a)g(rigid)f Fv(N)k FH(=)16 b(2)i(ab)q(elian)f(gauge)i(theory)e
(con)o(taining)g Fv(n)h FH(v)o(ector)-5 2329 y(m)o(ultiplets)c(and)i
(coupled)g(to)h Fv(m)f FH(h)o(yp)q(erm)o(ultipl)o(ets)e(is)i(the)g
(follo)o(wing)g(one:)356 2436 y FE(L)390 2411 y Ft(Y)9
b(M)t FB(j)p Ft(B)r(ose)390 2449 y(ung)q(aug)q(ed)588
2436 y FH(=)41 b Fv(g)690 2443 y Ft(ij)718 2434 y Fm(?)739
2436 y FH(\()p Fv(z)r(;)p 805 2410 V 8 w(z)q FH(\))8
b Fv(@)885 2416 y Ft(\026)909 2436 y Fv(z)934 2416 y
Ft(i)956 2436 y Fv(@)982 2443 y Ft(\026)p 1005 2410 V
1005 2436 a Fv(z)1030 2416 y Ft(j)1046 2404 y Fm(?)1085
2436 y FH(+)20 b Fv(h)1171 2443 y Ft(uv)1212 2436 y FH(\()p
Fv(q)r FH(\))8 b Fv(@)1311 2416 y Ft(\026)1333 2436 y
Fv(q)1357 2416 y Ft(u)1387 2436 y Fv(@)1413 2443 y Ft(\026)1436
2436 y Fv(q)1460 2416 y Ft(v)667 2522 y FH(+)g(i)744
2473 y Fs(\020)p 768 2483 49 2 v 768 2522 a FE(N)817
2529 y Ft(I)s(J)859 2522 y FE(F)900 2501 y FB(\000)p
Ft(I)895 2534 y(\026\027)947 2522 y FE(F)988 2501 y FB(\000)p
Ft(J)s FB(j)p Ft(\026\027)1110 2522 y FE(\000)19 b(N)1209
2529 y Ft(I)s(J)1251 2522 y FE(F)1292 2501 y FC(+)p Ft(I)1287
2534 y(\026\027)1339 2522 y FE(F)1380 2501 y FC(+)p Ft(J)s
FB(j)p Ft(\026\027)1483 2473 y Fs(\021)1785 2600 y FH(\(6.2\))-5
2707 y(where)g(the)h Fv(n)f FH(complex)f(\014elds)h Fv(z)623
2689 y Ft(i)656 2707 y FH(span)i(some)d Fu(sp)n(e)n(cial)j(K\177)-25
b(ahler)21 b(manifold)g(of)f(the)h(rigid)f(typ)n(e)f
FE(S)t(M)-5 2768 y FH(and)h(the)e(4)p Fv(m)h FH(real)g(\014elds)f
Fv(q)514 2750 y Ft(u)555 2768 y FH(span)i(a)f(Hyp)q(erK\177)-24
b(ahler)18 b(manifold)g FE(HM)p FH(.)29 b(By)18 b Fv(g)1461
2775 y Ft(ij)1489 2766 y Fm(?)1529 2768 y FH(and)i Fv(h)1655
2775 y Ft(uv)1714 2768 y FH(w)o(e)f(ha)o(v)o(e)916 2892
y(26)p eop
%%Page: 27 28
27 27 bop -5 15 a FH(denoted)21 b(the)g(metrics)d(on)k(these)e(t)o(w)o
(o)h(manifolds.)34 b(The)20 b(p)q(erio)q(d)i(matrix)d
FE(N)1466 22 y Ft(I)s(J)1529 15 y FH(dep)q(ends)i(only)g(on)-5
76 y(the)h(sp)q(ecial)g(manifold)g(co)q(ordinates)h Fv(z)749
58 y Ft(i)763 76 y Fv(;)8 b(z)810 58 y Ft(j)826 46 y
Fm(?)868 76 y FH(and)23 b(it)f(is)g(expressed)g(in)g(terms)f(of)i(the)f
(symplectic)-5 136 y(sections)c(of)h(the)e(\015at)i(symplectic)c
(bundle)j(b)o(y)f(eq.)g(4.57)p
 (#equation.4.57) [[303 734 324 746] [1 1 1 [3 3]] [0 0 1]] pdfm (.)28
b(In)17 b(b)q(oth)i(theories)f(there)g(are)g(no)g(electric)-5
196 y(or)h(magnetic)e(curren)o(ts)g(and)i(w)o(e)f(ha)o(v)o(e)g(on)h
(shell)e Fu(symple)n(ctic)j(c)n(ovarianc)n(e)p FH(.)28
b(By)18 b(means)f(of)i(the)f(\014rst)-5 256 y(homomorphism)h(in)i(eq.)g
(2.33)p
 (#equation.2.33) [[190 706 210 718] [1 1 1 [3 3]] [0 0 1]] pdfm 
22 w(an)o(y)g(di\013eomorphism)e(of)j(the)f(scalar)h(manifold)e(can)i
(b)q(e)f(lifted)g(to)-5 316 y(a)g(symplectic)c(transformation)j(on)g
(the)g(electric{magnetic)d(\014eld)i(strengths,)i(the)f
Fu(p)n(erio)n(d)f FH(matrix)-5 377 y(transforming,)d(b)o(y)f
(construction,)h(co)o(v)m(arian)o(tly)f(as)i(required)e(b)o(y)g(eq.)h
(2.38)p
 (#equation.2.38) [[385 677 405 689] [1 1 1 [3 3]] [0 0 1]] pdfm (.)21
b(Under)16 b(this)g(lifting)f(an)o(y)-5 437 y(isometry)h(of)j(the)e
(scalar)h(manifold)f(b)q(ecomes)f(a)j(symmetry)14 b(of)k(the)g
(di\013eren)o(tial)e(system)h(made)g(b)o(y)-5 497 y(the)j(equations)h
(of)f(motions)g(plus)g(Bianc)o(hi)f(iden)o(tities.)31
b(There)20 b(are)g(in)g(fact)g(three)g(t)o(yp)q(e)g(of)g(these)-5
557 y(isometries:)55 654 y(1.)k Fu(The)18 b(classic)n(al)h(symmetries)p
FH(,)d(namely)f(those)i(isometries)d Fv(\030)26 b FE(2)d(I)12
b FH(\()p FE(M)1424 661 y Ft(scalar)1523 654 y FH(\))17
b(whose)g(image)e(in)117 714 y(the)h(symplectic)d(group)k(is)g(blo)q(c)
o(k{diagonal:)734 846 y Fv(\023)751 853 y Ft(\016)771
846 y FH(\()p Fv(\030)r FH(\))22 b(=)914 773 y Fs( )968
815 y Fv(A)1005 822 y Ft(\030)1127 815 y FH(0)984 875
y(0)57 b(\()p Fv(A)1121 857 y Ft(T)1121 887 y(\030)1148
875 y FH(\))1167 857 y FB(\000)p FC(1)1235 773 y Fs(!)1785
846 y FH(\(6.3\))117 978 y(These)24 b(transformations)h(are)f(exact)g
(ordinary)h(symme)o(tries)c(of)k(the)f(Lagrangian.)47
b(They)117 1038 y(clearly)15 b(form)g(a)i(subgroup)688
1142 y FE(C)s Fv(l)q(as)8 b FH(\()p FE(M)869 1149 y Ft(scalar)968
1142 y FH(\))22 b FE(\032)g(I)12 b FH(\()p FE(M)1188
1149 y Ft(scalar)1287 1142 y FH(\))479 b(\(6.4\))55 1265
y(2.)24 b Fu(The)16 b(p)n(erturb)n(ative)g(symmetries)p
FH(,)e(namely)e(those)j(isometries)d Fv(\030)25 b FE(2)d(I)12
b FH(\()p FE(M)1486 1272 y Ft(scalar)1585 1265 y FH(\))i(whose)h(image)
117 1326 y(in)h(the)g(symplectic)d(group)k(is)f(lo)o(w)o(er)g
(triangular:)730 1458 y Fv(\023)747 1465 y Ft(\016)766
1458 y FH(\()p Fv(\030)r FH(\))23 b(=)910 1385 y Fs( )964
1427 y Fv(A)1001 1434 y Ft(\030)1123 1427 y FH(0)965
1487 y Fv(C)1000 1494 y Ft(\030)1061 1487 y FH(\()p Fv(A)1117
1469 y Ft(T)1117 1499 y(\030)1144 1487 y FH(\))1163 1469
y FB(\000)p FC(1)1231 1385 y Fs(!)1785 1458 y FH(\(6.5\))117
1590 y(These)c(transformations)g(map)f(the)h(electric)e(\014eld)h
(strengths)h(in)o(to)g(linear)f(com)o(binations)g(of)117
1650 y(the)24 b(electric)e(\014eld)i(strengths)h(and)g(can)f(b)q(e)h
(reduced)e(to)i(linear)e(transformations)i(of)f(the)117
1710 y(gauge)18 b(p)q(oten)o(tials.)24 b(They)17 b(are)g(almost)f(in)o
(v)m(ariances)h(of)g(the)g(action.)24 b(Indeed)16 b(the)h(only)g(non{)
117 1770 y(in)o(v)m(ariance)f(comes)e(from)i(the)g(transformation)g(of)
g(the)g(p)q(erio)q(d)h(matrix)598 1874 y FE(N)29 b(\000)-9
b(!)22 b FH(\()p Fv(A)826 1854 y Ft(T)826 1887 y(\030)853
1874 y FH(\))872 1854 y FB(\000)p FC(1)928 1874 y FE(N)7
b FH(\()p Fv(A)1032 1881 y Ft(\030)1051 1874 y FH(\))1070
1854 y FB(\000)p FC(1)1136 1874 y FH(+)19 b Fv(C)1228
1881 y Ft(\030)1255 1874 y FH(\()p Fv(A)1311 1854 y Ft(T)1311
1887 y(\030)1338 1874 y FH(\))1357 1854 y FB(\000)p FC(1)1785
1874 y FH(\(6.6\))117 1978 y(Denoting)14 b(collectiv)o(el)o(y)c(all)j
(the)g(\014elds)f(of)i(the)f(theory)f(b)o(y)h(\010)g(and)h(utilizing)e
(eq.s)g(2.5)p
 (#equation.2.5) [[458 292 473 304] [1 1 1 [3 3]] [0 0 1]] pdfm (,)h
(2.8)p  (#equation.2.8) [[479 292 494 304] [1 1 1 [3 3]] [0 0 1]] pdfm 
(,)g(2.10)p
 (#equation.2.10) [[500 292 521 304] [1 1 1 [3 3]] [0 0 1]] pdfm (,)117
2038 y(2.11)p
 (#equation.2.11) [[100 278 121 290] [1 1 1 [3 3]] [0 0 1]] pdfm (,)k
(2.38)p
 (#equation.2.38) [[128 278 149 290] [1 1 1 [3 3]] [0 0 1]] pdfm (,)f
(under)g(a)h(p)q(erturbativ)o(e)f(transformation)g(the)g(action)g(c)o
(hanges)h(as)f(follo)o(ws:)468 2096 y Fs(Z)526 2154 y
FE(L)p FH(\(\010\))8 b Fv(d)666 2134 y FC(4)687 2154
y Fv(x)41 b FE(!)848 2096 y Fs(Z)906 2154 y FE(L)p FH(\(\010)994
2134 y FB(0)1006 2154 y FH(\))8 b Fv(d)1058 2134 y FC(4)1078
2154 y Fv(x)j FH(+)19 b(\001)p Fv(\022)1238 2161 y FC(\003\006)1306
2096 y Fs(Z)1356 2154 y Fv(F)1395 2134 y FC(\003)1432
2154 y FE(^)11 b Fv(F)1515 2134 y FC(\006)599 2270 y
FH(\001)p Fv(\022)663 2277 y FC(\003\006)762 2270 y FH(=)853
2236 y(1)p 853 2259 25 2 v 853 2304 a(2)899 2222 y Fs(h)918
2270 y Fv(C)953 2277 y Ft(\030)980 2270 y FH(\()p Fv(A)1036
2250 y Ft(T)1036 2283 y(\030)1063 2270 y FH(\))1082 2250
y FB(\000)p FC(1)1130 2222 y Fs(i)1149 2297 y FC(\003\006)1785
2270 y FH(\(6.7\))117 2407 y(The)16 b(added)g(term)e(is)i(a)g(total)h
(deriv)m(ativ)o(e)d(and)i(do)q(es)h(not)f(a\013ect)g(the)g(\014eld)f
(equations.)21 b(Quan-)117 2467 y(tum)f(mec)o(hanicall)o(y)l(,)e(ho)o
(w)o(ev)o(er,)i(it)g(is)h(relev)m(an)o(t.)33 b(It)20
b(corresp)q(onds)i(to)f(a)g(rede\014nition)e(of)i(the)117
2527 y Fv(theta)p FH({angle.)27 b(It)19 b(yields)e(a)i(symmetry)c(of)k
(the)f(path{in)o(tegral)h(as)g(long)g(as)h(the)e(added)h(term)117
2587 y(is)c(an)h(in)o(teger)e(m)o(ultiple)e(of)j(2)p
Fv(\031)r FH(\026)-25 b Fv(h)q FH(.)20 b(This)c(consideration)f(will)f
(restrict)g(the)h(p)q(ossible)g(p)q(erturba-)117 2647
y(tiv)o(e)h(transformations)h(to)h(a)g(discrete)e(subgroup.)25
b(In)17 b(an)o(y)g(case)g(the)g(group)h(of)g(p)q(erturbativ)o(e)117
2707 y(isometries)11 b(de\014ned)h(b)o(y)g(eq.)g(6.5)p
 (#equation.6.5) [[227 117 241 129] [1 1 1 [3 3]] [0 0 1]] pdfm 
13 w(con)o(tains)h(the)f(group)i(of)f(classical)f(isometries)f(as)i(a)g
(subgroup:)117 2768 y FE(I)f FH(\()p FE(M)235 2775 y
Ft(scalar)334 2768 y FH(\))i FE(\033)f(P)t Fv(er)q(t)8
b FH(\()p FE(M)609 2775 y Ft(scalar)708 2768 y FH(\))14
b FE(\033)f(C)s Fv(l)q(as)8 b FH(\()p FE(M)974 2775 y
Ft(scalar)1073 2768 y FH(\).)916 2892 y(27)p eop
%%Page: 28 29
28 28 bop 55 15 a FH(3.)24 b Fu(The)d(non{p)n(erturb)n(ative)g
(symmetries)f FH(namely)d(those)j(isometries)e Fv(\030)31
b FE(2)d(I)12 b FH(\()p FE(M)1620 22 y Ft(scalar)1719
15 y FH(\))19 b(whose)117 76 y(image)c(in)h(the)g(symplectic)d(group)k
(is)f(of)h(the)f(form:)775 214 y Fv(\023)792 221 y Ft(\016)811
214 y FH(\()p Fv(\030)r FH(\))23 b(=)955 141 y Fs( )1009
184 y Fv(A)1046 191 y Ft(\030)1108 184 y Fv(B)1145 191
y Ft(\030)1010 244 y Fv(C)1045 251 y Ft(\030)1106 244
y Fv(D)1146 251 y Ft(\030)1186 141 y Fs(!)1785 214 y
FH(\(6.8\))117 352 y(with)17 b Fv(B)266 359 y Ft(\030)300
352 y FE(6)p FH(=)e(0.)23 b(These)17 b(transformations)g(are)g(neither)
f(a)h(symmetry)d(of)j(the)g(classical)f(action)117 413
y(nor)22 b(of)f(the)g(p)q(erturbativ)o(e)f(path)i(in)o(tegral.)35
b(Y)l(et)20 b(they)h(are)g(a)g(symmetry)d(of)k(the)e(quan)o(tum)117
473 y(theory)l(.)h(They)16 b(exc)o(hange)f(electric)f(\014eld)h
(strengths)i(with)f(magnetic)e(ones,)i(electric)e(curren)o(ts)117
533 y(with)i(magnetic)f(ones)i(and)f(hence)g(elemen)o(tary)d
(excitations)j(with)g(soliton)g(states.)-5 635 y(The)k(ab)q(o)o(v)o(e)f
(discussion)g(of)h(dualit)o(y)e(symmetri)o(es)f(ma)o(y)g(b)q(e)j(in)o
(triguing)e(for)i(the)f(follo)o(wing)g(reason.)-5 695
y(Ho)o(w)c(can)h(w)o(e)f(talk)g(ab)q(out)h(non{p)q(erturbativ)o(e)g
(symmetri)o(es)c(that)k(exc)o(hange)f(electric)e(c)o(harges)i(with)-5
755 y(magnetic)j(c)o(harges)i(if,)f(so)h(far,)g(in)g(the)f(ab)q(elian)h
(theories)f(describ)q(ed)g(b)o(y)g(eq.s)f(6.1)p
 (#equation.6.1) [[431 586 446 598] [1 1 1 [3 3]] [0 0 1]] pdfm 
20 w(and)40 b(6.2)p
 (#equation.6.2) [[479 586 494 598] [1 1 1 [3 3]] [0 0 1]] pdfm 
20 w(there)-5 815 y(are)16 b(neither)f(electric)e(nor)j(magnetic)e
(couplings?)22 b(The)15 b(answ)o(er)h(is)g(that)g(the)f(same)g(general)
g(form)g(of)-5 875 y(ab)q(elian)i(theories)e(enco)q(ded)i(in)f(these)g
(equations)g(can)g(b)q(e)h(tak)o(en)f(to)g(represen)o(t)f(t)o(w)o(o)i
(quite)e(di\013eren)o(t)-5 936 y(things:)55 1037 y(1.)24
b(The)c(fundamen)o(tal)e(theory)h(prior)g(to)h(the)f(gauging.)33
b(It)19 b(is)g(neutral)g(and)h(ab)q(elian)g(since)e(the)117
1098 y(non{ab)q(elian)13 b(in)o(teractions)e(and)h(the)f(electric)f(c)o
(harges)h(are)h(in)o(tro)q(duced)f(only)h(b)o(y)f(the)g(gauging,)117
1158 y(but)17 b(it)e(con)o(tains)i(all)e(the)h(fundamen)o(tal)f
(\014elds.)55 1259 y(2.)24 b(The)17 b(e\013ectiv)o(e)e(theory)h(of)h
(the)g(massless)f(mo)q(des)g(of)h(the)g(non{ab)q(elian)h(theory)l(.)k
(It)16 b(is)h(ab)q(elian)117 1320 y(and)d(neutral)g(b)q(ecause)g(the)f
(only)h(\014elds)f(whic)o(h)g(remain)f(massless)h(are,)h(apart)g(from)f
(the)g(gra)o(vi-)117 1380 y(ton,)22 b(the)e(m)o(ultiple)o(ts)e(in)i
(the)g(Cartan)h(subalgebra)h FE(H)f(\032)f(G)j FH(of)e(the)f(gauge)h
(group)g(and)g(the)117 1440 y(neutral)16 b(h)o(yp)q(erm)o(ultiplets)d
(corresp)q(onding)k(to)g(\015at)g(directions)e(of)i(the)f(scalar)g(p)q
(oten)o(tial.)-5 1542 y(What)h(distinguishes)f(the)g(t)o(w)o(o)g(cases)
h(is)f(the)g(t)o(yp)q(e)g(of)g(scalar)h(manifolds)e(and)i(their)e
(isometries.)68 1602 y(In)h(case)h(1\))f(w)o(e)g(ha)o(v)o(e:)551
1712 y(dim)632 1719 y Ff(C)672 1712 y FE(S)t(M)41 b FH(=)g
Fv(n)14 b FE(\021)g FH(dim)7 b FE(G)503 1768 y FH(1)p
503 1790 25 2 v 503 1836 a(4)541 1802 y(dim)622 1809
y Ff(R)663 1802 y FE(HM)42 b FH(=)887 1798 y Fs(c)886
1802 y Fv(m)14 b FE(\021)g FH(#)8 b(of)16 b(all)g(h)o(yp)q(erm)o(ul.)
400 b(\(6.9\))68 1927 y(while)16 b(in)g(case)g(2\))h(w)o(e)e(ha)o(v)o
(e)h(instead:)503 2037 y(dim)584 2044 y Ff(C)624 2037
y FE(S)t(M)41 b FH(=)g Fv(r)16 b FE(\021)d FH(rank)c
FE(G)455 2093 y FH(1)p 455 2116 V 455 2161 a(4)493 2127
y(dim)574 2134 y Ff(R)615 2127 y FE(HM)42 b FH(=)f Fv(m)14
b FE(\021)f FH(#)8 b(of)17 b(mo)q(duli)e(h)o(yp)q(erm)o(ul.)327
b(\(6.10\))-5 2250 y(As)13 b(far)g(as)g(the)g(gauging)h(of)f(the)f
Fv(N)19 b FH(=)14 b(2)f(theory)g(is)f(concerned,)h(the)f(problem)f
(consists)i(in)g(iden)o(tifying)-5 2310 y(the)20 b(gauge)h(group)g
FE(G)i FH(as)e(a)f(subgroup,)j(at)d(most)f(of)i(dimension)d
Fv(n)c FH(+)g(1)20 b(of)h(the)f(isometries)e(of)i(the)-5
2370 y(pro)q(duct)d(space)797 2430 y FE(S)t(M)11 b(\002)f(HM)17
b Fv(:)676 b FH(\(6.11\))68 2518 y(Here)17 b(w)o(e)g(shall)h(mainly)e
(consider)h(t)o(w)o(o)h(cases)g(ev)o(en)e(if)h(more)g(general)g
(situations)i(are)e(p)q(ossible.)-5 2578 y(The)h(\014rst)f(is)g(when)g
(the)g(gauge)i(group)f Fv(G)f FH(is)g(non)h(ab)q(elian,)f(the)g(second)
h(is)f(when)g(it)g(is)g(the)g(ab)q(elian)-5 2638 y(group)i
Fv(G)d FH(=)g Fv(U)5 b FH(\(1\))343 2620 y Ft(n)364 2626
y Fm(V)392 2620 y FC(+1)439 2638 y FH(.)25 b(In)17 b(the)g(\014rst)h
(case)g(sup)q(ersymmetry)c(requires)i(that)i Fv(G)g FH(b)q(e)g(a)g
(subgroup)h(of)-5 2698 y(the)g(isometries)e(of)i FE(M)p
FH(,)g(since)g(the)f(scalars)i(\(more)e(precisely)l(,)f(the)i(sections)
g Fv(L)1495 2680 y FC(\003)1521 2698 y FH(\))g(m)o(ust)f(b)q(elong)i
(to)916 2892 y(28)p eop
%%Page: 29 30
29 29 bop -5 15 a FH(the)20 b(adjoin)o(t)g(represen)o(tation)g(of)h
Fv(G)p FH(.)33 b(In)20 b(suc)o(h)g(case)g(the)g(h)o(yp)q(erm)o(ultiple)
o(t)d(space)k(will)e(generically)-5 76 y(split)d(in)o(to[35)p
 (#cite.dere) [[120 749 132 761] [1 1 1 [3 3]] [0 0 1]] pdfm (])646
158 y Fv(n)675 165 y Ft(H)723 158 y FH(=)775 117 y Fs(X)799
208 y Ft(i)843 158 y Fv(n)872 165 y Ft(i)886 158 y Fv(R)923
165 y Ft(i)949 158 y FH(+)1003 124 y(1)p 1003 146 25
2 v 1003 192 a(2)1040 117 y Fs(X)1065 209 y Ft(l)1108
158 y Fv(n)1137 138 y Ft(P)1137 170 y(l)1167 158 y Fv(R)1204
138 y Ft(P)1204 170 y(l)1760 158 y FH(\(6.12\))-5 285
y(where)g Fv(R)173 292 y Ft(i)204 285 y FH(and)h Fv(R)336
267 y Ft(P)336 297 y(l)382 285 y FH(are)f(a)h(set)f(of)g(irreducible)e
(represen)o(tations)i(of)h Fv(G)g FH(and)g Fv(R)1457
267 y Ft(P)1457 297 y(l)1503 285 y FH(denote)f(pseudoreal)-5
345 y(represen)o(tations.)68 405 y(In)i(the)g(ab)q(elian)g(case,)g(the)
g(sp)q(ecial)f(manifold)g(is)h(not)g(required)f(to)i(ha)o(v)o(e)e(an)o
(y)h(isometry)e(and)j(if)-5 465 y(the)e(h)o(yp)q(erm)o(ultiple)o(ts)e
(are)i(c)o(harged)g(with)g(resp)q(ect)f(to)i(the)f Fv(n)1148
472 y Ft(V)1190 465 y FH(+)11 b(1)18 b Fv(U)5 b FH(\(1\)'s,)17
b(then)g(the)g FE(Q)f FH(manifold)-5 526 y(should)h(at)g(least)f(ha)o
(v)o(e)f Fv(n)465 533 y Ft(V)507 526 y FH(+)c(1)16 b(ab)q(elian)h
(isometries.)68 586 y(As)f(a)h(consequence)e(of)h(gauging)h(the)f
(Lagrangians)i(in)e(eq.s)f(6.1)p
 (#equation.6.1) [[361 626 376 638] [1 1 1 [3 3]] [0 0 1]] pdfm 
16 w(and)33 b(6.2)p
 (#equation.6.2) [[406 626 421 638] [1 1 1 [3 3]] [0 0 1]] pdfm 
16 w(get)16 b(mo)q(di\014ed)f(b)o(y)g(the)-5 646 y(replacemen)o(t)e(of)
j(ordinary)g(deriv)m(ativ)o(es)e(with)i(co)o(v)m(arian)o(t)f(deriv)m
(ativ)o(es)f(and)j(b)o(y)e(the)g(in)o(tro)q(duction)h(of)-5
706 y(new)h(terms)d(that)j(are)f(of)h(t)o(w)o(o)f(t)o(yp)q(es:)55
808 y(1.)24 b(fermion{fermion)13 b(bilinears)j(with)g(scalar)g(\014eld)
g(dep)q(enden)o(t)g(co)q(e\016cien)o(ts)55 910 y(2.)24
b(A)16 b(scalar)h(p)q(oten)o(tial)e(V)-5 1011 y(It)22
b(is)f(particularly)g(nice)g(and)h(rew)o(arding)g(that)g(all)f(the)h
(mo)q(di\014cations)f(of)h(the)g(Lagrangian)h(and)-5
1072 y(of)d(the)f(sup)q(ersymmetry)d(transformation)j(rules)g(can)g(b)q
(e)h(describ)q(ed)e(in)h(terms)f(of)i(a)f(v)o(ery)f(general)-5
1132 y(geometric)13 b(construction)h(asso)q(ciated)h(with)f(the)g
(action)h(of)f(Lie{Groups)i(on)f(manifolds)e(that)h(admit)-5
1192 y(a)21 b(symplectic)d(structure:)30 b Fu(the)22
b(momentum)g(map)p FH(.)35 b(In)20 b(sup)q(ersymmetry)e(indeed,)j(the)f
(geometric)-5 1252 y(notion)15 b(of)g Fu(momentum)h(map)e
FH(has)h(an)g(exact)f(corresp)q(ondence)g(with)g(the)g(notion)h(of)g
Fu(gauge)h(multiplet)-5 1312 y(auxiliary)k(\014elds)g
FH(or)f Fv(D)q Fu({\014elds)p FH(.)31 b(Next)18 b(section)g(is)h(dev)o
(oted)f(to)h(a)h(review)d(of)j(the)e(momen)o(tum)d(map)-5
1372 y(and)i(to)g(its)f(applications)g(in)g(N=2)g(theories.)-5
1539 y Fw(7)81 b(The)27 b(Momen)n(tum)g(Map)-5 1648 y
FH(The)21 b(momen)o(tum)c(map)k(is)g(a)g(construction)g(that)h(applies)
f(to)g(all)g(manifolds)f(with)h(a)g(symplectic)-5 1709
y(structure,)16 b(in)g(particular)g(to)g(K\177)-24 b(ahler,)16
b(Hyp)q(erK\177)-24 b(ahler)15 b(and)i(Quaternionic)e(manifolds.)68
1769 y(Let)j(us)g(b)q(egin)f(with)h(the)f(K\177)-24 b(ahler)17
b(case,)g(namely)f(with)h(the)h(momen)o(tum)13 b(map)j(of)i
(holomorphic)-5 1829 y(isometries.)23 b(The)17 b(Hyp)q(erK\177)-24
b(ahler)17 b(and)h(quaternionic)e(case)i(corresp)q(ond,)g(instead,)f
(to)h(the)f(momen-)-5 1889 y(tum)e(map)h(of)g(triholomorphic)f
(isometries.)-5 2034 y Fk(7.1)66 b(Holomorphic)24 b(momen)n(tum)f(map)f
(on)h(K\177)-33 b(ahler)21 b(manifolds)-5 2126 y FH(Let)c
Fv(g)106 2133 y Ft(ij)134 2124 y Fm(?)172 2126 y FH(b)q(e)g(the)g
(K\177)-24 b(ahler)17 b(metric)e(of)i(a)g(K\177)-24 b(ahler)17
b(manifold)f FE(M)p FH(:)23 b(it)16 b(app)q(ears)i(in)f(the)g(kinetic)e
(term)h(of)-5 2186 y(the)e(scalar)g(\014elds:)19 b(the)14
b(W)l(ess{Zumino)e(m)o(ultiplet)f(scalars)j(in)f(N=1)h(theories,)f(the)
h(v)o(ector)e(m)o(ultiplet)-5 2246 y(scalars)j(in)f(N=2)g(theories.)20
b(If)13 b(the)h(metric)e Fv(g)820 2253 y Ft(ij)848 2244
y Fm(?)883 2246 y FH(has)j(a)f(non)h(trivial)e(group)i(of)f(con)o(tin)o
(uous)g(isometries)-5 2306 y FE(G)j FH(generated)e(b)o(y)f(Killing)f(v)
o(ectors)h Fv(k)678 2288 y Ft(i)676 2319 y FC(\003)717
2306 y FH(\(\003)g(=)g(1)p Fv(;)8 b(:)g(:)g(:)g(;)g FH(dim)e
FE(G)s FH(\),)14 b(then)g(the)h(kinetic)d(Lagrangian)17
b(admits)-5 2367 y FE(G)i FH(as)e(a)g(group)g(of)f(global)h(space{time)
e(symmet)o(ries.)j(Indeed)e(under)g(an)h(in\014nitesimal)c(v)m
(ariation)752 2477 y Fv(z)777 2456 y Ft(i)805 2477 y
FE(!)g Fv(z)893 2456 y Ft(i)918 2477 y FH(+)e Fv(\017)987
2456 y FC(\003)1014 2477 y Fv(k)1041 2456 y Ft(i)1039
2489 y FC(\003)1066 2477 y FH(\()p Fv(z)r FH(\))656 b(\(7.1\))-5
2587 y FE(L)29 2594 y Ft(k)q(in)99 2587 y FH(remains)14
b(in)o(v)m(arian)o(t.)20 b(F)l(urthermore)13 b(if)i(all)f(the)h
(couplings)g(of)h(the)e(scalar)i(\014elds)e(are)h(p)q(erformed)-5
2647 y(in)j(a)h(di\013eomorphic)d(in)o(v)m(arian)o(t)i(w)o(a)o(y)l(,)g
(then)g(an)o(y)g(isometry)e(of)j Fv(g)1210 2654 y Ft(ij)1238
2645 y Fm(?)1277 2647 y FH(extends)e(from)g(a)i(symmetry)c(of)-5
2707 y FE(L)29 2714 y Ft(k)q(in)103 2707 y FH(to)k(a)h(symmetry)15
b(of)k(the)g(whole)g(Lagrangian.)31 b(Di\013eomorphic)17
b(in)o(v)m(ariance)h(means)g(that)h(the)-5 2767 y(scalar)f(\014elds)f
(can)g(app)q(ear)h(only)f(through)h(the)f(metric,)d(the)j
(Christo\013el)h(sym)o(b)q(ol)e(in)g(the)h(co)o(v)m(arian)o(t)916
2892 y(29)p eop
%%Page: 30 31
30 30 bop -5 15 a FH(deriv)m(ativ)o(e)15 b(and)i(through)h(the)e(curv)m
(ature.)23 b(Alternativ)o(ely)13 b(they)j(can)h(app)q(ear)h(through)f
(sections)g(of)-5 76 y(v)o(ector)h(bundles)g(constructed)g(o)o(v)o(er)f
FE(M)p FH(.)27 b(T)o(ypical)17 b(case)h(is)g(the)g(dep)q(endence)f(on)i
(the)f(scalar)g(\014elds)-5 136 y(in)o(tro)q(duced)e(b)o(y)g(the)g
Fu(p)n(erio)n(d)g(matrix)g FE(N)7 b FH(.)68 196 y(Let)14
b Fv(k)180 178 y Ft(i)178 208 y FC(\003)205 196 y FH(\()p
Fv(z)r FH(\))f(b)q(e)h(a)f(basis)h(of)g(holomorphic)e(Killing)g(v)o
(ectors)h(for)h(the)f(metric)e Fv(g)1473 203 y Ft(ij)1501
194 y Fm(?)1522 196 y FH(.)20 b(Holomorphicit)o(y)-5
256 y(means)c(the)g(follo)o(wing)g(di\013eren)o(tial)e(constrain)o(t:)
640 366 y Fv(@)666 373 y Ft(j)682 364 y Fn(\003)702 366
y Fv(k)729 346 y Ft(i)727 379 y FC(\003)754 366 y FH(\()p
Fv(z)r FH(\))g(=)f(0)i FE($)e Fv(@)1010 373 y Ft(j)1028
366 y Fv(k)1055 346 y Ft(i)1067 334 y Fn(\003)1053 379
y FC(\003)1087 366 y FH(\()p 1106 340 25 2 v Fv(z)r FH(\))h(=)g(0)545
b(\(7.2\))-5 476 y(while)16 b(the)g(generic)f(Killing)g(equation)h
(\(suppressing)h(the)f(gauge)h(index)e(\003\):)753 586
y FE(r)795 593 y Ft(\026)818 586 y Fv(k)843 593 y Ft(\027)876
586 y FH(+)c FE(r)967 593 y Ft(\026)990 586 y Fv(k)1015
593 y Ft(\027)1051 586 y FH(=)j(0)658 b(\(7.3\))-5 696
y(in)16 b(holomorphic)f(indices)g(reads)i(as)g(follo)o(ws:)470
806 y FE(r)512 813 y Ft(i)526 806 y Fv(k)551 813 y Ft(j)580
806 y FH(+)11 b FE(r)671 813 y Ft(j)689 806 y Fv(k)714
813 y Ft(i)770 806 y FH(=)41 b(0)h(;)f FE(r)1012 813
y Ft(i)1024 804 y Fn(\003)1044 806 y Fv(k)1069 813 y
Ft(j)1099 806 y FH(+)11 b FE(r)1190 813 y Ft(j)1208 806
y Fv(k)1233 813 y Ft(i)1245 804 y Fn(\003)1306 806 y
FH(=)42 b(0)375 b(\(7.4\))-5 916 y(where)16 b(the)g(co)o(v)m(arian)o(t)
g(comp)q(onen)o(ts)g(are)g(de\014ned)g(as)h Fv(k)1033
923 y Ft(j)1065 916 y FH(=)d Fv(g)1140 923 y Ft(j)r(i)1168
914 y Fn(\003)1189 916 y Fv(k)1216 898 y Ft(i)1228 886
y Fn(\003)1264 916 y FH(\(and)j(similarly)c(for)k Fv(k)1677
923 y Ft(i)1689 914 y Fn(\003)1709 916 y FH(\).)68 976
y(The)c(v)o(ectors)f Fv(k)354 958 y Ft(i)352 989 y FC(\003)391
976 y FH(are)g(generators)i(of)e(in\014nitesimal)e(holomorphic)h(co)q
(ordinate)i(transformations:)796 1086 y Fv(\016)r(z)845
1066 y Ft(i)872 1086 y FH(=)h Fv(\017)944 1066 y FC(\003)970
1086 y Fv(k)997 1066 y Ft(i)995 1099 y FC(\003)1022 1086
y FH(\()p Fv(z)r FH(\))700 b(\(7.5\))-5 1196 y(whic)o(h)13
b(lea)o(v)o(e)e(the)i(metric)e(in)o(v)m(arian)o(t.)19
b(In)13 b(the)g(same)f(w)o(a)o(y)h(as)h(the)f(metric)e(is)i(the)g
(deriv)m(ativ)o(e)e(of)j(a)f(more)-5 1257 y(fundamen)o(tal)e(ob)s
(ject,)h(the)g(Killing)f(v)o(ectors)h(in)f(a)i(K\177)-24
b(ahler)12 b(manifold)f(are)h(the)g(deriv)m(ativ)o(es)f(of)h(suitable)
-5 1317 y(prep)q(oten)o(tials.)20 b(Indeed)12 b(the)h(\014rst)h(of)f
(eq.s)f(7.4)p
 (#equation.7.4) [[260 451 275 463] [1 1 1 [3 3]] [0 0 1]] pdfm 
14 w(is)h(automatically)e(satis\014ed)i(b)o(y)g(holomorphic)f(v)o
(ectors)-5 1377 y(and)17 b(the)f(second)h(equation)f(reduces)f(to)i
(the)f(follo)o(wing)g(one:)645 1487 y Fv(k)672 1466 y
Ft(i)670 1499 y FC(\003)711 1487 y FH(=)e Fv(ig)805 1466
y Ft(ij)833 1455 y Fn(\003)853 1487 y Fv(@)879 1494 y
Ft(j)895 1485 y Fn(\003)915 1487 y FE(P)950 1494 y FC(\003)976
1487 y Fv(;)57 b FE(P)1086 1466 y FB(\003)1082 1499 y
FC(\003)1122 1487 y FH(=)14 b FE(P)1209 1494 y FC(\003)1785
1487 y FH(\(7.6\))-5 1597 y(In)k(other)g(w)o(ords)g(if)g(w)o(e)f(can)h
(\014nd)g(a)g(real)g(function)f FE(P)1008 1579 y FC(\003)1053
1597 y FH(suc)o(h)g(that)i(the)e(expression)h Fv(ig)1636
1579 y Ft(ij)1664 1567 y Fn(\003)1684 1597 y Fv(@)1710
1604 y Ft(j)1726 1595 y Fn(\003)1746 1597 y FE(P)1781
1605 y FC(\(\003\))1852 1597 y FH(is)-5 1657 y(holomorphic,)d(then)h
(eq.)f(7.6)p
 (#equation.7.6) [[186 369 201 381] [1 1 1 [3 3]] [0 0 1]] pdfm 
17 w(de\014nes)h(a)h(Killing)d(v)o(ector.)68 1717 y(The)e(construction)
g(of)f(the)h(Killing)e(prep)q(oten)o(tial)h(can)g(b)q(e)h(stated)g(in)f
(a)h(more)e(precise)g(geometrical)-5 1778 y(form)o(ulation)j(whic)o(h)g
(in)o(v)o(olv)o(es)f(the)h(notion)h(of)h Fu(momentum)g(map)p
FH(.)20 b(Let)14 b(us)h(review)d(this)i(construction)-5
1838 y(whic)o(h)i(rev)o(eals)f(another)i(deep)f(connection)f(b)q(et)o
(w)o(een)h(sup)q(ersymmetry)d(and)k(geometry)l(.)68 1898
y(Consider)c(a)h(K\177)-24 b(ahlerian)12 b(manifold)f
FE(M)i FH(of)g(real)f(dimension)f(2)p Fv(n)p FH(.)21
b(Consider)13 b(a)g(compact)f(Lie)g(group)-5 1958 y FE(G)21
b FH(acting)d(on)h FE(M)e FH(b)o(y)h(means)f(of)h(Killing)f(v)o(ector)g
(\014elds)h FD(X)g FH(whic)o(h)g(are)g(holomorphic)e(with)i(resp)q(ect)
-5 2018 y(to)d(the)f(complex)f(structure)h Fv(J)19 b
FH(of)c FE(M)p FH(;)f(then)h(these)f(v)o(ector)g(\014elds)g(preserv)o
(e)f(also)i(the)f(K\177)-24 b(ahler)14 b(2-form)118 2127
y FE(L)152 2134 y Fe(X)180 2127 y Fv(g)i FH(=)e(0)52
b FE($)d(r)488 2134 y FC(\()p Ft(\026)524 2127 y Fv(X)564
2134 y Ft(\027)r FC(\))614 2127 y FH(=)14 b(0)115 2187
y FE(L)149 2194 y Fe(X)177 2187 y Fv(J)k FH(=)c(0)699
2084 y Fs(\))774 2157 y FE(\))41 b FH(0)14 b(=)g FE(L)989
2164 y Fe(X)1017 2157 y Fv(K)k FH(=)c Fv(i)1145 2164
y Fe(X)1172 2157 y Fv(dK)h FH(+)c Fv(d)p FH(\()p Fv(i)1363
2164 y Fe(X)1391 2157 y Fv(K)t FH(\))j(=)g Fv(d)p FH(\()p
Fv(i)1582 2164 y Fe(X)1609 2157 y Fv(K)t FH(\))112 b(\(7.7\))-5
2295 y(Here)18 b FE(L)147 2302 y Fe(X)194 2295 y FH(and)i
Fv(i)309 2302 y Fe(X)355 2295 y FH(denote)f(resp)q(ectiv)o(ely)e(the)h
(Lie)h(deriv)m(ativ)o(e)e(along)j(the)f(v)o(ector)f(\014eld)g
FD(X)i FH(and)f(the)-5 2355 y(con)o(traction)d(\(of)h(forms\))e(with)h
(it.)68 2416 y(If)k FE(M)f FH(is)h(simply)e(connected,)h
Fv(d)p FH(\()p Fv(i)719 2423 y Ff(X)752 2416 y Fv(K)t
FH(\))h(=)g(0)g(implies)d(the)j(existence)e(of)i(a)g(function)g
FE(P)1739 2423 y Ff(X)1791 2416 y FH(suc)o(h)-5 2476
y(that)765 2546 y FE(\000)835 2512 y FH(1)p 820 2534
54 2 v 820 2580 a(2)p Fv(\031)879 2546 y(d)p FE(P)939
2553 y Ff(X)985 2546 y FH(=)14 b Fv(i)1054 2553 y Fe(X)1081
2546 y Fv(K)663 b FH(\(7.8\))-5 2646 y(The)21 b(function)g
FE(P)331 2653 y Ff(X)384 2646 y FH(is)g(de\014ned)f(up)h(to)g(a)h
(constan)o(t,)g(whic)o(h)e(can)h(b)q(e)g(arranged)g(so)h(as)f(to)h(mak)
o(e)d(it)-5 2706 y(equiv)m(arian)o(t:)788 2766 y FD(X)p
FE(P)865 2773 y Ff(Y)912 2766 y FH(=)14 b FE(P)999 2774
y FC([)p Ff(X)p Ft(;)p Ff(Y)q FC(])1785 2766 y FH(\(7.9\))916
2892 y(30)p eop
%%Page: 31 32
31 31 bop -5 15 a FE(P)30 22 y Ff(X)79 15 y FH(constitutes)16
b(then)g(a)h Fu(momentum)h(map)p FH(.)j(This)16 b(can)g(b)q(e)h
(regarded)f(as)h(a)g(map)729 125 y FE(P)g FH(:)d FE(M)21
b(\000)-8 b(!)22 b FH(I)-9 b(R)11 b FE(\012)p 1107 125
2 33 v 6 w FH(G)1132 104 y FB(\003)1760 125 y FH(\(7.10\))-5
234 y(where)p 145 234 V 12 w(G)171 213 y FB(\003)208
234 y FH(denotes)17 b(the)g(dual)g(of)h(the)e(Lie)h(algebra)p
983 234 V 13 w(G)h(of)f(the)g(group)h FE(G)s FH(.)24
b(Indeed)16 b(let)h Fv(x)e FE(2)p 1708 234 V 11 w FH(G)i(b)q(e)g(the)-5
294 y(Lie)f(algebra)h(elemen)o(t)c(corresp)q(onding)k(to)g(the)f
(Killing)f(v)o(ector)g FD(X)p FH(;)h(then,)g(for)g(a)h(giv)o(en)e
Fv(m)f FE(2)g(M)645 404 y Fv(\026)p FH(\()p Fv(m)p FH(\))22
b(:)g Fv(x)g FE(\000)-9 b(!)22 b(P)1000 411 y Ff(X)1032
404 y FH(\()p Fv(m)p FH(\))g FE(2)h FH(I)-9 b(R)524 b(\(7.11\))-5
513 y(is)17 b(a)h(linear)e(functional)h(on)p 530 513
V 13 w(G.)24 b(If)17 b(w)o(e)g(expand)g FD(X)f FH(=)f
Fv(a)1023 495 y FC(\003)1049 513 y Fv(k)1074 520 y FC(\003)1118
513 y FH(in)i(a)h(basis)f(of)h(Killing)e(v)o(ectors)g
Fv(k)1747 520 y FC(\003)1791 513 y FH(suc)o(h)-5 573
y(that)757 634 y([)p Fv(k)796 641 y FC(\003)823 634 y
Fv(;)8 b(k)870 641 y FC(\000)894 634 y FH(])13 b(=)h
Fv(f)1035 613 y FC(\001)997 646 y(\003\000)1066 634 y
Fv(k)1091 641 y FC(\001)1760 634 y FH(\(7.12\))-5 721
y(w)o(e)i(ha)o(v)o(e)g(also)809 781 y FE(P)844 788 y
Ff(X)898 781 y FH(=)22 b Fv(a)984 760 y FC(\003)1010
781 y FE(P)1045 788 y FC(\003)1760 781 y FH(\(7.13\))-5
868 y(In)i(the)f(follo)o(wing)h(w)o(e)f(use)g(the)h(shorthand)h
(notation)g FE(L)1106 875 y FC(\003)1132 868 y Fv(;)8
b(i)1171 875 y FC(\003)1221 868 y FH(for)24 b(the)g(Lie)f(deriv)m(ativ)
o(e)f(and)i(the)-5 928 y(con)o(traction)16 b(along)h(the)f(c)o(hosen)g
(basis)h(of)g(Killing)e(v)o(ectors)g Fv(k)1147 935 y
FC(\003)1174 928 y FH(.)68 988 y(F)l(rom)22 b(a)h(geometrical)e(p)q
(oin)o(t)i(of)g(view)f(the)h(prep)q(oten)o(tial,)g(or)h(momen)o(tum)18
b(map,)24 b FE(P)1713 995 y FC(\003)1762 988 y FH(is)e(the)-5
1048 y(Hamiltonian)11 b(function)g(pro)o(viding)h(the)g(P)o(oissonian)h
(realization)e(of)i(the)f(Lie)f(algebra)i(on)g(the)e(K\177)-24
b(ahler)-5 1108 y(manifold.)20 b(This)15 b(is)f(just)h(another)g(w)o(a)
o(y)g(of)g(stating)g(the)g(already)g(men)o(tioned)d Fu(e)n(quivarianc)n
(e)p FH(.)22 b(Indeed)-5 1169 y(the)c(v)o(ery)g(existence)e(of)j(the)f
(closed)g(2-form)g Fv(K)k FH(guaran)o(tees)d(that)g(ev)o(ery)e(K\177)
-24 b(ahler)18 b(space)g(is)g(a)h(sym-)-5 1229 y(plectic)c(manifold)g
(and)h(that)h(w)o(e)f(can)g(de\014ne)g(a)h(P)o(oisson)g(brac)o(k)o(et.)
68 1289 y(Consider)d(Eqs.)f(7.6)p
 (#equation.7.6) [[162 458 177 470] [1 1 1 [3 3]] [0 0 1]] pdfm (.)20
b(T)l(o)14 b(ev)o(ery)d(generator)j(of)f(the)g(abstract)h(Lie)f
(algebra)p 1453 1289 V 9 w(G)g(w)o(e)g(ha)o(v)o(e)f(asso)q(ciated)-5
1349 y(a)17 b(function)f FE(P)262 1356 y FC(\003)304
1349 y FH(on)h FE(M)p FH(;)f(the)g(P)o(oisson)h(brac)o(k)o(et)e(of)h
FE(P)984 1356 y FC(\003)1027 1349 y FH(with)g FE(P)1173
1356 y FC(\006)1216 1349 y FH(is)g(de\014ned)g(as)h(follo)o(ws:)696
1459 y FE(fP)756 1466 y FC(\003)782 1459 y Fv(;)8 b FE(P)839
1466 y FC(\006)866 1459 y FE(g)13 b(\021)h FH(4)p Fv(\031)r(K)t
FH(\(\003)p Fv(;)8 b FH(\006\))575 b(\(7.14\))-5 1573
y(where)16 b Fv(K)t FH(\(\003)p Fv(;)8 b FH(\006\))14
b FE(\021)g Fv(K)t FH(\()438 1560 y Fv(~)441 1573 y(k)466
1580 y FC(\003)492 1573 y Fv(;)512 1560 y(~)514 1573
y(k)539 1580 y FC(\006)567 1573 y FH(\))i(is)h(the)f(v)m(alue)g(of)g
Fv(K)k FH(along)d(the)f(pair)h(of)f(Killing)f(v)o(ectors.)68
1633 y(In)h(reference)f([24)p
 (#cite.DFF) [[156 375 167 387] [1 1 1 [3 3]] [0 0 1]] pdfm (])h(w)o(e)
g(pro)o(v)o(ed)f(the)h(follo)o(wing)g(lemma.)-5 1734
y FD(Lemma)g(7.1)24 b Fu(The)17 b(fol)r(lowing)j(identity)e(is)g(true:)
663 1844 y FE(fP)723 1851 y FC(\003)749 1844 y Fv(;)8
b FE(P)806 1851 y FC(\006)833 1844 y FE(g)14 b FH(=)f
Fv(f)988 1823 y FC(\000)947 1856 y(\003\006)1012 1844
y FE(P)1047 1851 y FC(\000)1082 1844 y FH(+)e Fv(C)1166
1851 y FC(\003\006)1760 1844 y FH(\(7.15\))-5 1953 y
Fu(wher)n(e)18 b Fv(C)168 1960 y FC(\003\006)237 1953
y Fu(is)g(a)f(c)n(onstant)h(ful\014l)r(ling)j(the)d(c)n(o)n(cycle)g(c)n
(ondition)576 2063 y Fv(f)640 2042 y FC(\000)600 2075
y(\003\005)664 2063 y Fv(C)699 2070 y FC(\000\006)760
2063 y FH(+)11 b Fv(f)873 2042 y FC(\000)833 2075 y(\005\006)897
2063 y Fv(C)932 2070 y FC(\000\003)992 2063 y FH(+)g
Fv(f)1105 2042 y FC(\000)1065 2075 y(\006\003)1129 2063
y Fv(C)1164 2070 y FC(\000\005)1228 2063 y FH(=)j(0)456
b(\(7.16\))-5 2172 y(If)17 b(the)g(Lie)g(algebra)p 393
2172 V 13 w(G)g(has)h(a)g(trivial)e(second)h(cohomology)g(group)h
Fv(H)1320 2154 y FC(2)1340 2172 y FH(\()p 1367 2172 V
-5 w(G)q(\))d(=)h(0,)h(then)g(the)g(co)q(cycle)-5 2232
y Fv(C)30 2239 y FC(\003\006)98 2232 y FH(is)g(a)f(cob)q(oundary;)h
(namely)e(w)o(e)g(ha)o(v)o(e)791 2342 y Fv(C)826 2349
y FC(\003\006)892 2342 y FH(=)f Fv(f)1006 2321 y FC(\000)968
2354 y(\003\006)1030 2342 y Fv(C)1065 2349 y FC(\000)1760
2342 y FH(\(7.17\))-5 2451 y(where)i Fv(C)171 2458 y
FC(\000)212 2451 y FH(are)g(suitable)g(constan)o(ts.)23
b(Hence,)15 b(assuming)h Fv(H)1126 2433 y FC(2)1146 2451
y FH(\()p 1173 2451 V -5 w(G)q(\))e(=)g(0)j(w)o(e)f(can)g(reabsorb)i
Fv(C)1720 2458 y FC(\000)1760 2451 y FH(in)e(the)-5 2511
y(de\014nition)g(of)h FE(P)303 2518 y FC(\003)329 2511
y FH(:)779 2571 y FE(P)814 2578 y FC(\003)854 2571 y
FE(!)d(P)953 2578 y FC(\003)990 2571 y FH(+)d Fv(C)1074
2578 y FC(\003)1760 2571 y FH(\(7.18\))-5 2658 y(and)17
b(w)o(e)f(obtain)h(the)f(stronger)h(equation)737 2768
y FE(fP)797 2775 y FC(\003)824 2768 y Fv(;)8 b FE(P)881
2775 y FC(\006)908 2768 y FE(g)13 b FH(=)h Fv(f)1060
2747 y FC(\000)1022 2780 y(\003\006)1084 2768 y FE(P)1119
2775 y FC(\000)1760 2768 y FH(\(7.19\))916 2892 y(31)p
eop
%%Page: 32 33
32 32 bop -5 15 a FH(Note)16 b(that)g Fv(H)262 -3 y FC(2)282
15 y FH(\()p 309 15 2 33 v -5 w(G\))e(=)g(0)i(is)f(true)h(for)g(all)f
(semi-simpl)o(e)e(Lie)i(algebras.)22 b(Using)15 b(eq.)g(7.15)p
 (#equation.7.15) [[436 763 457 775] [1 1 1 [3 3]] [0 0 1]] pdfm (,)h
(eq.)e(7.19)p
 (#equation.7.19) [[482 763 503 775] [1 1 1 [3 3]] [0 0 1]] pdfm 
17 w(can)-5 76 y(b)q(e)j(rewritten)e(in)h(comp)q(onen)o(ts)f(as)i
(follo)o(ws:)609 172 y Fv(i)p 605 194 25 2 v 605 240
a FH(2)634 206 y Fv(g)657 213 y Ft(ij)685 204 y Fn(\003)706
206 y FH(\()p Fv(k)752 185 y Ft(i)750 218 y FC(\003)777
206 y Fv(k)804 182 y Ft(j)820 170 y Fn(\003)802 218 y
FC(\006)851 206 y FE(\000)11 b Fv(k)928 185 y Ft(i)926
218 y FC(\006)954 206 y Fv(k)981 182 y Ft(j)997 170 y
Fn(\003)979 218 y FC(\003)1017 206 y FH(\))j(=)1106 172
y(1)p 1106 194 V 1106 240 a(2)1136 206 y Fv(f)1198 185
y FC(\000)1160 218 y(\003\006)1222 206 y FE(P)1257 213
y FC(\000)1760 206 y FH(\(7.20\))-5 328 y(Equation)j(7.20)p
 (#equation.7.20) [[121 688 142 700] [1 1 1 [3 3]] [0 0 1]] pdfm 
17 w(is)f(iden)o(tical)e(with)j(the)f(equiv)m(ariance)f(condition)h(in)
g(eq.)f(7.9)p
 (#equation.7.9) [[402 688 417 700] [1 1 1 [3 3]] [0 0 1]] pdfm (.)68
389 y(Comparing)g(the)f(de\014nition)g(of)h(the)f(K\177)-24
b(ahler)14 b(p)q(oten)o(tial)g(in)g(eq.)g(C.54)p
 (#equation.C.54) [[371 674 394 686] [1 1 1 [3 3]] [0 0 1]] pdfm 
15 w(with)g(the)g(de\014nition)h(of)f(the)-5 449 y(momen)o(tum)e
(function)j(in)h(eq.)e(7.6)p
 (#equation.7.6) [[210 659 225 671] [1 1 1 [3 3]] [0 0 1]] pdfm (,)i(w)
o(e)f(obtain)h(an)g(expression)g(for)g(the)f(momen)o(tum)c(map)k
(function)-5 509 y(in)h(terms)f(of)h(deriv)m(ativ)o(es)f(of)i(the)f
(K\177)-24 b(ahler)16 b(p)q(oten)o(tial:)377 638 y(i)8
b FE(P)434 645 y FC(\003)482 638 y FH(=)547 605 y(1)p
547 627 V 547 673 a(2)585 590 y Fs(\020)609 638 y Fv(k)636
618 y Ft(i)634 651 y FC(\003)670 638 y Fv(@)696 645 y
Ft(i)709 638 y FE(K)k(\000)f Fv(k)836 618 y Ft(i)848
606 y Fm(?)834 651 y FC(\003)876 638 y Fv(@)902 645 y
Ft(i)914 636 y Fm(?)934 638 y FE(K)973 590 y Fs(\021)1020
638 y FH(=)22 b Fv(k)1107 618 y Ft(i)1105 651 y FC(\003)1140
638 y Fv(@)1166 645 y Ft(i)1180 638 y FE(K)h FH(=)f FE(\000)p
Fv(k)1367 618 y Ft(i)1379 606 y Fm(?)1365 651 y FC(\003)1407
638 y Fv(@)1433 645 y Ft(i)1445 636 y Fm(?)1465 638 y
FE(K)257 b FH(\(7.21\))-5 761 y(Eq.)17 b(7.21)p
 (#equation.7.21) [[92 584 113 596] [1 1 1 [3 3]] [0 0 1]] pdfm 
18 w(is)h(true)f(if)g(the)g(K\177)-24 b(ahler)17 b(p)q(oten)o(tial)g
(is)g(exactly)g(in)o(v)m(arian)o(t)f(under)i(the)f(transformations)h
(of)-5 821 y(the)e(isometry)e(group)j FE(G)h FH(and)f(not)f(only)g(up)g
(to)g(a)h(K\177)-24 b(ahler)15 b(transformation)h(as)h(de\014ned)e(in)h
(eq.)f(C.55)p
 (#equation.C.55) [[498 570 521 582] [1 1 1 [3 3]] [0 0 1]] pdfm (.)-5
882 y(In)h(other)h(w)o(ords)f(eq.)g(7.21)p
 (#equation.7.21) [[168 555 189 567] [1 1 1 [3 3]] [0 0 1]] pdfm 
17 w(is)g(true)g(if)610 992 y(0)23 b(=)f FE(L)751 971
y FC(\003)786 992 y FE(K)h FH(=)f Fv(k)934 971 y Ft(i)932
1004 y FC(\003)967 992 y Fv(@)993 999 y Ft(i)1007 992
y FE(K)12 b FH(+)f Fv(k)1133 971 y Ft(i)1145 959 y Fm(?)1131
1004 y FC(\003)1173 992 y Fv(@)1199 999 y Ft(i)1211 990
y Fm(?)1231 992 y FE(K)491 b FH(\(7.22\))-5 1102 y(Not)17
b(all)f(the)h(isometries)e(of)i(a)g(general)g(K\177)-24
b(ahler)16 b(manifold)g(ha)o(v)o(e)g(suc)o(h)h(a)g(prop)q(ert)o(y)l(,)f
(but)h(those)h(that)-5 1162 y(in)j(a)h(suitable)f(co)q(ordinate)h
(frame)e(displa)o(y)h(a)h(linear)f(action)g(on)h(the)g(co)q(ordinates)g
(certainly)e(do.)-5 1222 y(Ho)o(w)o(ev)o(er,)13 b(in)h(Ho)q(dge)h
(K\177)-24 b(ahler)15 b(manifolds,)e(eq.)h(7.22)p
 (#equation.7.22) [[282 474 303 486] [1 1 1 [3 3]] [0 0 1]] pdfm 
15 w(can)h(b)q(e)f(replaced)g(b)o(y)g(the)h(follo)o(wing)f(one)h(whic)o
(h)-5 1282 y(is)h(certainly)f(true:)535 1392 y(0)42 b(=)g
FE(L)715 1372 y FC(\003)750 1392 y Fv(G)23 b FH(=)f Fv(k)898
1372 y Ft(i)896 1404 y FC(\003)931 1392 y Fv(@)957 1399
y Ft(i)971 1392 y Fv(G)11 b FH(+)g Fv(k)1096 1372 y Ft(i)1108
1360 y Fm(?)1094 1404 y FC(\003)1137 1392 y Fv(@)1163
1399 y Ft(i)1175 1390 y Fm(?)1195 1392 y Fv(G)411 1465
y(G)p FH(\()p Fv(z)r(;)p 515 1438 V 8 w(z)r FH(\))42
b FE(\021)f FH(log)e FE(k)13 b Fv(W)7 b FH(\()p Fv(z)r
FH(\))14 b FE(k)975 1444 y FC(2)1003 1465 y FH(=)22 b
FE(K)q FH(\()p Fv(z)r(;)p 1168 1438 V 8 w(z)q FH(\))d(+)h(Re)8
b Fv(W)f FH(\()p Fv(z)r FH(\))290 b(\(7.23\))-5 1575
y(where)17 b(the)f Fu(sup)n(erp)n(otential)i Fv(W)7 b
FH(\()p Fv(z)r FH(\))16 b(is)h(an)o(y)g(holomorphic)e(section)i(of)g
(the)g(Ho)q(dge)g(line{bundle.)22 b(In-)-5 1635 y(deed)13
b(the)f(transformation)h(under)g(the)g(isometry)e(of)i(the)g(K\177)-24
b(ahler)12 b(p)q(oten)o(tial)h(is)g(comp)q(ensated)f(b)o(y)g(the)-5
1695 y(transformation)17 b(of)g(the)f(sup)q(erp)q(oten)o(tial.)23
b(Consequen)o(tly)l(,)15 b(in)h(Ho)q(dge{K\177)-24 b(ahler)17
b(manifolds)f(eq.)f(7.21)p
 (#equation.7.21) [[504 360 524 372] [1 1 1 [3 3]] [0 0 1]] pdfm 
-5 1755 a(can)i(b)q(e)f(rewritten)f(as)377 1875 y(i)8
b FE(P)434 1882 y FC(\003)482 1875 y FH(=)547 1841 y(1)p
547 1863 V 547 1909 a(2)585 1827 y Fs(\020)610 1875 y
Fv(k)637 1855 y Ft(i)635 1887 y FC(\003)670 1875 y Fv(@)696
1882 y Ft(i)710 1875 y Fv(G)j FE(\000)g Fv(k)836 1855
y Ft(i)848 1843 y Fm(?)834 1887 y FC(\003)877 1875 y
Fv(@)903 1882 y Ft(i)915 1873 y Fm(?)934 1875 y Fv(G)972
1827 y Fs(\021)1020 1875 y FH(=)22 b Fv(k)1107 1855 y
Ft(i)1105 1887 y FC(\003)1140 1875 y Fv(@)1166 1882 y
Ft(i)1180 1875 y Fv(G)h FH(=)f FE(\000)p Fv(k)1367 1855
y Ft(i)1379 1843 y Fm(?)1365 1887 y FC(\003)1407 1875
y Fv(@)1433 1882 y Ft(i)1445 1873 y Fm(?)1465 1875 y
Fv(G)257 b FH(\(7.24\))-5 1998 y(and)17 b(holds)g(true)f(for)g(an)o(y)g
(isometry)l(.)68 2058 y(In)d Fv(N)19 b FH(=)14 b(1)f(sup)q(ersymmetry)d
(the)i(K\177)-24 b(ahlerian)12 b(momen)o(tum)d(maps)j
FE(P)1326 2065 y FC(\000)1363 2058 y FH(app)q(ear)h(as)h(auxiliary)d
(\014elds)-5 2118 y(of)k(the)g(v)o(ector)e(m)o(ultiplets.)18
b(F)l(or)d Fv(N)k FH(=)14 b(1)h(sup)q(ergra)o(vit)o(y)f(the)g(scalar)h
(manifold)f(is)g(of)h(the)f(Ho)q(dge)i(t)o(yp)q(e)-5
2178 y(and)h(eq.)e(7.24)p
 (#equation.7.24) [[112 244 133 256] [1 1 1 [3 3]] [0 0 1]] pdfm 
17 w(can)i(alw)o(a)o(ys)f(b)q(e)g(emplo)o(y)o(ed.)68
2239 y(On)j(the)g(other)g(hand,)h(in)e Fv(N)24 b FH(=)18
b(2)h(sup)q(ersymmetry)d(the)j(auxiliary)f(\014elds)g(of)h(the)g(v)o
(ector)f(m)o(ul-)-5 2299 y(tiplets,)g(that)h(form)e(an)j
Fv(S)s(U)5 b FH(\(2\))19 b(triplet,)e(are)i(giv)o(en)e(b)o(y)h(the)h
(momen)o(tum)14 b(map)k(of)h(triholomorphic)-5 2359 y(isometries)h(on)i
(the)g(h)o(yp)q(erm)o(ultipl)o(et)d(manifold)h(\(Hyp)q(erK\177)-24
b(ahlerian)21 b(or)h(quaternionic)f(dep)q(ending)-5 2419
y(on)e(the)f(lo)q(cal)h(or)f(rigid)g(nature)h(of)g(sup)q(ersymmetry\).)
24 b(The)19 b(triholomorphic)d(momen)o(tum)f(map)i(is)-5
2479 y(discussed)e(in)g(the)g(subsection)g(after)g(the)f(next.)21
b(Y)l(et,)14 b(although)i(not)f(iden)o(ti\014ed)e(with)i(the)g
(auxiliary)-5 2540 y(\014elds,)f(the)g(holomorphic)g(momen)o(tum)c(map)
k(pla)o(ys)g(a)g(role)g(also)h(in)f Fv(N)20 b FH(=)13
b(2)i(theories)f(in)g(the)g Fu(gauging)-5 2600 y FH(of)j(the)f
Fv(U)5 b FH(\(1\))17 b(connection)32 b(4.13)p
 (#equation.4.13) [[195 143 216 155] [1 1 1 [3 3]] [0 0 1]] pdfm (,)16
b(as)h(w)o(e)f(sho)o(w)h(shortly)f(from)f(no)o(w.)916
2892 y(32)p eop
%%Page: 33 34
33 33 bop -5 15 a Fk(7.2)66 b(Holomorphic)24 b(momen)n(tum)f(map)f(on)h
(Sp)r(ecial)g(K\177)-33 b(ahler)22 b(manifolds)-5 108
y FH(Here)d(the)h(K\177)-24 b(ahler)19 b(manifold)g(is)g(not)i(only)e
(Ho)q(dge)i(but)f(it)f(is)h(sp)q(ecial.)32 b(Corresp)q(ondingly)20
b(w)o(e)g(can)-5 168 y(write)e(a)g(form)o(ula)f(for)h
FE(P)456 175 y FC(\003)500 168 y FH(in)g(terms)f(of)h(symplectic)d(in)o
(v)m(arian)o(ts.)26 b(In)18 b(this)g(con)o(text,)f(to)h(distinguish)-5
228 y(the)f(holomorphic)e(momen)o(tum)d(map)k(from)g(the)g
(triholomorphic)f(one)i FE(P)1384 210 y Ft(x)1380 241
y FC(\003)1422 228 y FH(that)g(carries)f(an)h Fv(S)s(U)5
b FH(\(2\))-5 288 y(index)15 b Fv(x)f FH(=)g(1)p Fv(;)8
b FH(2)p Fv(;)g FH(3,)16 b(w)o(e)g(adopt)h(the)f(notation)g
FE(P)893 270 y FC(0)889 301 y(\003)916 288 y FH(.)21
b(The)16 b(request)f(that)i(the)e(isometry)g(group)i(should)-5
349 y(b)q(e)g(em)o(b)q(edded)d(in)o(to)i(the)g(symplectic)d(group)k(is)
f(form)o(ulated)f(b)o(y)h(writing:)447 459 y FE(L)481
466 y FC(\003)516 459 y Fv(V)34 b FE(\021)22 b Fv(k)666
438 y Ft(i)664 471 y FC(\003)699 459 y Fv(@)725 466 y
Ft(i)739 459 y Fv(V)30 b FH(+)20 b Fv(k)882 438 y Ft(i)894
426 y Fm(?)880 471 y FC(\003)922 459 y Fv(@)948 466 y
Ft(i)960 457 y Fm(?)980 459 y Fv(V)33 b FH(=)22 b Fv(T)1130
466 y FC(\003)1165 459 y Fv(V)30 b FH(+)11 b Fv(V)20
b(f)1344 466 y FC(\003)1370 459 y FH(\()p Fv(z)r FH(\))327
b(\(7.25\))-5 569 y(where)18 b Fv(V)29 b FH(is)18 b(the)g(co)o(v)m
(arian)o(tly)f(holomorphic)g(section)h(of)g(the)g(v)o(ector)f(bundle)h
FE(H)26 b(\000)-9 b(!)25 b(M)18 b FH(de\014ned)-5 629
y(in)e(eq.)f(4.27)p
 (#equation.4.27) [[103 616 124 628] [1 1 1 [3 3]] [0 0 1]] pdfm (,)560
710 y Fv(T)589 717 y FC(\003)638 710 y FH(=)698 649 y
Fs(\022)737 680 y Fv(a)763 687 y FC(\003)840 680 y Fv(b)861
687 y FC(\003)739 740 y Fv(c)760 747 y FC(\003)838 740
y Fv(d)863 747 y FC(\003)898 649 y Fs(\023)950 710 y
FE(2)23 b FD(Sp)p FH(\()p FD(2n)11 b FH(+)g FD(2)p Fv(;)d
FH(I)-9 b(R\))440 b(\(7.26\))-5 821 y(is)11 b(some)g(elemen)o(t)d(of)k
(the)f(real)g(symplectic)d(Lie)j(algebra)h(and)g Fv(f)1144
828 y FC(\003)1170 821 y FH(\()p Fv(z)r FH(\))g(corresp)q(onds)g(to)g
(an)g(in\014nitesimal)-5 881 y(K\177)-24 b(ahler)16 b(transformation.)
68 942 y(The)21 b(classical)g(or)g(p)q(erturbativ)o(e)f(isometries)f
(\()i Fv(b)1009 949 y FC(\003)1057 942 y FH(=)h(0\))f(that)h(are)f
(relev)m(an)o(t)f(to)h(the)g(gauging)-5 1002 y(pro)q(cedure)c(are)f
(normally)e(c)o(haracterized)h(b)o(y)838 1112 y Fv(f)862
1119 y FC(\003)889 1112 y FH(\()p Fv(z)r FH(\))f(=)f(0)719
b(\(7.27\))-5 1222 y(Under)16 b(condition)g(7.27)p
 (#equation.7.27) [[158 474 178 486] [1 1 1 [3 3]] [0 0 1]] pdfm (,)h
(recalling)e(eq.s)g(4.25)p
 (#equation.4.25) [[256 474 276 486] [1 1 1 [3 3]] [0 0 1]] pdfm 
17 w(and)33 b(4.26)p
 (#equation.4.26) [[307 474 328 486] [1 1 1 [3 3]] [0 0 1]] pdfm (,)17
b(from)e(eq.)g(7.25)p
 (#equation.7.25) [[381 474 402 486] [1 1 1 [3 3]] [0 0 1]] pdfm 
17 w(w)o(e)h(obtain:)610 1332 y FE(L)644 1311 y FC(\003)680
1332 y FE(K)22 b FH(=)h Fv(k)828 1311 y Ft(i)826 1344
y FC(\003)861 1332 y Fv(@)887 1339 y Ft(i)901 1332 y
FE(K)11 b FH(+)g Fv(k)1026 1311 y Ft(i)1038 1299 y Fm(?)1024
1344 y FC(\003)1067 1332 y Fv(@)1093 1339 y Ft(i)1105
1330 y Fm(?)1125 1332 y FE(K)22 b FH(=)g(0)491 b(\(7.28\))-5
1442 y(that)17 b(is)f(iden)o(tical)e(with)j(eq.)e(7.22)p
 (#equation.7.22) [[200 421 221 433] [1 1 1 [3 3]] [0 0 1]] pdfm (.)22
b(Hence)15 b(w)o(e)g(can)i(use)f(eq.)f(7.21)p
 (#equation.7.21) [[342 421 362 433] [1 1 1 [3 3]] [0 0 1]] pdfm (,)i
(that)g(w)o(e)e(rewrite)h(as:)646 1552 y(i)8 b FE(P)707
1531 y FC(0)703 1564 y(\003)751 1552 y FH(=)22 b Fv(k)838
1531 y Ft(i)836 1564 y FC(\003)871 1552 y Fv(@)897 1559
y Ft(i)911 1552 y FE(K)h FH(=)f FE(\000)p Fv(k)1098 1531
y Ft(i)1110 1519 y Fm(?)1096 1564 y FC(\003)1138 1552
y Fv(@)1164 1559 y Ft(i)1176 1550 y Fm(?)1196 1552 y
FE(K)526 b FH(\(7.29\))-5 1662 y(Utilizing)14 b(the)i(de\014nition)g
(in)g(eq.)f(4.29)p
 (#equation.4.29) [[223 368 244 380] [1 1 1 [3 3]] [0 0 1]] pdfm 
17 w(w)o(e)h(easily)g(obtain:)584 1772 y Fv(k)611 1751
y Ft(i)609 1784 y FC(\003)645 1772 y Fv(U)683 1751 y
Ft(i)719 1772 y FH(=)22 b Fv(T)808 1779 y FC(\003)843
1772 y Fv(V)d FH(exp[)p Fv(f)1003 1779 y FC(\003)1029
1772 y FH(\()p Fv(z)r FH(\)])10 b(+)h(i)d FE(P)1226 1751
y FC(0)1222 1784 y(\003)1257 1772 y Fv(V)475 b FH(\(7.30\))-5
1882 y(T)l(aking)17 b(the)g(symplectic)c(scalar)k(pro)q(duct)g(of)g
(eq.)f(7.30)p
 (#equation.7.30) [[297 315 318 327] [1 1 1 [3 3]] [0 0 1]] pdfm 
17 w(with)p 1154 1843 40 2 v 17 w Fv(V)28 b FH(and)17
b(recalling)e(eq.)h(4.27)p
 (#equation.4.27) [[451 315 471 327] [1 1 1 [3 3]] [0 0 1]] pdfm 
17 w(w)o(e)h(\014nally)-5 1924 y FC(4)p
 (#Hfootnote.4) [[71 301 76 313] [1 1 1 [3 3]] [0 0 1]] pdfm 
31 1942 a FH(get:)391 2002 y FE(P)430 1982 y FC(0)426
2014 y(\003)474 2002 y FH(=)22 b FE(h)p 553 1963 V Fv(V)e
FE(j)8 b Fv(T)652 2009 y FC(\003)687 2002 y Fv(V)j FE(i)23
b FH(=)f FE(h)p Fv(V)e FE(j)8 b Fv(T)946 2009 y FC(\003)p
980 1963 V 980 2002 a Fv(V)k FE(i)22 b FH(=)g(exp)8 b([)o
FE(K)q FH(])16 b FE(h)p 1305 1963 36 2 v FH(\012)9 b
FE(j)f Fv(T)1400 2009 y FC(\003)1435 2002 y FH(\012)p
FE(i)271 b FH(\(7.31\))-5 2089 y(In)24 b(the)f(gauging)i(pro)q(cedure)f
(w)o(e)f(are)h(in)o(terested)f(in)g(groups)i(the)e(symplectic)e(image)h
(of)i(whose)-5 2149 y(generators)17 b(is)f(blo)q(c)o(k{diagonal)h(and)g
(coincides)e(with)h(the)g(adjoin)o(t)h(represen)o(tation)e(in)h(eac)o
(h)g(blo)q(c)o(k.)-5 2210 y(Namely)679 2291 y Fv(T)708
2298 y FC(\003)757 2291 y FH(=)817 2230 y Fs(\022)855
2261 y Fv(f)884 2243 y FC(\006)905 2273 y(\003\001)1068
2261 y FD(0)894 2321 y(0)88 b FE(\000)p Fv(f)1078 2303
y FC(\006)1098 2333 y(\003\001)1162 2230 y Fs(\023)1760
2291 y FH(\(7.32\))-5 2399 y(Then)17 b(eq.)e(7.31)p
 (#equation.7.31) [[120 191 141 203] [1 1 1 [3 3]] [0 0 1]] pdfm 
17 w(b)q(ecomes)502 2515 y FE(P)541 2494 y FC(0)537 2527
y(\003)586 2515 y FH(=)22 b Fv(e)669 2494 y FB(K)714
2467 y Fs(\020)747 2515 y Fv(F)779 2522 y FC(\001)819
2515 y Fv(f)848 2494 y FC(\001)872 2527 y(\003\006)p
932 2476 45 2 v 932 2515 a Fv(X)977 2486 y FC(\006)1024
2515 y FH(+)p 1081 2476 39 2 v 19 w Fv(F)1119 2522 y
FC(\001)1159 2515 y Fv(f)1188 2494 y FC(\001)1213 2527
y(\003\006)1273 2515 y Fv(X)1317 2494 y FC(\006)1345
2467 y Fs(\021)1760 2515 y FH(\(7.33\))p -5 2574 756
2 v 51 2604 a Fq(4)70 2619 y Fx(The)11 b(follo)o(wing)d(and)j(the)g
(next)g(t)o(w)o(o)f(form)o(ulae)f(ha)o(v)o(e)h(b)q(een)i(obtained)f(in)
f(priv)n(ate)g(discussions)i(of)e(one)h(of)f(us)h(\(P)m(.F)m(r)o(\023)
-20 b(e\))-5 2669 y(with)14 b(A.)f(V)m(an)h(Pro)q(ey)o(en)h(and)e(B.)h
(de)g(Wit)916 2892 y FH(33)p eop
%%Page: 34 35
34 34 bop -5 15 a Fk(7.3)66 b(The)28 b(triholomorphic)i(momen)n(tum)e
(map)g(on)f(Hyp)r(erK\177)-33 b(ahler)28 b(and)148 90
y(Quaternionic)c(manifolds)-5 183 y FH(Next)12 b(w)o(e)h(turn)h(to)f(a)
h(discussion)f(of)h(isometries)d(of)j(the)e(manifold)g
FE(HM)i FH(asso)q(ciated)g(with)f(h)o(yp)q(erm)o(ul-)-5
243 y(tiplets.)27 b(As)19 b(w)o(e)f(kno)o(w,)g(it)g(can)h(b)q(e)g
(either)e(Hyp)q(erK\177)-24 b(ahlerian)17 b(or)i(quaternionic.)27
b(F)l(or)19 b(applications)-5 303 y(to)i Fv(N)k FH(=)20
b(2)g(theories)g(w)o(e)f(m)o(ust)g(assume)g(that)h(on)h
FE(HM)f FH(w)o(e)g(ha)o(v)o(e)f(an)h(action)g(b)o(y)g(triholomorphic)-5
363 y(isometries)c(of)h(the)h(same)e(Lie)h(group)i FE(G)h
FH(that)d(acts)h(on)g(the)f(Sp)q(ecial)g(K\177)-24 b(ahler)17
b(manifold)f FE(S)t(M)p FH(.)25 b(This)-5 423 y(means)16
b(that)g(on)h FE(HM)g FH(w)o(e)e(ha)o(v)o(e)h(Killing)f(v)o(ectors)811
556 y Fv(~)813 569 y(k)838 576 y FC(\003)879 569 y FH(=)f
Fv(k)958 549 y Ft(u)956 582 y FC(\003)1013 522 y Fv(~)1011
536 y(@)p 988 558 75 2 v 988 603 a(@)s(q)1041 589 y Ft(u)1760
569 y FH(\(7.34\))-5 702 y(satisfying)21 b(the)f(same)f(Lie)h(algebra)h
(as)g(the)f(corresp)q(onding)i(Killing)d(v)o(ectors)h(on)g
FE(S)t(M)p FH(.)34 b(In)20 b(other)-5 762 y(w)o(ords)668
796 y Fs(b)664 814 y Fv(~)666 827 y(k)693 834 y FC(\003)733
827 y FH(=)14 b Fv(k)812 806 y Ft(i)810 839 y FC(\003)839
814 y Fv(~)837 827 y(@)863 834 y Ft(i)888 827 y FH(+)d
Fv(k)964 806 y Ft(i)976 795 y Fn(\003)962 839 y FC(\003)998
814 y Fv(~)996 827 y(@)1022 834 y Ft(i)1034 825 y Fn(\003)1065
827 y FH(+)g Fv(k)1141 806 y Ft(u)1139 839 y FC(\003)1168
814 y Fv(~)1166 827 y(@)1192 834 y Ft(u)1760 827 y FH(\(7.35\))-5
914 y(is)16 b(a)h(Killing)e(v)o(ector)g(of)i(the)f(blo)q(c)o(k)f
(diagonal)j(metric:)708 1041 y Fs(b)705 1045 y Fv(g)e
FH(=)796 985 y Fs(\022)860 1015 y Fv(g)883 1022 y Ft(ij)911
1013 y Fn(\003)1055 1015 y FH(0)884 1075 y(0)124 b Fv(h)1060
1082 y Ft(uv)1136 985 y Fs(\023)1760 1045 y FH(\(7.36\))-5
1176 y(de\014ned)17 b(on)h(the)e(pro)q(duct)i(manifold)e
FE(S)t(M)11 b(\012)h(HM)p FH(.)24 b(T)l(riholomorphicit)o(y)14
b(means)i(that)i(the)e(Killing)-5 1236 y(v)o(ector)24
b(\014elds)g(lea)o(v)o(e)f(the)h(Hyp)q(erK\177)-24 b(ahler)23
b(structure)i(in)o(v)m(arian)o(t)e(up)i(to)g Fv(S)s(U)5
b FH(\(2\))25 b(rotations)g(in)f(the)-5 1297 y Fv(S)s(U)5
b FH(\(2\){bundle)17 b(de\014ned)f(b)o(y)g(eq.)f(5.2)p
 (#equation.5.2) [[222 456 237 468] [1 1 1 [3 3]] [0 0 1]] pdfm (.)22
b(Namely:)483 1407 y FE(L)517 1414 y FC(\003)544 1407
y Fv(K)589 1388 y Ft(x)652 1407 y FH(=)42 b Fv(\017)752
1388 y Ft(xy)q(z)810 1407 y Fv(K)855 1388 y Ft(y)876
1407 y Fv(W)929 1388 y Ft(z)922 1419 y FC(\003)990 1407
y FH(;)f FE(L)1079 1414 y FC(\003)1106 1407 y Fv(!)1138
1388 y Ft(x)1202 1407 y FH(=)g FE(r)p Fv(W)1376 1388
y Ft(x)1369 1419 y FC(\003)1760 1407 y FH(\(7.37\))-5
1517 y(where)16 b Fv(W)189 1499 y Ft(x)182 1529 y FC(\003)228
1517 y FH(is)g(an)h Fv(S)s(U)5 b FH(\(2\))17 b(comp)q(ensator)g(asso)q
(ciated)g(with)f(the)h(Killing)e(v)o(ector)g Fv(k)1543
1499 y Ft(u)1541 1529 y FC(\003)1568 1517 y FH(.)22 b(The)17
b(comp)q(en-)-5 1577 y(sator)g Fv(W)170 1559 y Ft(x)163
1589 y FC(\003)209 1577 y FH(necessarily)e(ful\014ls)g(the)h(co)q
(cycle)f(condition:)523 1687 y FE(L)557 1694 y FC(\003)584
1687 y Fv(W)637 1666 y Ft(x)630 1699 y FC(\006)669 1687
y FE(\000)c(L)753 1694 y FC(\006)781 1687 y Fv(W)834
1666 y Ft(x)827 1699 y FC(\003)867 1687 y FH(+)g Fv(\017)936
1666 y Ft(xy)q(z)994 1687 y Fv(W)1047 1663 y Ft(y)1040
1699 y FC(\003)1068 1687 y Fv(W)1121 1666 y Ft(z)1114
1699 y FC(\006)1155 1687 y FH(=)j Fv(f)1236 1666 y FB(\001\001)p
FC(\000)1231 1699 y(\003\006)1283 1687 y Fv(W)1336 1666
y Ft(x)1329 1699 y FC(\000)1760 1687 y FH(\(7.38\))-5
1797 y(In)f(the)g(Hyp)q(erK\177)-24 b(ahler)12 b(case)h(the)g
Fv(S)s(U)5 b FH(\(2\){bundle)14 b(is)f(\015at)h(and)f(the)g(comp)q
(ensator)g(can)h(b)q(e)f(reabsorb)q(ed)-5 1857 y(in)o(to)j(the)g
(de\014nition)g(of)h(the)f(Hyp)q(erK\177)-24 b(ahler)15
b(forms.)20 b(In)c(other)g(w)o(ords)h(w)o(e)f(can)g(alw)o(a)o(ys)h
(\014nd)f(a)h(map)653 1967 y FE(HM)23 b(\000)-9 b(!)22
b Fv(L)913 1946 y Ft(x)933 1979 y(y)954 1967 y FH(\()p
Fv(q)r FH(\))g FE(2)g Fv(S)s(O)q FH(\(3\))534 b(\(7.39\))-5
2077 y(that)17 b(trivializes)d(the)i FE(S)t(U)5 b FH({bundle)16
b(globally)l(.)21 b(Rede\014ning:)756 2187 y Fv(K)801
2166 y Ft(x)p FB(0)855 2187 y FH(=)h Fv(L)948 2166 y
Ft(x)968 2199 y(y)989 2187 y FH(\()p Fv(q)r FH(\))8 b
Fv(K)1104 2166 y Ft(y)1760 2187 y FH(\(7.40\))-5 2297
y(the)16 b(new)h(Hyp)q(erK\177)-24 b(ahler)15 b(form)g(ob)q(eys)i(the)f
(stronger)h(equation:)818 2407 y FE(L)852 2414 y FC(\003)879
2407 y Fv(K)924 2386 y Ft(x)p FB(0)978 2407 y FH(=)22
b(0)698 b(\(7.41\))-5 2517 y(On)12 b(the)f(other)h(hand,)h(in)e(the)g
(quaternionic)g(case,)h(the)f(non{trivialit)o(y)f(of)i(the)f
FE(S)t(U)5 b FH({bundle)12 b(forbids)g(to)-5 2577 y(eliminate)e(the)i
Fv(W)7 b FH({comp)q(ensator)12 b(completely)l(.)17 b(Due)c(to)f(the)g
(iden)o(ti\014cation)g(b)q(et)o(w)o(een)f(Hyp)q(erK\177)-24
b(ahler)-5 2637 y(forms)16 b(and)h Fv(S)s(U)5 b FH(\(2\))16
b(curv)m(atures)h(eq.)e(7.37)p
 (#equation.7.37) [[237 134 258 146] [1 1 1 [3 3]] [0 0 1]] pdfm 
17 w(is)h(rewritten)f(as:)493 2747 y FE(L)527 2754 y
FC(\003)554 2747 y FH(\012)589 2729 y Ft(x)652 2747 y
FH(=)42 b Fv(\017)752 2729 y Ft(xy)q(z)810 2747 y FH(\012)845
2729 y Ft(y)866 2747 y Fv(W)919 2729 y Ft(z)912 2759
y FC(\003)980 2747 y FH(;)f FE(L)1069 2754 y FC(\003)1096
2747 y Fv(!)1128 2729 y Ft(x)1192 2747 y FH(=)g FE(r)p
Fv(W)1366 2729 y Ft(x)1359 2759 y FC(\003)1760 2747 y
FH(\(7.42\))916 2892 y(34)p eop
%%Page: 35 36
35 35 bop -5 15 a FH(In)21 b(b)q(oth)g(cases,)g(an)o(yho)o(w,)h(and)f
(in)f(full)g(analogy)h(with)g(the)f(case)h(of)f(K\177)-24
b(ahler)21 b(manifolds,)f(to)h(eac)o(h)-5 76 y(Killing)13
b(v)o(ector)g(w)o(e)h(can)g(asso)q(ciate)h(a)g(triplet)e
FE(P)882 58 y Ft(x)878 88 y FC(\003)904 76 y FH(\()p
Fv(q)r FH(\))h(of)g(0-form)g(prep)q(oten)o(tials.)20
b(Indeed)14 b(w)o(e)f(can)i(set:)541 183 y FD(i)557 190
y FC(\003)583 183 y Fv(K)628 162 y Ft(x)664 183 y FH(=)f
FE(\000rP)836 162 y Ft(x)832 195 y FC(\003)871 183 y
FE(\021)g(\000)p FH(\()p Fv(d)p FE(P)1046 162 y Ft(x)1042
195 y FC(\003)1079 183 y FH(+)d Fv(\017)1148 162 y Ft(xy)q(z)1206
183 y Fv(!)1238 162 y Ft(y)1259 183 y FE(P)1298 162 y
Ft(z)1294 195 y FC(\003)1320 183 y FH(\))421 b(\(7.43\))-5
290 y(where)16 b FE(r)g FH(denotes)g(the)g Fv(S)s(U)5
b FH(\(2\))17 b(co)o(v)m(arian)o(t)f(exterior)f(deriv)m(ativ)o(e.)68
351 y(As)h(in)g(the)g(K\177)-24 b(ahler)16 b(case)h(eq.)e(7.43)p
 (#equation.7.43) [[221 683 242 695] [1 1 1 [3 3]] [0 0 1]] pdfm 
17 w(de\014nes)h(a)g(momen)o(tum)d(map:)719 458 y FE(P)k
FH(:)d FE(M)22 b(\000)-9 b(!)22 b FH(I)-9 b(R)1028 437
y FC(3)1059 458 y FE(\012)p 1117 458 2 33 v 6 w FH(G)1142
437 y FB(\003)1760 458 y FH(\(7.44\))-5 565 y(where)p
145 565 V 12 w(G)171 544 y FB(\003)208 565 y FH(denotes)17
b(the)g(dual)g(of)h(the)e(Lie)h(algebra)p 983 565 V 13
w(G)h(of)f(the)g(group)h FE(G)s FH(.)24 b(Indeed)16 b(let)h
Fv(x)e FE(2)p 1708 565 V 11 w FH(G)i(b)q(e)g(the)-5 626
y(Lie)f(algebra)h(elemen)o(t)c(corresp)q(onding)k(to)g(the)f(Killing)f
(v)o(ector)g FD(X)p FH(;)h(then,)g(for)g(a)h(giv)o(en)e
Fv(m)f FE(2)g(M)635 733 y Fv(\026)p FH(\()p Fv(m)p FH(\))22
b(:)g Fv(x)g FE(\000)-9 b(!)22 b(P)990 740 y Ff(X)1023
733 y FH(\()p Fv(m)p FH(\))f FE(2)i FH(I)-9 b(R)1225
712 y FC(3)1760 733 y FH(\(7.45\))-5 840 y(is)17 b(a)g(linear)f
(functional)g(on)p 528 840 V 13 w(G.)23 b(If)16 b(w)o(e)g(expand)h
FD(X)e FH(=)f Fv(a)1016 822 y FC(\003)1042 840 y Fv(k)1067
847 y FC(\003)1111 840 y FH(on)j(a)g(basis)g(of)g(Killing)f(v)o(ectors)
g Fv(k)1748 847 y FC(\003)1791 840 y FH(suc)o(h)-5 900
y(that)757 961 y([)p Fv(k)796 968 y FC(\003)823 961 y
Fv(;)8 b(k)870 968 y FC(\000)894 961 y FH(])13 b(=)h
Fv(f)1035 940 y FC(\001)997 973 y(\003\000)1066 961 y
Fv(k)1091 968 y FC(\001)1760 961 y FH(\(7.46\))-5 1047
y(and)j(w)o(e)f(also)h(c)o(ho)q(ose)f(a)h(basis)g FD(i)591
1054 y Ft(x)621 1047 y FH(\()p Fv(x)c FH(=)h(1)p Fv(;)8
b FH(2)p Fv(;)g FH(3\))17 b(for)g(I)-9 b(R)1004 1026
y FC(3)1040 1047 y FH(w)o(e)16 b(get:)786 1154 y FE(P)821
1161 y Ff(X)875 1154 y FH(=)22 b Fv(a)961 1134 y FC(\003)988
1154 y FE(P)1027 1134 y Ft(x)1023 1166 y FC(\003)1057
1154 y FD(i)1073 1161 y Ft(x)1760 1154 y FH(\(7.47\))-5
1261 y(F)l(urthermore)15 b(w)o(e)h(need)f(a)i(generalization)f(of)g
(the)g(equiv)m(ariance)f(de\014ned)h(b)o(y)g(eq.)f(7.9)p
 (#equation.7.9) [[443 464 458 476] [1 1 1 [3 3]] [0 0 1]] pdfm 
756 1369 a FD(X)c FE(\016)g(P)880 1376 y Ff(Y)936 1369
y FH(=)22 b FE(P)1031 1377 y FC([)p Ff(X)p Ft(;)p Ff(Y)q
FC(])1760 1369 y FH(\(7.48\))-5 1476 y(In)16 b(the)f(Hyp)q(erK\177)-24
b(ahler)15 b(case,)g(the)g(left{hand)h(side)f(of)h(eq.)f(7.48)p
 (#equation.7.48) [[330 413 350 425] [1 1 1 [3 3]] [0 0 1]] pdfm 
16 w(is)g(de\014ned)h(as)g(the)f(usual)h(action)g(of)g(a)-5
1536 y(v)o(ector)g(\014eld)f(on)i(a)g(0{form:)582 1656
y FD(X)11 b FE(\016)g(P)706 1663 y Ff(Y)762 1656 y FH(=)22
b FD(i)838 1663 y Ff(X)878 1656 y Fv(d)p FE(P)938 1663
y Ff(Y)994 1656 y FH(=)g Fv(X)1098 1635 y Ft(u)1157 1622
y Fv(@)p 1134 1644 75 2 v 1134 1690 a(@)s(q)1187 1676
y Ft(u)1222 1656 y FE(P)1257 1663 y Ff(Y)1760 1656 y
FH(\(7.49\))-5 1786 y(The)11 b(equiv)m(ariance)f(condition)h(implies)e
(that)j(w)o(e)e(can)i(in)o(tro)q(duce)e(a)i(triholomorphic)d(P)o
(oisson)j(brac)o(k)o(et)-5 1846 y(de\014ned)k(as)h(follo)o(ws:)688
1906 y FE(fP)748 1913 y FC(\003)774 1906 y Fv(;)8 b FE(P)831
1913 y FC(\006)858 1906 y FE(g)883 1886 y Ft(x)919 1906
y FE(\021)14 b FH(2)p Fv(K)1041 1886 y Ft(x)1063 1906
y FH(\(\003)p Fv(;)8 b FH(\006\))568 b(\(7.50\))-5 1992
y(leading)16 b(to)h(the)f(triholomorphic)e(P)o(oissonian)j(realization)
f(of)h(the)f(Lie)f(algebra:)705 2100 y FE(fP)765 2107
y FC(\003)791 2100 y Fv(;)8 b FE(P)848 2107 y FC(\006)875
2100 y FE(g)900 2075 y Ft(x)944 2100 y FH(=)22 b Fv(f)1033
2079 y FC(\001)1057 2112 y(\003\006)1118 2100 y FE(P)1157
2079 y Ft(x)1153 2112 y FC(\001)1760 2100 y FH(\(7.51\))-5
2207 y(whic)o(h)16 b(in)g(comp)q(onen)o(ts)f(reads:)686
2287 y Fv(K)731 2266 y Ft(x)727 2299 y(uv)777 2287 y
Fv(k)804 2266 y Ft(u)802 2299 y FC(\003)837 2287 y Fv(k)864
2266 y Ft(v)862 2299 y FC(\006)912 2287 y FH(=)977 2253
y(1)p 977 2275 25 2 v 977 2321 a(2)1015 2287 y Fv(f)1044
2266 y FC(\001)1068 2299 y(\003\006)1128 2287 y FE(P)1167
2266 y Ft(x)1163 2299 y FC(\001)1760 2287 y FH(\(7.52\))-5
2385 y(In)h(the)g(quaternionic)g(case,)f(instead,)h(the)g(left{hand)h
(side)f(of)g(eq.)f(7.48)p
 (#equation.7.48) [[372 195 392 207] [1 1 1 [3 3]] [0 0 1]] pdfm 
17 w(is)h(in)o(terpreted)f(as)i(follo)o(ws:)584 2493
y FD(X)11 b FE(\016)g(P)708 2500 y Ff(Y)764 2493 y FH(=)22
b FD(i)840 2500 y Ff(X)880 2493 y FE(rP)957 2500 y Ff(Y)1012
2493 y FH(=)g Fv(X)1116 2472 y Ft(u)1148 2493 y FE(r)1190
2500 y Ft(u)1220 2493 y FE(P)1255 2500 y Ff(Y)1760 2493
y FH(\(7.53\))-5 2600 y(where)13 b FE(r)g FH(is)h(the)f
Fv(S)s(U)5 b FH(\(2\){co)o(v)m(arian)o(t)14 b(di\013eren)o(tial.)19
b(Corresp)q(ondingly)l(,)14 b(the)g(triholomorphic)d(P)o(oisson)-5
2660 y(brac)o(k)o(et)k(is)h(de\014ned)g(as)h(follo)o(ws:)529
2768 y FE(fP)589 2775 y FC(\003)615 2768 y Fv(;)8 b FE(P)672
2775 y FC(\006)699 2768 y FE(g)724 2747 y Ft(x)760 2768
y FE(\021)13 b FH(2)p Fv(K)881 2747 y Ft(x)904 2768 y
FH(\(\003)p Fv(;)8 b FH(\006\))j FE(\000)f Fv(\025)e(")1152
2747 y Ft(xy)q(z)1220 2768 y FE(P)1259 2744 y Ft(y)1255
2780 y FC(\003)1289 2768 y FE(P)1328 2747 y Ft(z)1324
2780 y FC(\006)1760 2768 y FH(\(7.54\))916 2892 y(35)p
eop
%%Page: 36 37
36 36 bop -5 15 a FH(and)17 b(leads)f(to)h(the)f(P)o(oissonian)h
(realization)e(of)i(the)f(Lie)g(algebra)705 125 y FE(fP)765
132 y FC(\003)791 125 y Fv(;)8 b FE(P)848 132 y FC(\006)875
125 y FE(g)900 101 y Ft(x)944 125 y FH(=)22 b Fv(f)1033
105 y FC(\001)1057 138 y(\003\006)1118 125 y FE(P)1157
105 y Ft(x)1153 138 y FC(\001)1760 125 y FH(\(7.55\))-5
235 y(whic)o(h)16 b(in)g(comp)q(onen)o(ts)f(reads:)513
367 y Fv(K)558 347 y Ft(x)554 380 y(uv)604 367 y Fv(k)631
347 y Ft(u)629 380 y FC(\003)664 367 y Fv(k)691 347 y
Ft(v)689 380 y FC(\006)736 367 y FE(\000)799 334 y Fv(\025)p
799 356 29 2 v 801 402 a FH(2)841 367 y Fv(")864 347
y Ft(xy)q(z)931 367 y FE(P)970 344 y Ft(y)966 380 y FC(\003)1000
367 y FE(P)1039 347 y Ft(z)1035 380 y FC(\006)1085 367
y FH(=)1150 334 y(1)p 1150 356 25 2 v 1150 402 a(2)1187
367 y Fv(f)1216 347 y FC(\001)1241 380 y(\003\006)1301
367 y FE(P)1340 347 y Ft(x)1336 380 y FC(\001)1760 367
y FH(\(7.56\))-5 490 y(Eq.)21 b(7.56)p
 (#equation.7.56) [[93 649 114 661] [1 1 1 [3 3]] [0 0 1]] pdfm (,)h
(whic)o(h)e(is)h(the)g(most)f(con)o(v)o(enien)o(t)f(w)o(a)o(y)h(of)h
(expressing)g(equiv)m(ariance)f(in)g(a)h(co)q(ordinate)-5
550 y(basis,)d(pla)o(ys)e(a)i(fundamen)o(tal)d(role)i(in)g(the)g
(construction)g(of)g(the)g(sup)q(ersymmetric)c(action,)k(sup)q(er-)-5
611 y(symmetry)g(transformation)k(rules)e(and)i(of)g(the)f(sup)q(erp)q
(oten)o(tial)h(for)f Fv(N)26 b FH(=)21 b(2)g(sup)q(ergra)o(vit)o(y)f
(on)h(a)-5 671 y(general)d(quaternionic)f(manifold.)24
b(It)18 b(is)f(also)i(v)o(ery)d(con)o(v)o(enien)o(t)g(to)i(retriev)o(e)
e(the)h(rigid)h(sup)q(ersym-)-5 739 y(metry)c(limit.)k(Indeed,)d(using)
h(ph)o(ysical)f(units,)g(w)o(e)h(ma)o(y)e(set)i Fv(\025)e
FH(=)1252 715 y Fs(b)1254 720 y Ft(\025)p 1245 728 39
2 v 1245 757 a(\026)1266 747 y Fr(2)1304 739 y FH(where)h
Fv(\026)h FH(is)g(the)f(Planc)o(k)h(mass)-5 804 y(\(see)i(section)g
(9\);)i(letting)d Fv(\026)h FE(!)g(1)g FH(eq.)f(7.56)p
 (#equation.7.56) [[253 574 274 586] [1 1 1 [3 3]] [0 0 1]] pdfm 
20 w(reduces)h(to)g(eq.)g(7.52)p
 (#equation.7.52) [[355 574 375 586] [1 1 1 [3 3]] [0 0 1]] pdfm (.)28
b(Eq.)18 b(7.56)p
 (#equation.7.56) [[407 574 428 586] [1 1 1 [3 3]] [0 0 1]] pdfm 
19 w(w)o(as)h(in)o(tro)q(duced)f(in)-5 865 y(the)g(ph)o(ysical)e
(literature)h(in)g([24)p
 (#cite.DFF) [[206 559 217 571] [1 1 1 [3 3]] [0 0 1]] pdfm 
1 w(])g(where)g(the)h(general)f(form)g(of)h Fv(N)j FH(=)16
b(2)i(sup)q(ergra)o(vit)o(y)g(b)q(ey)o(ond)f(the)-5 925
y(limitations)d(of)j(tensor)g(calculus)e(w)o(as)i(giv)o(en.)-5
1069 y Fk(7.4)66 b(Gauging)23 b(of)f(the)g(comp)r(osite)g(connections)
-5 1162 y FH(Using)17 b(the)g(concepts)h(and)g(the)f(geometric)e
(structures)i(in)o(tro)q(duced)g(in)g(the)g(previous)g(sections)g(the)
-5 1222 y(form)f(of)i(the)f(Lagrangian)i(and)f(of)g(the)e
(transformation)i(rules)e(for)i Fv(N)j FH(=)15 b(2)j(sup)q(ergra)o(vit)
o(y)e(can)i(no)o(w)-5 1282 y(b)q(e)e(giv)o(en.)k(The)c(essen)o(tial)e
(thing)i(is)f(that)h(the)g(fermions)e(of)i(the)f(theory)l(,)g(b)q(eha)o
(v)o(e)g(as)h(sections)f(of)h(the)-5 1342 y(bundles)i(w)o(e)g(ha)o(v)o
(e)f(in)o(tro)q(duced)h(so)g(far.)27 b(In)18 b(particular)f(he)h(gra)o
(vitino)g(\014eld)f Fv( )1475 1324 y Ft(A)1473 1355 y(\026)1521
1342 y FH(apart)i(from)e(b)q(eing)-5 1402 y(a)h(spinor{v)m(alued)g
(1{form)f(on)h(space{time,)d(b)q(eha)o(v)o(es)i(as)h(a)g(section)e(of)i
(the)f(bundle)g FE(L)12 b(\012)g(S)t(U)5 b FH(.)24 b(The)-5
1463 y(gaugino)c(\014eld)f Fv(\025)316 1445 y Ft(i)p
FB(j)p Ft(A)385 1463 y FH(apart)h(from)d(b)q(eing)i(a)h(section)e(of)h
(the)g(spinor)g(bundle,)f(b)q(eha)o(v)o(es)h(as)g(a)g(section)-5
1523 y(of)j FE(L)15 b(\012)f(T)f(S)t(M)i(\012)f(S)t(U)5
b FH(.)37 b(Finally)20 b(the)h(h)o(yp)q(erino)g(\014eld)g
Fv(\020)1084 1505 y Ft(\013)1131 1523 y FH(is)g(a)h(section)f(of)h(the)
f(rank)g(2)p Fv(m)h FH(v)o(ector)-5 1583 y(bundle)17
b(with)g(structural)h(group)g Fv(S)s(p)p FH(\(2)p Fv(m;)8
b FH(I)-9 b(R\))17 b(that)h(one)f(obtains)h(b)o(y)f(deleting)f(the)h
Fv(S)s(U)5 b FH(\(2\))18 b(part)g(of)-5 1643 y(the)d(holonom)o(y)f
(group)i(on)g FE(HM)p FH(.)21 b(In)14 b(other)i(w)o(ords)f(it)g(is)f(a)
i(section)f(of)g(the)g(bundle)f FE(T)f(HM)c(\012)f(S)t(U)1824
1622 y FB(\000)p FC(1)1871 1643 y FH(.)-5 1703 y(Corresp)q(ondingly)17
b(the)g(co)o(v)m(arian)o(t)f(deriv)m(ativ)o(es)f(of)h(the)h(fermions)d
(app)q(earing)k(in)e(the)g(action)g(and)h(in)-5 1764
y(the)f(transformation)g(rules)g(in)o(v)o(olv)o(es)e(the)i(comp)q
(osite)g(connections)g FE(Q)g FH(,)f(\000)1404 1745 y
Ft(i)1417 1776 y(j)1435 1764 y FH(,)h Fv(!)1497 1745
y Ft(x)1535 1764 y FH(and)h(\001)1671 1745 y Ft(\013\014)1733
1764 y FH(de\014ned)-5 1824 y(on)e(these)g(bundles.)20
b(Gauging)c(just)f(mo)q(di\014es)f(these)g(comp)q(osite)g(connections)h
(b)o(y)f(means)f(of)i(Killing)-5 1884 y(v)o(ectors)h(and)h(momen)o(tum)
12 b(map)j(functions.)21 b(Explicitly)14 b(w)o(e)i(ha)o(v)o(e:)170
1994 y FE(T)d(S)t(M)135 b FH(:)41 b(tangen)o(t)17 b(bundle)54
b(\000)900 1976 y Ft(i)913 2006 y(j)986 1994 y FE(!)1220
1978 y Fs(b)1216 1994 y FH(\000)1246 1976 y Ft(i)1259
2006 y(j)1291 1994 y FH(=)14 b(\000)1373 1976 y Ft(i)1385
2006 y(j)1414 1994 y FH(+)d Fv(g)g(A)1534 1976 y FC(\003)1568
1994 y Fv(@)1594 2001 y Ft(j)1612 1994 y Fv(k)1639 1976
y Ft(i)1637 2006 y FC(\003)220 2059 y FE(L)185 b FH(:)84
b(line)15 b(bundle)107 b FE(Q)65 b(!)1268 2043 y Fs(b)1254
2059 y FE(Q)13 b FH(=)h FE(Q)d FH(+)g Fv(g)f(A)1531 2041
y FC(\003)1566 2059 y FE(P)1605 2041 y FC(0)1601 2071
y(\003)202 2119 y FE(S)t(U)172 b FH(:)55 b Fv(S)s(U)5
b FH(\(2\))17 b(bundle)72 b Fv(!)906 2101 y Ft(x)986
2119 y FE(!)1245 2115 y Fs(b)1240 2119 y Fv(!)1272 2101
y Ft(x)1308 2119 y FH(=)14 b Fv(!)1392 2101 y Ft(x)1425
2119 y FH(+)d Fv(g)g(A)1545 2101 y FC(\003)1579 2119
y FE(P)1618 2101 y Ft(x)1614 2131 y FC(\003)77 2184 y
FE(S)t(U)147 2163 y FB(\000)p FC(1)205 2184 y FE(\012)g(T)i(HM)42
b FH(:)f Fv(S)s(p)p FH(\(2)p Fv(m)p FH(\))16 b(bundle)41
b(\001)898 2166 y Ft(\013\014)986 2184 y FE(!)1086 2167
y Fs(b)1077 2184 y FH(\001)1118 2166 y Ft(\013\014)1178
2184 y FH(=)14 b(\001)1271 2166 y Ft(\013\014)1328 2184
y FH(+)d Fv(g)f(A)1447 2166 y FC(\003)1481 2184 y Fv(@)1507
2191 y Ft(u)1530 2184 y Fv(k)1557 2166 y Ft(v)1555 2196
y FC(\003)1590 2184 y FE(U)1626 2166 y Ft(u)p FB(j)p
Ft(\013A)1716 2184 y FE(U)1752 2160 y Ft(\014)1747 2198
y(v)q FB(j)p Ft(A)1760 2248 y FH(\(7.57\))-5 2308 y(Corresp)q(ondingly)
17 b(the)f(gauged)i(curv)m(atures)e(are:)454 2402 y Fs(b)442
2418 y Fv(R)479 2397 y Ft(i)491 2430 y(j)551 2418 y FH(=)42
b Fv(R)668 2397 y Ft(i)680 2430 y(j)r(`)710 2421 y Fm(?)728
2430 y Ft(k)758 2418 y FE(r)p 800 2392 25 2 v Fv(z)824
2397 y Ft(`)838 2386 y Fm(?)870 2418 y FE(^)11 b(r)p
Fv(z)981 2397 y Ft(k)1021 2418 y FH(+)20 b Fv(g)10 b(F)1151
2397 y FC(\003)1185 2418 y Fv(@)1211 2425 y Ft(j)1229
2418 y Fv(k)1256 2397 y Ft(i)1254 2430 y FC(\003)469
2485 y Fs(c)465 2501 y Fv(K)45 b FH(=)d Fv(K)672 2508
y Ft(ij)700 2499 y Fm(?)729 2501 y FE(r)p 771 2474 V
Fv(z)795 2480 y Ft(i)820 2501 y FE(^)11 b(r)p Fv(z)931
2480 y Ft(j)947 2468 y Fm(?)986 2501 y FH(+)20 b Fv(g)10
b(F)1116 2480 y FC(\003)1150 2501 y FE(P)1189 2480 y
FC(0)1185 2513 y(\003)459 2557 y Fs(b)452 2573 y FH(\012)487
2553 y Ft(x)551 2573 y FH(=)42 b(\012)666 2553 y Ft(x)666
2586 y(uv)715 2573 y FE(r)p Fv(q)781 2553 y Ft(u)813
2573 y FE(^)12 b(r)p Fv(q)924 2553 y Ft(v)962 2573 y
FH(+)20 b Fv(g)10 b(F)1092 2553 y FC(\003)1126 2573 y
FE(P)1165 2553 y Ft(x)1161 2586 y FC(\003)420 2643 y
Fs(c)419 2659 y FH(I)-9 b(R)463 2625 y Ft(\013\014)551
2659 y FH(=)42 b(I)-9 b(R)675 2639 y Ft(\013\014)675
2672 y(uv)730 2659 y FE(r)p Fv(q)796 2639 y Ft(u)828
2659 y FE(^)12 b(r)p Fv(q)939 2639 y Ft(v)977 2659 y
FH(+)20 b Fv(g)10 b(A)1105 2639 y FC(\003)1140 2659 y
Fv(@)1166 2666 y Ft(u)1188 2659 y Fv(k)1215 2639 y Ft(v)1213
2672 y FC(\003)1248 2659 y FE(U)1284 2639 y Ft(u)p FB(j)p
Ft(\013A)1374 2659 y FE(U)1410 2636 y Ft(\014)1405 2674
y(v)q FB(j)p Ft(A)1760 2659 y FH(\(7.58\))916 2892 y(36)p
eop
%%Page: 37 38
37 37 bop -5 15 a Fw(8)81 b(The)27 b(Complete)g(N=2)g(Sup)r(ergra)n
(vit)n(y)f(Theory)-5 125 y FH(In)18 b(this)h(section)f(w)o(e)g(write)f
(the)i(sup)q(ersymmetri)o(c)c(in)o(v)m(arian)o(t)j(action)h(and)g(sup)q
(ersymmetry)c(trans-)-5 185 y(formation)h(rules)g(for)g(a)h(completely)
c(general)j Fv(N)j FH(=)14 b(2)j(sup)q(ergra)o(vit)o(y)l(.)68
245 y(Suc)o(h)f(a)h(theory)f(includes)55 347 y(1.)24
b Fu(the)g(gr)n(avitational)g(multiplet)p FH(,)h(describ)q(ed)d(b)o(y)g
(the)h(vielb)q(ein)e(1{form)h Fv(V)1499 329 y Ft(a)1520
347 y FH(,)i(\()p Fv(a)g FH(=)g(0)p Fv(;)8 b FH(1)p Fv(;)g
FH(2)p Fv(;)g FH(3\),)117 407 y(the)24 b(spin{connection)f(1{form)h
Fv(!)775 389 y Ft(ab)811 407 y FH(,)h(the)e Fv(S)s(U)5
b FH(\(2\))25 b(doublet)e(of)h(gra)o(vitino)f(1-forms)h
Fv( )1775 389 y Ft(A)1803 407 y Fv(;)8 b( )1857 414 y
Ft(A)117 467 y FH(\()p Fv(A)21 b FH(=)h(1)p Fv(;)8 b
FH(2)22 b(and)f(the)g(upp)q(er)g(or)g(lo)o(w)o(er)f(p)q(osition)i(of)f
(the)g(index)f(denotes)h(left,)f(resp)q(ectiv)o(ely)117
528 y(righ)o(t)c(c)o(hiralit)o(y\),)e(the)i(gra)o(viphoton)h(1-form)e
Fv(A)1006 510 y FC(0)55 629 y FH(2.)24 b Fv(n)18 b Fu(ve)n(ctor)h
(multiplets)p FH(.)26 b(Eac)o(h)17 b(v)o(ector)f(m)o(ultiplet)f(con)o
(tains)i(a)h(gauge)g(b)q(oson)h(1{form)e Fv(A)1750 611
y Ft(I)1787 629 y FH(\()p Fv(I)i FH(=)117 690 y(1)p Fv(;)8
b(:)g(:)g(:)g(;)g(n)p FH(\),)14 b(a)g(doublet)g(of)g(gauginos)i
(\(0{form)e(spinors\))g Fv(\025)1182 671 y Ft(iA)1223
690 y FH(,)g Fv(\025)1279 671 y Ft(i)1291 660 y Fm(?)1279
702 y Ft(A)1312 690 y FH(,)g(and)g(a)h(complex)c(scalar)k(\014eld)117
750 y(\(0{form\))h Fv(z)344 732 y Ft(i)374 750 y FH(\()p
Fv(i)d FH(=)p Fv(;)8 b FH(1)p Fv(;)g(:)g(:)g(:)g(;)g(n)p
FH(\).)21 b(The)16 b(scalar)h(\014elds)e Fv(z)1088 732
y Ft(i)1118 750 y FH(can)i(b)q(e)f(regarded)g(as)h(co)q(ordinates)g(on)
g(a)117 810 y(sp)q(ecial)f(manifold)f FE(S)t(M)h FH(whic)o(h)f(can)i(b)
q(e)f(c)o(hosen)g Fu(arbitr)n(arily)p FH(.)838 920 y(dim)919
927 y Ff(C)959 920 y FE(S)t(M)22 b FH(=)g Fv(n)621 b
FH(\(8.1\))55 1051 y(3.)24 b Fv(m)17 b Fu(hyp)n(ermultiplets)p
FH(.)23 b(Eac)o(h)17 b(h)o(yp)q(erm)o(ultipl)o(et)d(con)o(tains)i(a)i
(doublet)e(of)h(0{form)g(spinors,)g(that)117 1111 y(is)22
b(the)g(h)o(yp)q(erinos)g Fv(\020)514 1093 y Ft(\013)560
1111 y FH(\()p Fv(\013)i FH(=)g(1)p Fv(;)8 b(:)g(:)g(:)g(;)g
FH(2)p Fv(m)22 b FH(and)g(here)g(the)g(lo)o(w)o(er)f(or)h(upp)q(er)g(p)
q(osition)h(of)f(the)117 1171 y(index)d(denotes)h(left,)g(resp)q(ectiv)
o(ely)e(righ)o(t)h(c)o(hiralit)o(y\))f(and)j(four)f(real)f(scalar)i
(\014elds)e Fv(q)1738 1153 y Ft(u)1780 1171 y FH(\()p
Fv(u)h FH(=)117 1231 y(1)p Fv(;)8 b(:)g(:)g(:)g(;)g FH(4)p
Fv(m)p FH(\),)22 b(that)g(can)f(b)q(e)h(regarded)f(as)h(co)q(ordinates)
g(of)g(a)f(quaternionic)g(manifold)f FE(HM)117 1291 y
FH(whic)o(h)c(can)g(b)q(e)h(c)o(hosen)f(arbitrarily.)558
1401 y(dim)p 645 1418 2 33 v 632 1418 a(Q)680 1401 y
FE(HM)782 1408 y Ft(m)838 1401 y FH(=)22 b Fv(m)105 b
FH(dim)1128 1408 y FC(I)-9 b(R)1168 1401 y FE(HM)1270
1408 y Ft(m)1318 1401 y FH(=)22 b(4)p Fv(m)340 b FH(\(8.2\))117
1517 y(As)21 b(explained)f(in)h(the)f(previous)h(sections)g(an)o(y)g
(quaternionic)f(manifold)g(has)i(a)f(holonom)o(y)117
1577 y(group:)608 1637 y FE(H)p Fv(ol)10 b FH(\()p FE(HM)819
1644 y Ft(m)852 1637 y FH(\))23 b FE(\032)e Fv(S)s(U)5
b FH(\(2\))20 b FE(\012)f Fv(S)s(p)p FH(\(2)p Fv(m;)8
b FH(I)-9 b(R\))391 b(\(8.3\))117 1724 y(and)20 b(the)e(index)g
Fv(\013)h FH(of)g(the)f(h)o(yp)q(erinos)h(transforms)g(in)f(the)g
Fu(fundamental)j FH(represen)o(tation)d(of)117 1784 y
Fv(S)s(p)p FH(\(2)p Fv(m;)8 b FH(I)-9 b(R\))-5 1886 y(Using)17
b(the)g(information)f(collected)g(in)h(the)f(previous)h(sections)g(w)o
(e)g(can)g(immediatel)o(y)d(write)j(do)o(wn)-5 1946 y(the)f
(de\014nition)f(of)h(the)f(curv)m(atures)h(and)h(co)o(v)m(arian)o(t)e
(deriv)m(ativ)o(es)f(for)i(all)g(the)f(\014elds.)21 b(The)16
b(de\014nition)-5 2006 y(of)h(curv)m(atures)f(in)g(the)g(gra)o
(vitational)g(sector)h(is)f(giv)o(en)f(b)o(y:)296 2116
y Fv(T)332 2096 y Ft(a)394 2116 y FE(\021)41 b(D)q Fv(V)553
2096 y Ft(a)585 2116 y FE(\000)11 b FH(i)p 657 2077 34
2 v 8 w Fv( )690 2128 y Ft(A)730 2116 y FE(^)g Fv(\015)802
2096 y Ft(a)823 2116 y Fv( )857 2096 y Ft(A)1785 2116
y FH(\(8.4\))299 2212 y Fv(\032)324 2219 y Ft(A)394 2212
y FE(\021)41 b Fv(d )531 2219 y Ft(A)571 2212 y FE(\000)626
2179 y FH(1)p 626 2201 25 2 v 626 2246 a(4)655 2212 y
Fv(\015)680 2219 y Ft(ab)725 2212 y Fv(!)757 2192 y Ft(ab)804
2212 y FE(^)11 b Fv( )880 2219 y Ft(A)919 2212 y FH(+)979
2179 y(i)p 973 2201 V 973 2246 a(2)1017 2196 y Fs(b)1003
2212 y FE(Q)f(^)i Fv( )1131 2219 y Ft(A)1170 2212 y FH(+)1223
2208 y Fs(b)1219 2212 y Fv(!)1267 2192 y Ft(B)1249 2225
y(A)1309 2212 y FE(^)f Fv( )1385 2219 y Ft(B)1429 2212
y FE(\021)i(r)p Fv( )1555 2219 y Ft(A)1785 2212 y FH(\(8.5\))299
2330 y Fv(\032)324 2309 y Ft(A)394 2330 y FE(\021)41
b Fv(d )533 2309 y Ft(A)573 2330 y FE(\000)627 2296 y
FH(1)p 627 2318 V 627 2364 a(4)657 2330 y Fv(\015)682
2337 y Ft(ab)726 2330 y Fv(!)758 2309 y Ft(ab)805 2330
y FE(^)12 b Fv( )884 2309 y Ft(A)923 2330 y FE(\000)983
2296 y FH(i)p 978 2318 V 978 2364 a(2)1021 2314 y Fs(b)1007
2330 y FE(Q)f(^)g Fv( )1137 2309 y Ft(A)1176 2330 y FH(+)1230
2326 y Fs(b)1225 2330 y Fv(!)1257 2309 y Ft(A)1282 2342
y(B)1323 2330 y FE(^)h Fv( )1402 2309 y Ft(B)1445 2330
y FE(\021)i(r)p Fv( )1574 2309 y Ft(A)1785 2330 y FH(\(8.6\))279
2424 y Fv(R)316 2404 y Ft(ab)394 2424 y FE(\021)41 b
Fv(d!)531 2404 y Ft(ab)579 2424 y FE(\000)11 b Fv(!)661
2404 y Ft(a)678 2436 y(c)706 2424 y FE(^)g Fv(!)782 2404
y Ft(cb)1785 2424 y FH(\(8.7\))-5 2534 y(where)16 b Fv(!)184
2516 y Ft(B)166 2546 y(A)228 2534 y FH(=)289 2515 y FC(i)p
285 2523 18 2 v 285 2551 a(2)308 2534 y Fv(!)340 2516
y Ft(x)362 2534 y FH(\()p Fv(\033)409 2541 y Ft(x)430
2534 y FH(\))449 2516 y Ft(B)449 2546 y(A)495 2534 y
FH(and)h Fv(!)622 2516 y Ft(A)636 2546 y(B)680 2534 y
FH(=)d Fv(\017)752 2516 y Ft(AC)808 2534 y Fv(\017)828
2541 y Ft(D)q(B)888 2534 y Fv(!)936 2516 y Ft(D)918 2546
y(C)968 2534 y FH(,)i(and)g(where)f(the)h(gauged)h(connections)e(for)h
(the)-5 2594 y FE(S)t(U)22 b FH(and)17 b FE(L)h FH(bundles)e(w)o(ere)g
(in)o(tro)q(duced)h(in)f(eq.s)g(7.57)p
 (#equation.7.57) [[293 144 313 156] [1 1 1 [3 3]] [0 0 1]] pdfm (.)23
b(In)17 b(all)f(the)h(ab)q(o)o(v)o(e)f(form)o(ulae)f(the)i(pull{bac)o
(k)-5 2655 y(on)g(space{time)e(through)i(the)f(maps)463
2765 y Fv(z)488 2746 y Ft(i)544 2765 y FH(:)41 b Fv(M)646
2772 y FC(4)688 2765 y FE(\000)-9 b(!)22 b(S)t(M)42 b
FH(;)f Fv(q)1005 2746 y Ft(u)1068 2765 y FH(:)g Fv(M)1170
2772 y FC(4)1212 2765 y FE(\000)-8 b(!)22 b(HM)368 b
FH(\(8.8\))916 2892 y(37)p eop
%%Page: 38 39
38 38 bop -5 15 a FH(is)12 b(ob)o(viously)g(understo)q(o)q(d.)22
b(In)12 b(this)g(w)o(a)o(y)g(the)g(comp)q(osite)f(connections)i(b)q
(ecome)d(1{forms)j(on)g(space{)-5 76 y(time.)68 136 y(In)j(the)g(v)o
(ector)g(m)o(ultiple)o(t)e(sector)i(the)g(curv)m(atures)g(and)h(co)o(v)
m(arian)o(t)f(deriv)m(ativ)o(es)f(are:)197 246 y FE(r)p
Fv(z)264 225 y Ft(i)319 246 y FH(=)42 b Fv(dz)449 225
y Ft(i)483 246 y FH(+)19 b Fv(g)11 b(A)611 225 y FC(\003)645
246 y Fv(k)672 225 y Ft(i)670 258 y FC(\003)697 246 y
FH(\()p Fv(z)r FH(\))1025 b(\(8.9\))179 319 y FE(r)p
221 292 25 2 v Fv(z)245 298 y Ft(i)257 286 y Fm(?)319
319 y FH(=)42 b Fv(d)p 424 292 V(z)449 298 y Ft(i)461
286 y Fm(?)501 319 y FH(+)19 b Fv(g)11 b(A)629 298 y
FC(\003)663 319 y Fv(k)690 298 y Ft(i)702 286 y Fm(?)688
331 y FC(\003)722 319 y FH(\()p 741 292 V Fv(z)r FH(\))975
b(\(8.10\))167 414 y FE(r)p Fv(\025)237 394 y Ft(iA)319
414 y FE(\021)41 b Fv(d\025)452 394 y Ft(iA)505 414 y
FE(\000)559 381 y FH(1)p 559 403 V 559 449 a(4)589 414
y Fv(\015)614 421 y Ft(ab)658 414 y Fv(!)690 394 y Ft(ab)726
414 y Fv(\025)754 394 y Ft(iA)806 414 y FE(\000)867 381
y FH(i)p 861 403 V 861 449 a(2)905 398 y Fs(b)891 414
y FE(Q)o Fv(\025)959 394 y Ft(iA)1011 414 y FH(+)1064
398 y Fs(b)1060 414 y FH(\000)1090 394 y Ft(i)1103 427
y(j)1121 414 y Fv(\025)1149 394 y Ft(j)r(A)1205 414 y
FH(+)1259 410 y Fs(b)1254 414 y Fv(!)1286 394 y Ft(A)1301
427 y(B)1342 414 y FE(^)12 b Fv(\025)1415 394 y Ft(iB)175
532 y FE(r)p Fv(\025)245 511 y Ft(i)257 500 y Fm(?)245
544 y Ft(A)319 532 y FE(\021)41 b Fv(d\025)452 511 y
Ft(i)464 500 y Fm(?)452 544 y Ft(A)496 532 y FE(\000)551
498 y FH(1)p 551 520 V 551 566 a(4)580 532 y Fv(\015)605
539 y Ft(ab)650 532 y Fv(!)682 511 y Ft(ab)718 532 y
Fv(\025)746 511 y Ft(i)758 500 y Fm(?)746 544 y Ft(A)790
532 y FH(+)849 498 y(i)p 844 520 V 844 566 a(2)887 516
y Fs(b)873 532 y FE(Q)p Fv(\025)942 511 y Ft(i)954 500
y Fm(?)942 544 y Ft(A)985 532 y FH(+)1038 516 y Fs(b)1034
532 y FH(\000)1064 511 y Ft(i)1076 500 y Fm(?)1076 544
y Ft(j)1092 535 y Fm(?)1113 532 y Fv(\025)1141 508 y
Ft(j)1157 497 y Fm(?)1141 544 y Ft(A)1188 532 y FH(+)1242
528 y Fs(b)1237 532 y Fv(!)1286 511 y Ft(B)1267 544 y(A)1327
532 y FE(^)11 b Fv(\025)1399 511 y Ft(i)1411 500 y Fm(?)1399
544 y Ft(B)213 648 y Fv(F)252 628 y FC(\003)319 648 y
FE(\021)41 b Fv(dA)461 628 y FC(\003)507 648 y FH(+)569
615 y(1)p 569 637 V 569 683 a(2)607 648 y Fv(g)10 b(f)669
628 y FC(\003)689 661 y(\006\000)747 648 y Fv(A)784 628
y FC(\006)830 648 y FE(^)20 b Fv(A)920 628 y FC(\000)963
648 y FH(+)p 1020 609 34 2 v 19 w Fv(L)1054 619 y FC(\003)p
1080 609 V 1080 648 a Fv( )1114 660 y Ft(A)1153 648 y
FE(^)11 b Fv( )1229 655 y Ft(B)1259 648 y Fv(\017)1279
628 y Ft(AB)1347 648 y FH(+)g Fv(L)1429 628 y FC(\003)p
1456 609 V 1456 648 a Fv( )1489 619 y Ft(A)1529 648 y
FE(^)g Fv( )1607 628 y Ft(B)1637 648 y Fv(\017)1657 655
y Ft(AB)1760 648 y FH(\(8.11\))-5 783 y(where)16 b(the)g(gauged)h
(Levi{Civita)e(connection)895 767 y Fs(b)891 783 y FH(\000)921
765 y Ft(i)934 795 y(j)968 783 y FH(on)i FE(S)t(M)e FH(is)h(also)h(giv)
o(en)e(b)o(y)g(eq.)g(7.57)p
 (#equation.7.57) [[447 579 468 591] [1 1 1 [3 3]] [0 0 1]] pdfm 
17 w(and)h(where)-5 855 y Fv(L)28 837 y FC(\003)80 855
y FH(=)24 b Fv(e)170 823 y Fn(K)p 170 829 24 2 v 174
849 a Fr(2)200 855 y Fv(X)244 837 y FC(\003)294 855 y
FH(is)e(the)g(upp)q(er)h(half)f(\(electric\))f(of)i(the)f(symplectic)d
(section)j(of)h FE(H)g FH(in)o(tro)q(duced)f(in)-5 915
y(equation)44 b(4.26)p
 (#equation.4.26) [[125 547 146 559] [1 1 1 [3 3]] [0 0 1]] pdfm (.)38
b(The)21 b(lo)o(w)o(er)g(part)h Fv(M)756 922 y FC(\003)805
915 y FH(of)f(suc)o(h)h(a)g(symplectic)c(section)k(w)o(ould)f(app)q
(ear)i(in)e(the)-5 975 y(magnetic)15 b(\014eld)h(strengths)h(if)e(w)o
(e)h(did)g(in)o(tro)q(duce)g(them.)68 1035 y(Finally)f(in)h(the)g(h)o
(yp)q(erm)o(ultiplet)d(sector)j(the)g(co)o(v)m(arian)o(t)g(deriv)m
(ativ)o(es)f(are:)447 1145 y FE(U)483 1125 y Ft(A\013)576
1145 y FE(\021)41 b(U)692 1125 y Ft(A\013)687 1158 y(v)743
1145 y FE(r)p Fv(q)809 1125 y Ft(v)851 1145 y FE(\021)22
b(U)948 1125 y Ft(A\013)943 1158 y(v)1007 1097 y Fs(\020)1032
1145 y Fv(d)8 b(q)1089 1125 y Ft(v)1129 1145 y FH(+)19
b Fv(g)11 b(A)1257 1125 y FC(\003)1291 1145 y Fv(k)1318
1125 y Ft(v)1316 1158 y FC(\003)1343 1145 y FH(\()p Fv(q)r
FH(\))1405 1097 y Fs(\021)1760 1145 y FH(\(8.12\))447
1253 y FE(r)p Fv(\020)510 1260 y Ft(\013)576 1253 y FE(\021)41
b Fv(d\020)702 1260 y Ft(\013)747 1253 y FE(\000)810
1220 y FH(1)p 810 1242 25 2 v 810 1288 a(4)839 1253 y
Fv(!)871 1233 y Ft(ab)916 1253 y Fv(\015)941 1260 y Ft(ab)985
1253 y Fv(\020)1006 1260 y Ft(\013)1042 1253 y FE(\000)1102
1220 y FH(i)p 1097 1242 V 1097 1288 a(2)1141 1237 y Fs(b)1126
1253 y FE(Q)8 b Fv(\020)1196 1260 y Ft(\013)1241 1253
y FH(+)1299 1237 y Fs(b)1290 1253 y FH(\001)1353 1233
y Ft(\014)1331 1266 y(\013)1377 1253 y Fv(\020)1398 1260
y Ft(\014)1760 1253 y FH(\(8.13\))443 1371 y FE(r)p Fv(\020)510
1350 y Ft(\013)576 1371 y FE(\021)41 b Fv(d\020)706 1350
y Ft(\013)750 1371 y FE(\000)814 1337 y FH(1)p 814 1359
V 814 1405 a(4)843 1371 y Fv(!)875 1350 y Ft(ab)919 1371
y Fv(\015)944 1378 y Ft(ab)989 1371 y Fv(\020)1014 1350
y Ft(\013)1050 1371 y FH(+)1109 1337 y(i)p 1104 1359
V 1104 1405 a(2)1147 1355 y Fs(b)1133 1371 y FE(Q)8 b
Fv(\020)1207 1350 y Ft(\013)1251 1371 y FH(+)1309 1355
y Fs(b)1300 1371 y FH(\001)1341 1350 y Ft(\013)1364 1383
y(\014)1387 1371 y Fv(\020)1412 1350 y Ft(\014)1760 1371
y FH(\(8.14\))-5 1505 y(where)148 1489 y Fs(b)139 1505
y FH(\001)202 1487 y Ft(\014)180 1518 y(\013)244 1505
y FH(is)19 b(the)g(gauged)g(Levi{Civita)g(connection)f(on)h
FE(HM)g FH(de\014ned)g(in)f(eq.)g(7.57)p
 (#equation.7.57) [[447 406 468 418] [1 1 1 [3 3]] [0 0 1]] pdfm (,)i
(satisfying)-5 1565 y(the)c(condition)g(to)h(b)q(e)f
Fv(S)s(p)p FH(\(2)p Fv(m;)8 b FH(I)-9 b(R\))17 b(Lie{algebra)f(v)m
(alued)g(and)592 1659 y Fs(b)583 1675 y FH(\001)646 1655
y Ft(\014)624 1688 y(\013)692 1675 y FE(\021)762 1659
y Fs(b)753 1675 y FH(\001)794 1655 y Ft(\015)r(\014)p
854 1675 2 33 v 841 1675 a FH(C)876 1682 y Ft(\015)r(\013)929
1675 y FH(;)968 1659 y Fs(b)959 1675 y FH(\001)1000 1655
y Ft(\013)1023 1688 y(\014)1068 1675 y FE(\021)p 1138
1675 V 18 w FH(C)1160 1682 y Ft(\014)r(\015)1221 1659
y Fs(b)1212 1675 y FH(\001)1253 1655 y Ft(\013\015)1760
1675 y FH(\(8.15\))68 1785 y(Let)24 b(us)g(note)g(that)g(the)g
(de\014nition)f(of)h(the)f(generalized)f(curv)m(atures)i(as)h(giv)o(en)
d(in)i(eq.s)e(8.4)p
 (#equation.8.4) [[505 339 520 351] [1 1 1 [3 3]] [0 0 1]] pdfm (-)-5
1846 y(8.7)p
 (#equation.8.4) [[71 324 86 336] [1 1 1 [3 3]] [0 0 1]] pdfm 
20 w(and)e(8.11)p
 (#equation.8.9) [[114 324 135 336] [1 1 1 [3 3]] [0 0 1]] pdfm 
20 w(has)g(b)q(een)g(c)o(hosen)f(in)g(suc)o(h)g(a)h(w)o(a)o(y)f(that)h
(when)g(all)f(the)g(p-forms)g(are)g(extended)g(to)-5
1906 y(sup)q(erforms)12 b(in)g(sup)q(erspace)g(they)g(giv)o(e)f(the)h
(correct)f(sup)q(ercurv)m(atures)i(of)f(the)g Fv(N)19
b FH(=)14 b(2)f(sup)q(eralgebra;)-5 1966 y(that)g(means)e(that)h(if)f
(w)o(e)h(set)g(all)f(sup)q(ercurv)m(atures)h(to)h(zero)e(the)h(corresp)
q(onding)h(equations)f(represen)o(t)-5 2026 y(the)19
b Fv(N)k FH(=)18 b(2)i(sup)q(eralgebra)f(in)g(dual)g(form.)27
b(Giv)o(en)18 b(these)h(de\014nitions)f(our)h(next)g(task)g(is)f(to)i
(write)-5 2086 y(do)o(wn)13 b(the)f(space-time)f(Lagrangian)j(and)f
(the)f(sup)q(ersymmetry)d(transformation)k(la)o(ws)f(of)h(the)f
(\014elds.)-5 2147 y(The)18 b(metho)q(d)f(emplo)o(y)o(ed)e(for)k(this)e
(construction)h(is)g(based)g(on)h(the)e(geometrical)f(approac)o(h:)25
b(for)19 b(a)-5 2207 y(review)14 b(see)g([31)p
 (#cite.CaDFb) [[129 237 141 249] [1 1 1 [3 3]] [0 0 1]] pdfm (].)20
b(The)15 b(rheonomic)e(deriv)m(ation)h(of)h(the)f(N=2)g(theory)g(is)h
(explained)e(in)h(App)q(endix)g(A.)-5 2267 y(Actually)j(one)i(solv)o
(es)f(the)g(Bianc)o(hi)f(iden)o(tities)f(in)i Fv(N)23
b FH(=)17 b(2)i(sup)q(erspace)f(and)h(then)g(constructs)f(the)-5
2327 y(rheonomic)e(sup)q(erspace)i(Lagrangian)i(in)d(suc)o(h)g(a)h(w)o
(a)o(y)f(that)h(the)g(sup)q(erspace)g("curv)m(atures")g(giv)o(en)-5
2387 y(b)o(y)h(the)g(solution)h(of)f(the)h(Bianc)o(hi)d(iden)o(tities)h
(are)h(repro)q(duced)h(b)o(y)f(the)g(v)m(ariational)g(equations)h(of)-5
2448 y(motion)f(deriv)o(ed)e(from)i(the)g(Lagrangian.)32
b(After)19 b(this)g(pro)q(cedure)g(is)h(completed)d(the)i(space-time)-5
2508 y(Lagrangian)f(is)e(immedi)o(ately)d(retriev)o(ed)h(b)o(y)h
(restricting)g(the)h(sup)q(erspace)g(p-forms)g(to)g(space-time.)68
2568 y(Using)i(the)f(results)g(of)h(App)q(endix)e(B)h(one)h(\014nds)g
(the)f(space-time)f Fv(N)21 b FH(=)15 b(2)j(sup)q(ergra)o(vit)o(y)f
(action)-5 2628 y(that)g(can)f(b)q(e)h(split)e(in)h(the)g(follo)o(wing)
g(w)o(a)o(y:)562 2750 y Fv(S)45 b FH(=)716 2692 y Fs(Z)766
2713 y FE(p)p 808 2713 64 2 v 37 x(\000)p Fv(g)10 b(d)905
2730 y FC(4)933 2750 y Fv(x)969 2702 y Fs(h)989 2750
y FE(L)1023 2757 y Ft(k)1056 2750 y FH(+)h FE(L)1139
2757 y FC(4)p Ft(f)1190 2750 y FH(+)g FE(L)1273 2730
y FB(0)1273 2763 y Ft(g)1294 2702 y Fs(i)1338 2750 y
Fv(;)916 2892 y FH(38)p eop
%%Page: 39 40
39 39 bop 540 15 a FE(L)574 22 y Ft(k)637 15 y FH(=)41
b FE(L)750 -5 y Ft(inv)750 28 y(k)q(in)816 15 y FH(+)11
b FE(L)899 22 y Ft(P)5 b(auli)1008 15 y Fv(;)521 88 y
FE(L)555 95 y FC(4)p Ft(f)637 88 y FH(=)41 b FE(L)750
68 y Ft(inv)750 100 y FC(4)p Ft(f)816 88 y FH(+)11 b
FE(L)899 68 y Ft(non)c(inv)899 100 y FC(4)p Ft(f)1035
88 y Fv(;)541 161 y FE(L)575 140 y FB(0)575 173 y Ft(g)637
161 y FH(=)41 b FE(L)750 168 y Ft(mass)846 161 y FE(\000)11
b Fv(V)g FH(\()p Fv(z)r(;)p 1001 134 25 2 v 8 w(z)r(;)d(q)r
FH(\))15 b Fv(;)640 b FH(\(8.16\))-5 256 y(where)20 b
FE(L)174 238 y Ft(inv)174 268 y(k)q(in)249 256 y FH(consists)g(of)h
(the)e(true)h(kinetic)e(terms)h(as)h(w)o(ell)f(as)h(P)o(auli-lik)o(e)e
(terms)h(con)o(taining)g(the)-5 316 y(deriv)m(ativ)o(es)e(of)i(the)g
(scalar)f(\014elds.)28 b(The)19 b(mo)q(di\014cations)f(due)h(to)g(the)f
(gauging)i(are)e(con)o(tained)h(not)-5 376 y(only)e(in)f
FE(L)194 358 y FB(0)194 388 y Ft(g)231 376 y FH(but)h(also)g(in)g(the)f
(gauged)i(co)o(v)m(arian)o(t)e(deriv)m(ativ)o(es)g(in)g(the)g(rest)h
(of)g(the)g(lagrangian.)23 b(W)l(e)-5 436 y(collect)15
b(the)h(v)m(arious)h(terms)e(of)h(\(8.16)p
 (#equation.8.16) [[218 662 239 674] [1 1 1 [3 3]] [0 0 1]] pdfm (\))h
(in)f(the)g(table)g(b)q(elo)o(w.)p 609 543 662 2 v 634
646 a Fu(N=2)i(Sup)n(er)n(gr)n(avity)e(lagr)n(angian)p
609 726 V 123 880 a FE(L)157 859 y Ft(inv)157 892 y(k)q(in)254
880 y FH(=)42 b FE(\000)378 846 y FH(1)p 378 868 25 2
v 378 914 a(2)407 880 y Fv(R)11 b FH(+)g Fv(g)527 887
y Ft(ij)555 878 y Fm(?)576 880 y FE(r)618 859 y Ft(\026)641
880 y Fv(z)666 859 y Ft(i)680 880 y FE(r)722 887 y Ft(\026)p
745 853 V 745 880 a Fv(z)769 859 y Ft(j)785 847 y Fm(?)817
880 y FH(+)g Fv(h)894 887 y Ft(uv)935 880 y FE(r)977
887 y Ft(\026)1000 880 y Fv(q)1024 859 y Ft(u)1045 880
y FE(r)1087 859 y Ft(\026)1110 880 y Fv(q)1134 859 y
Ft(v)1165 880 y FH(+)1220 846 y Fv(\017)1240 828 y Ft(\026\027)r
(\025\033)p 1219 868 106 2 v 1219 879 a FE(p)p 1261 879
64 2 v 35 x(\000)p Fv(g)1338 831 y Fs(\020)p 1363 840
34 2 v 49 x Fv( )1396 850 y Ft(A)1396 892 y(\026)1425
880 y Fv(\015)1450 887 y Ft(\033)1473 880 y Fv(\032)1498
887 y Ft(A\027)r(\025)1578 880 y FE(\000)p 1628 840 V
11 w Fv( )1662 891 y Ft(A\026)1711 880 y Fv(\015)1736
887 y Ft(\033)1760 880 y Fv(\032)1785 859 y Ft(A)1785
892 y(\027)r(\025)1827 831 y Fs(\021)253 1010 y FE(\000)344
977 y FH(i)p 339 999 25 2 v 339 1044 a(2)368 1010 y Fv(g)391
1017 y Ft(ij)419 1008 y Fm(?)448 962 y Fs(\020)p 473
971 29 2 v 48 x Fv(\025)501 981 y Ft(iA)542 1010 y Fv(\015)570
990 y Ft(\026)593 1010 y FE(r)635 1017 y Ft(\026)658
1010 y Fv(\025)686 987 y Ft(j)702 975 y Fm(?)686 1022
y Ft(A)734 1010 y FH(+)p 783 971 V 11 w Fv(\025)811 981
y Ft(j)827 969 y Fm(?)811 1023 y Ft(A)847 1010 y Fv(\015)875
990 y Ft(\026)899 1010 y FE(r)941 1017 y Ft(\026)963
1010 y Fv(\025)991 990 y Ft(iA)1032 962 y Fs(\021)1068
1010 y FE(\000)g FH(i)1140 962 y Fs(\020)p 1165 971 26
2 v 48 x Fv(\020)1190 981 y Ft(\013)1215 1010 y Fv(\015)1243
990 y Ft(\026)1266 1010 y FE(r)1308 1017 y Ft(\026)1331
1010 y Fv(\020)1352 1017 y Ft(\013)1388 1010 y FH(+)p
1437 971 V 11 w Fv(\020)1462 1022 y Ft(\013)1487 1010
y Fv(\015)1515 990 y Ft(\026)1538 1010 y FE(r)1580 1017
y Ft(\026)1603 1010 y Fv(\020)1628 990 y Ft(\013)1652
962 y Fs(\021)254 1111 y FH(+)42 b(i)356 1063 y Fs(\020)p
380 1072 49 2 v 380 1111 a FE(N)429 1118 y FC(\003\006)481
1111 y FE(F)522 1090 y FB(\000)p FC(\003)517 1123 y Ft(\026\027)575
1111 y FE(F)616 1090 y FB(\000)p FC(\006)p Ft(\026\027)723
1111 y FE(\000)11 b(N)814 1118 y FC(\003\006)866 1111
y FE(F)907 1090 y FC(+\003)902 1123 y Ft(\026\027)960
1111 y FE(F)1001 1090 y FC(+\006)p Ft(\026\027)1097 1063
y Fs(\021)1133 1111 y FH(+)1182 1063 y Fs(n)1220 1111
y FE(\000)g Fv(g)1293 1118 y Ft(ij)1321 1109 y Fm(?)1342
1111 y FE(r)1384 1118 y Ft(\026)p 1407 1084 25 2 v 1407
1111 a Fv(z)1432 1090 y Ft(j)1448 1079 y Fm(?)p 1468
1071 34 2 v 1468 1111 a Fv( )1501 1081 y Ft(\026)1501
1123 y(A)1530 1111 y Fv(\025)1558 1090 y Ft(iA)253 1205
y FE(\000)42 b FH(2)p FE(U)394 1184 y Ft(A\013)389 1217
y(u)445 1205 y FE(r)487 1212 y Ft(\026)510 1205 y Fv(q)534
1184 y Ft(u)p 556 1165 V 556 1205 a Fv( )590 1175 y Ft(\026)590
1217 y(A)618 1205 y Fv(\020)639 1212 y Ft(\013)675 1205
y FH(+)11 b Fv(g)747 1212 y Ft(ij)775 1203 y Fm(?)796
1205 y FE(r)838 1212 y Ft(\026)p 861 1178 25 2 v 861
1205 a Fv(z)886 1184 y Ft(j)902 1173 y Fm(?)p 922 1165
29 2 v 922 1205 a Fv(\025)950 1175 y Ft(iA)991 1205 y
Fv(\015)1019 1184 y Ft(\026\027)1062 1205 y Fv( )1094
1212 y Ft(A\027)1152 1205 y FH(+)g(2)p FE(U)1261 1184
y Ft(\013A)1256 1217 y(u)1313 1205 y FE(r)1355 1212 y
Ft(\026)1378 1205 y Fv(q)1402 1184 y Ft(u)p 1424 1165
26 2 v 1424 1205 a Fv(\020)1449 1217 y Ft(\013)1474 1205
y Fv(\015)1502 1184 y Ft(\026\027)1544 1205 y Fv( )1576
1212 y Ft(A\027)1635 1205 y FH(+)g(h)p Fv(:)p FH(c)p
Fv(:)1760 1157 y Fs(o)1760 1284 y FH(\(8.17\))86 1366
y FE(L)120 1373 y Ft(P)5 b(auli)254 1366 y FH(=)334 1318
y Fs(n)361 1366 y FE(F)402 1345 y FB(\000)p FC(\003)397
1378 y Ft(\026\027)464 1366 y FH(\(Im)15 b FE(N)7 b FH(\))625
1380 y FC(\003\006)685 1366 y FH([4)p Fv(L)756 1345 y
FC(\006)p 784 1326 34 2 v 784 1366 a Fv( )818 1336 y
Ft(A\026)867 1366 y Fv( )901 1345 y Ft(B)r(\027)951 1366
y Fv(\017)971 1373 y Ft(AB)1038 1366 y FE(\000)k FH(4i)p
1126 1326 30 2 v Fv(f)1155 1336 y FC(\006)1155 1378 y
Ft(i)1167 1369 y Fm(?)p 1187 1326 29 2 v 1187 1366 a
Fv(\025)1216 1336 y Ft(i)1228 1324 y Fm(?)1216 1378 y
Ft(A)1248 1366 y Fv(\015)1276 1345 y Ft(\027)1297 1366
y Fv( )1331 1342 y Ft(\026)1329 1378 y(B)1359 1366 y
Fv(\017)1379 1345 y Ft(AB)1447 1366 y FH(+)254 1473 y(+)339
1439 y(1)p 339 1462 25 2 v 339 1507 a(2)368 1473 y FE(r)410
1480 y Ft(i)424 1473 y Fv(f)453 1453 y FC(\006)448 1485
y Ft(j)p 481 1434 29 2 v 481 1473 a Fv(\025)509 1443
y Ft(iA)550 1473 y Fv(\015)578 1453 y Ft(\026\027)620
1473 y Fv(\025)648 1453 y Ft(j)r(B)695 1473 y Fv(\017)715
1480 y Ft(AB)783 1473 y FE(\000)g Fv(L)866 1453 y FC(\006)p
893 1434 26 2 v 893 1473 a Fv(\020)918 1485 y Ft(\013)943
1473 y Fv(\015)971 1453 y Ft(\026\027)1014 1473 y Fv(\020)1035
1480 y Ft(\014)p 1067 1473 2 33 v 1054 1473 a FH(C)1089
1452 y Ft(\013\014)1136 1473 y FH(])f(+)h(h)p Fv(:)p
FH(c)p Fv(:)1285 1425 y Fs(o)1760 1473 y FH(\(8.18\))124
1637 y FE(L)158 1617 y Ft(inv)158 1650 y FC(4)p Ft(f)254
1637 y FH(=)344 1604 y(i)p 339 1626 25 2 v 339 1671 a(2)376
1589 y Fs(\020)401 1637 y Fv(g)424 1644 y Ft(ij)452 1635
y Fm(?)p 473 1598 29 2 v 473 1637 a Fv(\025)501 1607
y Ft(iA)542 1637 y Fv(\015)567 1644 y Ft(\033)590 1637
y Fv(\025)618 1614 y Ft(j)634 1602 y Fm(?)618 1649 y
Ft(B)666 1637 y FE(\000)g FH(2)p Fv(\016)764 1617 y Ft(A)762
1650 y(B)p 792 1598 26 2 v 792 1637 a Fv(\020)817 1607
y Ft(\013)842 1637 y Fv(\015)867 1644 y Ft(\033)891 1637
y Fv(\020)912 1644 y Ft(\013)937 1589 y Fs(\021)p 970
1598 34 2 v 970 1637 a Fv( )1004 1649 y Ft(A\026)1053
1637 y Fv(\015)1078 1644 y Ft(\025)1101 1637 y Fv( )1135
1617 y Ft(B)1133 1650 y(\027)1171 1604 y Fv(\017)1191
1585 y Ft(\026\027)r(\025\033)p 1170 1626 106 2 v 1170
1637 a FE(p)p 1212 1637 64 2 v 34 x(\000)p Fv(g)253 1767
y FE(\000)347 1733 y FH(1)p 347 1755 25 2 v 347 1801
a(6)393 1719 y Fs(\020)418 1767 y Fv(C)453 1774 y Ft(ij)r(k)p
502 1727 29 2 v 502 1767 a Fv(\025)531 1737 y Ft(iA)571
1767 y Fv(\015)599 1746 y Ft(\026)622 1767 y Fv( )656
1746 y Ft(B)654 1779 y(\026)p 695 1727 V 695 1767 a Fv(\025)723
1737 y Ft(j)r(C)769 1767 y Fv(\025)797 1746 y Ft(k)q(D)857
1767 y Fv(\017)877 1774 y Ft(AC)932 1767 y Fv(\017)952
1774 y Ft(B)r(D)1023 1767 y FH(+)g Fv(h:c:)1149 1719
y Fs(\021)253 1871 y FE(\000)42 b FH(2)p 358 1831 34
2 v Fv( )392 1841 y Ft(A)392 1883 y(\026)420 1871 y Fv( )454
1850 y Ft(B)452 1883 y(\027)p 492 1831 V 492 1871 a Fv( )526
1841 y Ft(\026)526 1883 y(A)554 1871 y Fv( )588 1850
y Ft(\027)586 1883 y(B)627 1871 y FH(+)11 b(2)p Fv(g)723
1878 y Ft(ij)751 1869 y Fm(?)p 781 1831 29 2 v 781 1871
a Fv(\025)809 1841 y Ft(iA)850 1871 y Fv(\015)875 1878
y Ft(\026)898 1871 y Fv( )932 1850 y Ft(B)930 1883 y(\027)p
970 1831 V 970 1871 a Fv(\025)999 1841 y Ft(i)1011 1829
y Fm(?)999 1883 y Ft(A)1031 1871 y Fv(\015)1059 1850
y Ft(\026)1082 1871 y Fv( )1116 1850 y Ft(\027)1114 1883
y(B)254 1972 y FH(+)339 1938 y(1)p 339 1960 25 2 v 339
2006 a(4)376 1911 y Fs(\022)407 1972 y Fv(R)444 1979
y Ft(ij)472 1970 y Fm(?)490 1979 y Ft(lk)520 1970 y Fm(?)560
1972 y FH(+)19 b Fv(g)640 1979 y Ft(ik)671 1970 y Fm(?)700
1972 y Fv(g)723 1979 y Ft(lj)750 1970 y Fm(?)790 1972
y FE(\000)853 1938 y FH(3)p 853 1960 V 853 2006 a(2)891
1972 y Fv(g)914 1979 y Ft(ij)942 1970 y Fm(?)971 1972
y Fv(g)994 1979 y Ft(lk)1024 1970 y Fm(?)1044 1911 y
Fs(\023)p 1083 1932 29 2 v 1083 1972 a Fv(\025)1112 1942
y Ft(iA)1152 1972 y Fv(\025)1180 1951 y Ft(lB)p 1222
1932 V 1222 1972 a Fv(\025)1250 1942 y Ft(j)1266 1931
y Fm(?)1250 1984 y Ft(A)1287 1972 y Fv(\025)1315 1951
y Ft(k)1334 1940 y Fm(?)1315 1984 y Ft(B)254 2092 y FH(+)339
2058 y(1)p 339 2080 25 2 v 339 2126 a(4)376 2092 y Fv(g)399
2099 y Ft(ij)427 2090 y Fm(?)p 456 2052 26 2 v 456 2092
a Fv(\020)481 2062 y Ft(\013)506 2092 y Fv(\015)531 2099
y Ft(\026)555 2092 y Fv(\020)576 2099 y Ft(\013)p 609
2052 29 2 v 609 2092 a Fv(\025)637 2062 y Ft(iA)678 2092
y Fv(\015)706 2071 y Ft(\026)729 2092 y Fv(\025)757 2068
y Ft(j)773 2056 y Fm(?)757 2104 y Ft(A)813 2092 y FH(+)876
2058 y(1)p 876 2080 25 2 v 876 2126 a(2)913 2092 y FE(R)955
2071 y Ft(\013)955 2104 y(\014)r(ts)1016 2092 y FE(U)1052
2071 y Ft(t)1047 2104 y(A\015)1105 2092 y FE(U)1141 2071
y Ft(s)1136 2104 y(B)r(\016)1183 2092 y Fv(\017)1203
2071 y Ft(AB)1268 2092 y Fv(C)1307 2071 y Ft(\016)q(\021)p
1344 2052 26 2 v 1344 2092 a Fv(\020)1369 2104 y Ft(\013)1402
2092 y Fv(\020)1423 2099 y Ft(\021)p 1453 2052 V 1453
2092 a Fv(\020)1478 2062 y Ft(\014)1510 2092 y Fv(\020)1535
2071 y Ft(\015)253 2209 y FE(\000)334 2149 y Fs(\024)378
2176 y FH(i)p 361 2198 49 2 v 361 2243 a(12)414 2209
y FE(r)456 2216 y Ft(m)497 2209 y Fv(C)532 2216 y Ft(j)r(k)q(l)p
581 2170 29 2 v 581 2209 a Fv(\025)609 2180 y Ft(j)r(A)654
2209 y Fv(\025)682 2189 y Ft(mB)p 744 2170 V 744 2209
a Fv(\025)772 2180 y Ft(k)q(C)821 2209 y Fv(\025)849
2189 y Ft(lD)893 2209 y Fv(\017)913 2216 y Ft(AC)968
2209 y Fv(\017)988 2216 y Ft(B)r(D)1059 2209 y FH(+)h
Fv(h:)8 b(c:)1202 2149 y Fs(\025)254 2326 y FH(+)42 b
Fv(g)357 2333 y Ft(ij)385 2324 y Fm(?)p 414 2286 34 2
v 414 2326 a Fv( )447 2296 y Ft(A)447 2338 y(\026)476
2326 y Fv(\025)504 2302 y Ft(j)520 2290 y Fm(?)504 2338
y Ft(A)p 549 2286 V 549 2326 a Fv( )582 2296 y Ft(\026)582
2338 y(B)612 2326 y Fv(\025)640 2305 y Ft(iB)703 2326
y FH(+)19 b(2)p 784 2286 V Fv( )818 2296 y Ft(A)818 2338
y(\026)846 2326 y Fv(\020)871 2305 y Ft(\013)p 896 2286
V 896 2326 a Fv( )930 2296 y Ft(\026)930 2338 y(A)958
2326 y Fv(\020)979 2333 y Ft(\013)1024 2326 y FH(+)1073
2265 y Fs(\022)1103 2326 y Fv(\017)1123 2333 y Ft(AB)p
1196 2326 2 33 v 1183 2326 a FH(C)1218 2333 y Ft(\013\014)p
1273 2286 34 2 v 1273 2326 a Fv( )1306 2296 y Ft(A)1306
2338 y(\026)1335 2326 y Fv(\020)1360 2305 y Ft(\013)p
1393 2286 V 1393 2326 a Fv( )1427 2296 y Ft(B)r FB(j)p
Ft(\026)1488 2326 y Fv(\020)1513 2305 y Ft(\014)1556
2326 y FH(+)g Fv(h:c:)1690 2265 y Fs(\023)1760 2326 y
FH(\(8.19\))58 2439 y FE(L)92 2418 y Ft(non)7 b(inv)92
2451 y FC(4)p Ft(f)254 2439 y FH(=)334 2391 y Fs(n)370
2439 y FH(\(Im)14 b FE(N)7 b FH(\))530 2453 y FC(\003\006)599
2391 y Fs(h)619 2439 y FH(2)p Fv(L)676 2418 y FC(\003)711
2439 y Fv(L)744 2418 y FC(\006)780 2391 y Fs(\020)p 805
2399 V 48 x Fv( )838 2409 y Ft(A)838 2451 y(\026)867
2439 y Fv( )901 2418 y Ft(B)899 2451 y(\027)931 2391
y Fs(\021)955 2400 y FB(\000)993 2391 y Fs(\020)p 1018
2399 V 48 x Fv( )1052 2409 y Ft(C)1052 2451 y(\026)1081
2439 y Fv( )1115 2418 y Ft(D)1113 2451 y(\027)1147 2391
y Fs(\021)1171 2400 y FB(\000)1209 2439 y Fv(\017)1229
2446 y Ft(AB)1294 2439 y Fv(\017)1314 2446 y Ft(C)r(D)253
2540 y FE(\000)42 b FH(8i)8 b Fv(L)413 2520 y FC(\003)p
440 2501 30 2 v 440 2540 a Fv(f)469 2511 y FC(\006)469
2553 y Ft(i)481 2543 y Fm(?)509 2492 y Fs(\020)p 534
2501 34 2 v 48 x Fv( )568 2511 y Ft(A)568 2553 y(\026)596
2540 y Fv( )630 2520 y Ft(B)628 2553 y(\027)660 2492
y Fs(\021)685 2501 y FB(\000)723 2492 y Fs(\020)p 747
2501 29 2 v 747 2540 a Fv(\025)776 2511 y Ft(i)788 2499
y Fm(?)776 2553 y Ft(A)808 2540 y Fv(\015)836 2520 y
Ft(\027)858 2540 y Fv( )892 2517 y Ft(\026)890 2553 y(B)920
2492 y Fs(\021)944 2500 y FB(\000)253 2642 y FE(\000)42
b FH(2)p 358 2602 30 2 v Fv(f)387 2612 y FC(\003)387
2654 y Ft(i)399 2645 y Fm(?)p 420 2602 V 420 2642 a Fv(f)449
2612 y FC(\006)449 2654 y Ft(j)465 2645 y Fm(?)493 2594
y Fs(\020)p 518 2602 29 2 v 48 x Fv(\025)547 2612 y Ft(i)559
2600 y Fm(?)547 2654 y Ft(A)579 2642 y Fv(\015)607 2621
y Ft(\027)628 2642 y Fv( )662 2618 y Ft(\026)660 2654
y(B)690 2594 y Fs(\021)715 2602 y FB(\000)753 2594 y
Fs(\020)p 778 2602 V 48 x Fv(\025)806 2612 y Ft(j)822
2600 y Fm(?)806 2654 y Ft(C)842 2642 y Fv(\015)867 2649
y Ft(\027)889 2642 y Fv( )921 2650 y Ft(D)q FB(j)p Ft(\026)984
2594 y Fs(\021)1009 2602 y FB(\000)1047 2642 y Fv(\017)1067
2621 y Ft(AB)1131 2642 y Fv(\017)1151 2621 y Ft(C)r(D)254
2750 y FH(+)344 2716 y(i)p 339 2738 25 2 v 339 2784 a(2)368
2750 y Fv(L)401 2730 y FC(\003)p 428 2711 30 2 v 428
2750 a Fv(f)457 2720 y FC(\006)457 2762 y Ft(`)471 2753
y Fm(?)500 2750 y Fv(g)525 2730 y Ft(k)q(`)558 2718 y
Fm(?)587 2750 y Fv(C)622 2757 y Ft(ij)r(k)680 2702 y
Fs(\020)p 705 2711 34 2 v 48 x Fv( )738 2720 y Ft(A)738
2762 y(\026)767 2750 y Fv( )801 2730 y Ft(B)799 2762
y(\027)830 2702 y Fs(\021)855 2711 y FB(\000)p 893 2711
29 2 v 893 2750 a Fv(\025)921 2720 y Ft(iC)963 2750 y
Fv(\015)991 2730 y Ft(\026\027)1034 2750 y Fv(\025)1062
2730 y Ft(j)r(D)1119 2750 y Fv(\017)1139 2757 y Ft(AB)1204
2750 y Fv(\017)1224 2757 y Ft(C)r(D)916 2892 y FH(39)p
eop
%%Page: 40 41
40 40 bop 254 26 a FH(+)p 334 -14 30 2 v 42 w Fv(f)363
-4 y FC(\003)363 38 y Ft(m)394 29 y Fm(?)p 414 -14 V
414 26 a Fv(f)444 -4 y FC(\006)444 38 y Ft(`)458 29 y
Fm(?)486 26 y Fv(g)511 5 y Ft(k)q(`)544 -7 y Fm(?)574
26 y Fv(C)609 33 y Ft(ij)r(k)666 -23 y Fs(\020)p 691
-14 29 2 v 49 x Fv(\025)720 -4 y Ft(m)751 -16 y Fm(?)720
38 y Ft(A)771 26 y Fv(\015)796 33 y Ft(\027)818 26 y
Fv( )850 33 y Ft(B)r(\026)901 -23 y Fs(\021)926 -14 y
FB(\000)p 964 -14 V 964 26 a Fv(\025)992 -4 y Ft(iA)1033
26 y Fv(\015)1061 5 y Ft(\026\027)1103 26 y Fv(\025)1131
5 y Ft(j)r(B)253 127 y FE(\000)42 b Fv(L)367 106 y FC(\003)393
127 y Fv(L)426 106 y FC(\006)462 78 y Fs(\020)p 487 87
34 2 v 49 x Fv( )521 97 y Ft(A)521 139 y(\026)549 127
y Fv( )583 106 y Ft(B)581 139 y(\027)613 78 y Fs(\021)638
87 y FB(\000)p 676 87 26 2 v 676 127 a Fv(\020)701 138
y Ft(\013)725 127 y Fv(\015)753 106 y Ft(\026\027)796
127 y Fv(\020)817 134 y Ft(\014)850 127 y Fv(\017)870
134 y Ft(AB)p 943 127 2 33 v 930 127 a FH(C)965 106 y
Ft(\013\014)254 228 y FH(+)g(i)p Fv(L)381 207 y FC(\003)p
407 188 30 2 v 407 228 a Fv(f)436 198 y FC(\006)436 240
y Ft(i)448 231 y Fm(?)477 180 y Fs(\020)p 501 188 29
2 v 501 228 a Fv(\025)530 198 y Ft(i)542 187 y Fm(?)530
240 y Ft(A)562 228 y Fv(\015)590 207 y Ft(\027)612 228
y Fv( )646 204 y Ft(\026)644 240 y(B)674 180 y Fs(\021)698
188 y FB(\000)p 736 188 26 2 v 736 228 a Fv(\020)761
240 y Ft(\013)786 228 y Fv(\015)811 235 y Ft(\026\027)854
228 y Fv(\020)875 235 y Ft(\014)907 228 y Fv(\017)927
207 y Ft(AB)p 992 228 2 33 v 979 228 a FH(C)1014 207
y Ft(\013\014)253 335 y FE(\000)351 302 y FH(1)p 339
324 49 2 v 339 369 a(32)401 335 y Fv(C)436 342 y Ft(ij)r(k)493
335 y Fv(C)528 342 y Ft(lmn)594 335 y Fv(g)619 315 y
Ft(k)q(r)655 303 y Fm(?)684 335 y Fv(g)709 315 y Ft(ns)746
303 y Fm(?)p 775 296 30 2 v 775 335 a Fv(f)804 306 y
FC(\003)804 348 y Ft(r)821 338 y Fm(?)p 849 296 V 849
335 a Fv(f)879 306 y FC(\006)879 348 y Ft(s)895 338 y
Fm(?)p 924 296 29 2 v 924 335 a Fv(\025)952 306 y Ft(iA)1001
335 y Fv(\015)1026 342 y Ft(\026\027)1077 335 y Fv(\025)1105
315 y Ft(j)r(B)p 1160 296 V 1160 335 a Fv(\025)1189 306
y Ft(k)q(C)1246 335 y Fv(\015)1274 315 y Ft(\026\027)1325
335 y Fv(\025)1353 315 y Ft(lD)1405 335 y Fv(\017)1425
342 y Ft(AB)1481 335 y Fv(\017)1501 342 y Ft(C)r(D)253
452 y FE(\000)339 418 y FH(1)p 339 440 25 2 v 339 486
a(8)376 452 y Fv(L)409 431 y FC(\003)436 452 y FE(r)478
459 y Ft(i)492 452 y Fv(f)521 431 y FC(\006)516 464 y
Ft(j)p 549 412 26 2 v 549 452 a Fv(\020)574 464 y Ft(\013)598
452 y Fv(\015)623 459 y Ft(\026\027)667 452 y Fv(\020)688
459 y Ft(\014)p 720 412 29 2 v 720 452 a Fv(\025)748
422 y Ft(iA)789 452 y Fv(\015)817 431 y Ft(\026\027)859
452 y Fv(\025)887 431 y Ft(j)r(B)951 452 y Fv(\017)971
459 y Ft(AB)p 1044 452 2 33 v 1031 452 a FH(C)1066 431
y Ft(\013\014)254 568 y FH(+)339 535 y(1)p 339 557 25
2 v 339 603 a(8)376 568 y Fv(L)409 548 y FC(\003)444
568 y Fv(L)477 548 y FC(\006)p 505 529 26 2 v 505 568
a Fv(\020)530 580 y Ft(\013)555 568 y Fv(\015)580 575
y Ft(\026\027)623 568 y Fv(\020)644 575 y Ft(\014)p 676
529 V 676 568 a Fv(\020)701 580 y Ft(\015)723 568 y Fv(\015)751
548 y Ft(\026\027)794 568 y Fv(\020)815 575 y Ft(\016)p
851 568 2 33 v 838 568 a FH(C)873 548 y Ft(\013\014)p
936 568 V 923 568 a FH(C)959 548 y Ft(\015)r(\016)998
520 y Fs(i)1028 568 y FH(+)11 b(h)p Fv(:)p FH(c)p Fv(:)1153
520 y Fs(o)1760 568 y FH(\(8.20\))93 714 y FE(L)127 721
y Ft(mass)254 714 y FH(=)42 b Fv(g)359 666 y Fs(h)378
714 y FH(2)p Fv(S)432 721 y Ft(AB)p 490 674 34 2 v 490
714 a Fv( )523 684 y Ft(A)523 726 y(\026)552 714 y Fv(\015)580
693 y Ft(\026\027)622 714 y Fv( )656 693 y Ft(B)654 726
y(\027)697 714 y FH(+)11 b(i)p Fv(g)783 721 y Ft(ij)811
712 y Fm(?)831 714 y Fv(W)884 693 y Ft(iAB)p 953 674
29 2 v 953 714 a Fv(\025)982 684 y Ft(j)998 672 y Fm(?)982
726 y Ft(A)1018 714 y Fv(\015)1043 721 y Ft(\026)1066
714 y Fv( )1100 690 y Ft(\026)1098 726 y(B)1139 714 y
FH(+)g(2i)p Fv(N)1270 693 y Ft(A)1265 726 y(\013)p 1299
674 26 2 v 1299 714 a Fv(\020)1324 684 y Ft(\013)1349
714 y Fv(\015)1374 721 y Ft(\026)1398 714 y Fv( )1432
690 y Ft(\026)1430 726 y(A)254 808 y FH(+)42 b FE(M)394
787 y Ft(\013\014)p 440 768 V 440 808 a Fv(\020)465 819
y Ft(\013)490 808 y Fv(\020)511 815 y Ft(\014)546 808
y FH(+)11 b FE(M)655 787 y Ft(\013)677 820 y(iB)p 719
768 V 719 808 a Fv(\020)744 819 y Ft(\013)769 808 y Fv(\025)797
787 y Ft(iB)851 808 y FH(+)g FE(M)960 815 y Ft(iA`B)p
1043 768 29 2 v 1043 808 a Fv(\025)1071 778 y Ft(iA)1112
808 y Fv(\025)1140 787 y Ft(`B)1185 760 y Fs(i)1216 808
y FH(+)g(h.c.)418 b(\(8.21\))20 901 y(V)q(\()o Fv(z)r(;)p
123 875 25 2 v 8 w(z)r(;)8 b(q)r FH(\))41 b(=)h Fv(g)359
881 y FC(2)379 853 y Fs(h)o(\020)423 901 y Fv(g)446 908
y Ft(ij)474 899 y Fm(?)495 901 y Fv(k)522 881 y Ft(i)520
913 y FC(\003)546 901 y Fv(k)573 877 y Ft(j)589 866 y
Fm(?)571 913 y FC(\006)621 901 y FH(+)11 b(4)p Fv(h)722
908 y Ft(uv)763 901 y Fv(k)790 881 y Ft(u)788 913 y FC(\003)815
901 y Fv(k)842 881 y Ft(v)840 913 y FC(\006)868 853 y
Fs(\021)p 901 862 34 2 v 901 901 a Fv(L)934 872 y FC(\003)961
901 y Fv(L)994 881 y FC(\006)1033 901 y FH(+)g Fv(g)1107
881 y Ft(ij)1135 869 y Fm(?)1155 901 y Fv(f)1184 881
y FC(\003)1179 913 y Ft(i)1211 901 y Fv(f)1240 881 y
FC(\006)1235 913 y Ft(j)1251 904 y Fm(?)1271 901 y FE(P)1310
881 y Ft(x)1306 913 y FC(\003)1332 901 y FE(P)1371 881
y Ft(x)1367 913 y FC(\006)1406 901 y FE(\000)g FH(3)p
1480 862 V Fv(L)1513 872 y FC(\003)1540 901 y Fv(L)1573
881 y FC(\006)1600 901 y FE(P)1639 881 y Ft(x)1635 913
y FC(\003)1662 901 y FE(P)1701 881 y Ft(x)1697 913 y
FC(\006)1724 853 y Fs(i)1760 901 y Fv(:)-14 b FH(\(8.22\))-5
1064 y(where)21 b FE(F)182 1046 y FB(\006)p FC(\003)177
1076 y Ft(\026\027)259 1064 y FH(=)324 1044 y FC(1)p
324 1052 18 2 v 324 1081 a(2)347 1064 y FH(\()p FE(F)407
1046 y FC(\003)402 1076 y Ft(\026\027)459 1064 y FE(\006)521
1044 y FC(i)p 517 1052 V 517 1081 a(2)540 1064 y Fv(\017)560
1046 y Ft(\026\027)r(\032\033)642 1064 y FE(F)683 1046
y FC(\003)678 1076 y Ft(\032\033)719 1064 y FH(\))g(and)h(\()p
Fv(:::)p FH(\))939 1046 y FB(\000)989 1064 y FH(denotes)f(the)g(self)g
(dual)g(part)h(of)g(the)f(fermion)-5 1124 y(bilinears.)g(The)16
b(mass{matrices)e(are)i(giv)o(en)g(b)o(y:)441 1234 y
Fv(S)471 1241 y Ft(AB)570 1234 y FH(=)660 1200 y(i)p
654 1223 25 2 v 654 1268 a(2)684 1234 y(\()p Fv(\033)731
1241 y Ft(x)752 1234 y FH(\))798 1214 y Ft(C)771 1246
y(A)827 1234 y Fv(\017)847 1241 y Ft(B)r(C)905 1234 y
FE(P)944 1214 y Ft(x)940 1246 y FC(\003)966 1234 y Fv(L)999
1214 y FC(\003)407 1337 y Fv(W)460 1317 y Ft(iAB)570
1337 y FH(=)41 b Fv(\017)669 1317 y Ft(AB)734 1337 y
Fv(k)761 1317 y Ft(i)759 1350 y FC(\003)p 786 1298 34
2 v 786 1337 a Fv(L)819 1308 y FC(\003)865 1337 y FH(+)19
b(i\()p Fv(\033)983 1344 y Ft(x)1004 1337 y FH(\))1051
1317 y Ft(B)1023 1350 y(C)1081 1337 y Fv(\017)1101 1317
y Ft(C)r(A)1157 1337 y FE(P)1196 1317 y Ft(x)1192 1350
y FC(\003)1218 1337 y Fv(g)1243 1317 y Ft(ij)1271 1305
y Fm(?)p 1291 1298 30 2 v 1291 1337 a Fv(f)1321 1308
y FC(\003)1321 1350 y Ft(j)1337 1340 y Fm(?)455 1425
y Fv(N)499 1404 y Ft(A)494 1437 y(\013)570 1425 y FH(=)41
b(2)8 b FE(U)717 1404 y Ft(A)712 1437 y(\013u)766 1425
y Fv(k)793 1404 y Ft(u)791 1437 y FC(\003)p 827 1386
34 2 v 827 1425 a Fv(L)860 1395 y FC(\003)422 1504 y
FE(M)482 1483 y Ft(\013\014)570 1504 y FH(=)41 b FE(\000)8
b(U)732 1483 y Ft(\013A)727 1516 y(u)792 1504 y FE(U)828
1483 y Ft(\014)r(B)823 1516 y(v)888 1504 y Fv(")911 1511
y Ft(AB)976 1504 y FE(r)1018 1483 y FC([)p Ft(u)1050
1504 y Fv(k)1077 1478 y Ft(v)q FC(])1075 1516 y(\003)1115
1504 y Fv(L)1148 1483 y FC(\003)403 1577 y FE(M)463 1556
y Ft(\013)486 1589 y(iB)570 1577 y FH(=)41 b FE(\000)p
FH(4)8 b FE(U)756 1556 y Ft(\013)751 1589 y(B)r(u)811
1577 y Fv(k)838 1556 y Ft(u)836 1589 y FC(\003)871 1577
y Fv(f)900 1556 y FC(\003)895 1589 y Ft(i)375 1671 y
FE(M)435 1679 y Ft(iA)p FB(j)p Ft(`B)570 1671 y FH(=)662
1638 y(1)p 662 1660 25 2 v 662 1705 a(3)700 1623 y Fs(\020)725
1671 y Fv(")748 1678 y Ft(AB)813 1671 y Fv(g)836 1678
y Ft(ij)864 1669 y Fm(?)884 1671 y Fv(k)911 1648 y Ft(j)927
1636 y Fm(?)909 1683 y FC(\003)948 1671 y Fv(f)977 1651
y FC(\003)972 1684 y Ft(`)1015 1671 y FH(+)j(i\()o Fv(\033)1124
1678 y Ft(x)1146 1671 y Fv(\017)1166 1651 y FB(\000)p
FC(1)1213 1671 y FH(\))1232 1686 y Ft(AB)1297 1671 y
FE(P)1336 1651 y Ft(x)1332 1684 y FC(\003)1366 1671 y
FE(r)1408 1678 y Ft(`)1424 1671 y Fv(f)1453 1651 y FC(\003)1448
1684 y Ft(i)1480 1623 y Fs(\021)1760 1671 y FH(\(8.23\))-5
1776 y(The)21 b(coupling)g(constan)o(t)g Fv(g)j FH(in)c
FE(L)643 1758 y FB(0)643 1788 y Ft(g)684 1776 y FH(is)h(just)g(a)h(sym)
o(b)q(olic)d(notation)i(to)h(remind)d(that)i(these)g(terms)-5
1836 y(are)16 b(en)o(tirely)d(due)j(to)g(the)f(gauging)i(and)g(v)m
(anish)f(in)f(the)g(ungauged)i(theory)l(,)e(where)h(also)g(all)f
(gauged)-5 1896 y(co)o(v)m(arian)o(t)j(deriv)m(ativ)o(es)f(reduce)g(to)
i(ordinary)f(ones.)27 b(Note)18 b(that)g(in)g(general)g(there)g(is)f
(not)i(a)g(single)-5 1956 y(coupling)g(constan)o(t,)h(but)f(rather)h
(there)e(are)h(as)h(man)o(y)e(indep)q(enden)o(t)g(coupling)h(constan)o
(ts)h(as)f(the)-5 2017 y(n)o(um)o(b)q(er)i(of)h(factors)h(in)f(the)g
(gauge)h(group.)40 b(The)22 b(normalization)f(of)i(the)f(kinetic)e
(term)h(for)h(the)-5 2077 y(quaternions)15 b(dep)q(ends)h(on)f(the)g
(scale)f Fv(\025)i FH(of)f(the)g(quaternionic)f(manifold,)f(app)q
(earing)j(in)f(eq.)20 b(\(5.10)p
 (#equation.5.10) [[496 269 516 281] [1 1 1 [3 3]] [0 0 1]] pdfm (\),)
-5 2137 y(for)d(whic)o(h)e(w)o(e)h(ha)o(v)o(e)g(c)o(hosen)g(the)g(v)m
(alue)g Fv(\025)e FH(=)g FE(\000)p FH(1.)68 2197 y(F)l(urthermore,)g
(using)j(the)f(geometric)d(approac)o(h,)k(the)f(form)f(of)h(the)g(sup)q
(ersymmetry)d(transfor-)-5 2257 y(mation)f(la)o(ws)h(is)f(also)h
(easily)f(deduced)g(from)g(the)g(solution)h(of)g(the)f(Bianc)o(hi)g
(iden)o(tities)e(in)j(sup)q(erspace)-5 2318 y(\(see)j(App)q(endix)g
(A\).)f(One)h(gets)p 357 2420 1167 2 v 382 2523 a Fu(Sup)n(er)n(gr)n
(avity)g(tr)n(ansformation)h(rules)h(of)f(the)h(F)l(ermi)f(\014elds)p
357 2603 V 113 2750 a Fv(\016)10 b( )177 2757 y Ft(A\026)268
2750 y FH(=)42 b FE(D)386 2757 y Ft(\026)418 2750 y Fv(\017)438
2757 y Ft(A)485 2750 y FE(\000)540 2716 y FH(1)p 540
2738 25 2 v 540 2784 a(4)578 2702 y Fs(\020)602 2750
y Fv(@)628 2757 y Ft(i)651 2750 y Fv(K)p 696 2711 29
2 v 4 w(\025)724 2720 y Ft(iB)766 2750 y Fv(\017)786
2757 y Ft(B)836 2750 y FE(\000)19 b Fv(@)920 2757 y Ft(i)932
2748 y Fm(?)960 2750 y Fv(K)p 1005 2711 V 4 w(\025)1034
2720 y Ft(i)1046 2709 y Fm(?)1034 2762 y Ft(B)1066 2750
y Fv(\017)1086 2730 y Ft(B)1116 2702 y Fs(\021)1149 2750
y Fv( )1181 2757 y Ft(A\026)916 2892 y FH(40)p eop
%%Page: 41 42
41 41 bop 348 15 a FE(\000)p Fv(!)445 -5 y Ft(B)417 28
y(Av)484 15 y FE(U)520 -5 y Ft(v)515 28 y(C)r(\013)584
-33 y Fs(\020)608 15 y Fv(\017)628 -5 y Ft(C)r(D)p 704
15 2 33 v 691 15 a FH(C)726 -5 y Ft(\013\014)p 781 -24
26 2 v 781 15 a Fv(\020)806 27 y Ft(\014)838 15 y Fv(\017)858
22 y Ft(D)909 15 y FH(+)p 975 -24 V 28 w Fv(\020)1000
-14 y Ft(\013)1033 15 y Fv(\017)1053 -5 y Ft(C)1082 -33
y Fs(\021)1115 15 y Fv( )1147 22 y Ft(B)r(\026)348 107
y FH(+)402 59 y Fs(\020)427 107 y Fv(A)490 86 y Ft(\027)r(B)464
119 y(A)540 107 y Fv(\021)564 114 y Ft(\026\027)618 107
y FH(+)11 b Fv(A)704 86 y FB(0)25 b Ft(\027)r(B)704 119
y(A)789 107 y Fv(\015)814 114 y Ft(\026\027)857 59 y
Fs(\021)890 107 y Fv(\017)910 114 y Ft(B)348 198 y FH(+)394
150 y Fs(h)413 198 y FH(i)8 b Fv(g)j(S)499 205 y Ft(AB)555
198 y Fv(\021)579 205 y Ft(\026\027)633 198 y FH(+)g
Fv(\017)702 205 y Ft(AB)759 198 y FH(\()p Fv(T)814 178
y FB(\000)807 210 y Ft(\026\027)869 198 y FH(+)19 b Fv(U)964
178 y FC(+)959 210 y Ft(\026\027)1002 198 y FH(\))1021
150 y Fs(i)1049 198 y Fv(\015)1077 178 y Ft(\027)1098
198 y Fv(\017)1118 178 y Ft(B)1760 198 y FH(\(8.24\))126
305 y Fv(\016)10 b(\025)186 285 y Ft(iA)268 305 y FH(=)353
272 y(1)p 353 294 25 2 v 353 340 a(4)390 257 y Fs(\020)415
305 y Fv(@)441 312 y Ft(j)467 305 y Fv(K)p 512 266 29
2 v 4 w(\025)541 276 y Ft(j)r(B)587 305 y Fv(\017)607
312 y Ft(B)657 305 y FE(\000)19 b Fv(@)741 312 y Ft(j)757
303 y Fm(?)785 305 y Fv(K)p 830 266 V 4 w(\025)859 276
y Ft(j)875 264 y Fm(?)859 318 y Ft(B)895 305 y Fv(\017)915
285 y Ft(B)945 257 y Fs(\021)978 305 y Fv(\025)1006 285
y Ft(iA)348 406 y FE(\000)p Fv(!)419 385 y Ft(A)443 418
y(B)r(v)500 406 y FE(U)536 385 y Ft(v)531 418 y(C)r(\013)600
358 y Fs(\020)625 406 y Fv(\017)645 385 y Ft(C)r(D)p
721 406 2 33 v 708 406 a FH(C)743 385 y Ft(\013\014)p
798 366 26 2 v 798 406 a Fv(\020)823 418 y Ft(\014)854
406 y Fv(\017)874 413 y Ft(D)926 406 y FH(+)p 991 366
V 27 w Fv(\020)1016 376 y Ft(\013)1049 406 y Fv(\017)1069
385 y Ft(C)1099 358 y Fs(\021)1132 406 y Fv(\025)1160
385 y Ft(iB)348 500 y FE(\000)8 b FH(\000)425 480 y Ft(i)437
513 y(j)r(k)p 475 461 29 2 v 475 500 a Fv(\025)503 471
y Ft(k)q(B)553 500 y Fv(\017)573 507 y Ft(B)611 500 y
Fv(\025)639 480 y Ft(j)r(A)695 500 y FH(+)j(i)774 452
y Fs(\020)799 500 y FE(r)841 507 y Ft(\026)872 500 y
Fv(z)897 480 y Ft(i)922 500 y FE(\000)p 972 461 V 11
w Fv(\025)1001 471 y Ft(iA)1041 500 y Fv( )1073 507 y
Ft(A\026)1123 452 y Fs(\021)1156 500 y Fv(\015)1184 480
y Ft(\026)1207 500 y Fv(\017)1227 480 y Ft(A)348 585
y FH(+)p Fv(G)424 565 y FB(\000)p Ft(i)424 597 y(\026\027)467
585 y Fv(\015)495 565 y Ft(\026\027)538 585 y Fv(\017)558
592 y Ft(B)588 585 y Fv(\017)608 565 y Ft(AB)683 585
y FH(+)20 b Fv(D)782 565 y Ft(iAB)851 585 y Fv(\017)871
592 y Ft(B)1760 585 y FH(\(8.25\))149 670 y Fv(\016)10
b(\020)202 677 y Ft(\013)268 670 y FH(=)42 b FE(\000)p
FH(\001)450 650 y Ft(\014)428 683 y(\013v)482 670 y FE(U)518
650 y Ft(v)513 683 y(\015)r(A)578 622 y Fs(\020)603 670
y Fv(\017)623 650 y Ft(AB)p 696 670 2 33 v 683 670 a
FH(C)718 649 y Ft(\015)r(\016)p 765 631 26 2 v 765 670
a Fv(\020)790 682 y Ft(\016)818 670 y Fv(\017)838 677
y Ft(B)887 670 y FH(+)p 953 631 V 28 w Fv(\020)978 641
y Ft(\015)1008 670 y Fv(\017)1028 650 y Ft(A)1056 622
y Fs(\021)1090 670 y Fv(\020)1111 677 y Ft(\014)348 778
y FH(+)391 744 y(1)p 391 766 25 2 v 391 812 a(4)428 729
y Fs(\020)453 778 y Fv(@)479 785 y Ft(i)501 778 y Fv(K)p
546 738 29 2 v 4 w(\025)575 748 y Ft(iB)617 778 y Fv(\017)637
785 y Ft(B)686 778 y FE(\000)19 b Fv(@)770 785 y Ft(i)782
776 y Fm(?)811 778 y Fv(K)p 856 738 V 4 w(\025)884 748
y Ft(i)896 736 y Fm(?)884 790 y Ft(B)916 778 y Fv(\017)936
757 y Ft(B)966 729 y Fs(\021)999 778 y Fv(\020)1020 785
y Ft(\013)348 881 y FH(+)8 b(i)424 833 y Fs(\020)449
881 y FE(U)485 861 y Ft(B)r(\014)480 894 y(u)545 881
y FE(r)587 888 y Ft(\026)618 881 y Fv(q)642 861 y Ft(u)683
881 y FE(\000)j Fv(\017)753 861 y Ft(B)r(C)p 827 881
2 33 v 814 881 a FH(C)850 860 y Ft(\014)r(\015)p 902
842 26 2 v 902 881 a Fv(\020)927 893 y Ft(\015)957 881
y Fv( )989 888 y Ft(C)1038 881 y FE(\000)p 1104 842 V
27 w Fv(\020)1129 851 y Ft(\014)1161 881 y Fv( )1195
861 y Ft(B)1225 833 y Fs(\021)1266 881 y Fv(\015)1294
861 y Ft(\026)1318 881 y Fv(\017)1338 861 y Ft(A)1366
881 y Fv(\017)1386 888 y Ft(AB)p 1459 881 2 33 v 1446
881 a FH(C)1481 888 y Ft(\013\014)1547 881 y FH(+)19
b Fv(g)11 b(N)1682 861 y Ft(A)1677 894 y(\013)1719 881
y Fv(\017)1739 888 y Ft(A)1760 881 y FH(\(8.26\))p 369
1011 1143 2 v 394 1114 a Fu(Sup)n(er)n(gr)n(avity)17
b(tr)n(ansformation)f(rules)i(of)f(the)h(Bose)g(\014elds)p
369 1194 V 439 1346 a Fv(\016)10 b(V)510 1325 y Ft(a)499
1358 y(\026)573 1346 y FH(=)41 b FE(\000)p FH(i)p 713
1306 34 2 v 8 w Fv( )746 1358 y Ft(A\026)804 1346 y Fv(\015)832
1325 y Ft(a)861 1346 y Fv(\017)881 1325 y Ft(A)921 1346
y FE(\000)10 b FH(i)p 992 1306 V 8 w Fv( )1026 1316 y
Ft(A)1026 1358 y(\026)1063 1346 y Fv(\015)1091 1325 y
Ft(a)1120 1346 y Fv(\017)1140 1353 y Ft(A)1760 1346 y
FH(\(8.27\))436 1434 y Fv(\016)g(A)505 1413 y FC(\003)505
1446 y Ft(\026)573 1434 y FH(=)41 b(2)p 676 1395 V Fv(L)710
1404 y FC(\003)p 736 1394 V 736 1434 a Fv( )770 1445
y Ft(A\026)819 1434 y Fv(\017)839 1441 y Ft(B)870 1434
y Fv(\017)890 1413 y Ft(AB)965 1434 y FH(+)20 b(2)p Fv(L)1080
1413 y FC(\003)p 1107 1394 V 1107 1434 a Fv( )1140 1404
y Ft(A)1140 1446 y(\026)1169 1434 y Fv(\017)1189 1413
y Ft(B)1219 1434 y Fv(\017)1239 1441 y Ft(AB)573 1522
y FH(+)652 1474 y Fs(\020)677 1522 y FH(i)8 b Fv(f)728
1501 y FC(\003)723 1534 y Ft(i)p 763 1482 29 2 v 763
1522 a Fv(\025)791 1492 y Ft(iA)832 1522 y Fv(\015)857
1529 y Ft(\026)881 1522 y Fv(\017)901 1501 y Ft(B)939
1522 y Fv(\017)959 1529 y Ft(AB)1026 1522 y FH(+)j(i)p
1097 1482 30 2 v 8 w Fv(f)1127 1492 y FC(\003)1127 1534
y Ft(i)1139 1525 y Fm(?)p 1167 1482 29 2 v 1167 1522
a Fv(\025)1195 1492 y Ft(i)1207 1481 y Fm(?)1195 1534
y Ft(A)1228 1522 y Fv(\015)1253 1529 y Ft(\026)1276 1522
y Fv(\017)1296 1529 y Ft(B)1334 1522 y Fv(\017)1354 1501
y Ft(AB)1411 1474 y Fs(\021)1760 1522 y FH(\(8.28\))460
1616 y Fv(\016)f(z)517 1595 y Ft(i)573 1616 y FH(=)p
652 1576 V 41 w Fv(\025)681 1586 y Ft(iA)721 1616 y Fv(\017)741
1623 y Ft(A)1760 1616 y FH(\(8.29\))442 1698 y Fv(\016)g(z)499
1678 y Ft(i)511 1666 y Fm(?)573 1698 y FH(=)p 652 1659
V 41 w Fv(\025)681 1668 y Ft(i)693 1657 y Fm(?)681 1710
y Ft(A)713 1698 y Fv(\017)733 1678 y Ft(A)1760 1698 y
FH(\(8.30\))454 1777 y Fv(\016)f(q)509 1756 y Ft(u)573
1777 y FH(=)41 b FE(U)688 1756 y Ft(u)683 1789 y(\013A)743
1729 y Fs(\020)p 768 1737 26 2 v 48 x Fv(\020)793 1747
y Ft(\013)817 1777 y Fv(\017)837 1756 y Ft(A)877 1777
y FH(+)p 934 1777 2 33 v 6 w(C)956 1756 y Ft(\013\014)1002
1777 y Fv(\017)1022 1756 y Ft(AB)p 1079 1737 26 2 v 1079
1777 a Fv(\020)1104 1789 y Ft(\014)1128 1777 y Fv(\017)1148
1784 y Ft(B)1178 1729 y Fs(\021)1760 1777 y FH(\(8.31\))-5
1876 y(where)16 b(w)o(e)g(ha)o(v)o(e:)p 480 1975 920
2 v 505 2077 a Fu(Sup)n(er)n(gr)n(avity)h(values)h(of)g(the)g
(auxiliary)f(\014elds)p 480 2157 V 287 2324 a Fv(A)350
2300 y Ft(\026B)324 2336 y(A)443 2324 y FH(=)42 b FE(\000)572
2290 y FH(i)p 567 2312 25 2 v 567 2358 a(4)604 2324 y
Fv(g)627 2331 y Ft(k)646 2322 y Fm(?)665 2331 y Ft(`)698
2275 y Fs(\020)p 723 2284 29 2 v 49 x Fv(\025)751 2294
y Ft(k)770 2282 y Fm(?)751 2336 y Ft(A)790 2324 y Fv(\015)818
2303 y Ft(\026)842 2324 y Fv(\025)870 2303 y Ft(`B)934
2324 y FE(\000)19 b Fv(\016)1016 2303 y Ft(B)1014 2336
y(A)p 1054 2284 V 1054 2324 a Fv(\025)1083 2294 y Ft(k)1102
2282 y Fm(?)1083 2336 y Ft(C)1122 2324 y Fv(\015)1150
2303 y Ft(\026)1173 2324 y Fv(\025)1201 2303 y Ft(`C)1246
2275 y Fs(\021)1760 2324 y FH(\(8.32\))278 2441 y Fv(A)315
2418 y FB(0)25 b Ft(\026B)315 2453 y(A)443 2441 y FH(=)533
2407 y(i)p 528 2430 25 2 v 528 2475 a(4)565 2441 y Fv(g)588
2448 y Ft(k)607 2439 y Fm(?)626 2448 y Ft(`)659 2381
y Fs(\022)p 690 2402 29 2 v 60 x Fv(\025)718 2411 y Ft(k)737
2400 y Fm(?)718 2453 y Ft(A)757 2441 y Fv(\015)785 2421
y Ft(\026)809 2441 y Fv(\025)837 2421 y Ft(`B)893 2441
y FE(\000)948 2407 y FH(1)p 948 2430 25 2 v 948 2475
a(2)985 2441 y Fv(\016)1009 2421 y Ft(B)1007 2453 y(A)p
1047 2402 29 2 v 1047 2441 a Fv(\025)1076 2411 y Ft(k)1095
2400 y Fm(?)1076 2453 y Ft(C)1115 2441 y Fv(\015)1143
2421 y Ft(\026)1167 2441 y Fv(\025)1195 2421 y Ft(C)r(`)1239
2381 y Fs(\023)1289 2441 y FE(\000)1357 2407 y FH(i)p
1352 2430 25 2 v 1352 2475 a(4)1390 2441 y Fv(\016)1414
2421 y Ft(B)1412 2453 y(A)p 1452 2402 26 2 v 1452 2441
a Fv(\020)1477 2453 y Ft(\013)1502 2441 y Fv(\015)1530
2421 y Ft(\026)1553 2441 y Fv(\020)1578 2421 y Ft(\013)1760
2441 y FH(\(8.33\))115 2627 y Fv(T)151 2607 y FB(\000)144
2639 y Ft(\026\027)228 2627 y FH(=)41 b(2i)8 b(\()q(Im)14
b FE(N)7 b FH(\))514 2642 y FC(\003\006)575 2627 y Fv(L)608
2607 y FC(\006)644 2567 y Fs(\022)686 2611 y(e)674 2627
y Fv(F)713 2607 y FC(\003)p FB(\000)706 2639 y Ft(\026\027)778
2627 y FH(+)832 2593 y(1)p 832 2616 25 2 v 832 2661 a(8)861
2627 y FE(r)903 2634 y Ft(i)925 2627 y Fv(f)954 2607
y FC(\003)949 2639 y Ft(j)p 989 2588 29 2 v 989 2627
a Fv(\025)1018 2597 y Ft(iA)1058 2627 y Fv(\015)1083
2634 y Ft(\026\027)1134 2627 y Fv(\025)1162 2607 y Ft(j)r(B)1218
2627 y Fv(\017)1238 2634 y Ft(AB)1305 2627 y FE(\000)1360
2593 y FH(1)p 1360 2616 25 2 v 1360 2661 a(4)p 1406 2627
2 33 v 1393 2627 a(C)1428 2606 y Ft(\013\014)p 1483 2588
26 2 v 1483 2627 a Fv(\020)1508 2639 y Ft(\013)1533 2627
y Fv(\015)1558 2634 y Ft(\026\027)1609 2627 y Fv(\020)1630
2634 y Ft(\014)1662 2627 y Fv(L)1695 2607 y FC(\003)1722
2567 y Fs(\023)1760 2627 y FH(\(8.34\))115 2747 y Fv(T)151
2726 y FC(+)144 2759 y Ft(\026\027)228 2747 y FH(=)41
b(2i)8 b(\()q(Im)14 b FE(N)7 b FH(\))514 2761 y FC(\003\006)p
575 2708 34 2 v 575 2747 a Fv(L)608 2718 y FC(\006)644
2686 y Fs(\022)686 2731 y(e)674 2747 y Fv(F)713 2726
y FC(\003+)706 2759 y Ft(\026\027)778 2747 y FH(+)832
2713 y(1)p 832 2735 25 2 v 832 2781 a(8)861 2747 y FE(r)903
2754 y Ft(i)915 2745 y Fm(?)p 943 2707 30 2 v 943 2747
a Fv(f)972 2717 y FC(\003)972 2759 y Ft(j)988 2750 y
Fm(?)p 1017 2707 29 2 v 1017 2747 a Fv(\025)1045 2717
y Ft(i)1057 2705 y Fm(?)1045 2759 y Ft(A)1077 2747 y
Fv(\015)1102 2754 y Ft(\026\027)1154 2747 y Fv(\025)1182
2723 y Ft(j)1198 2712 y Fm(?)1182 2759 y Ft(B)1218 2747
y Fv(\017)1238 2726 y Ft(AB)1306 2747 y FE(\000)1361
2713 y FH(1)p 1361 2735 25 2 v 1361 2781 a(4)p 1407 2747
2 33 v 1394 2747 a(C)1429 2754 y Ft(\013\014)p 1484 2707
26 2 v 1484 2747 a Fv(\020)1509 2717 y Ft(\013)1533 2747
y Fv(\015)1558 2754 y Ft(\026\027)1610 2747 y Fv(\020)1635
2726 y Ft(\014)p 1667 2708 34 2 v 1667 2747 a Fv(L)1700
2718 y FC(\003)1726 2686 y Fs(\023)1760 2747 y FH(\(8.35\))916
2892 y(41)p eop
%%Page: 42 43
42 42 bop 671 32 a Fv(U)709 12 y FB(\000)704 45 y Ft(\026\027)788
32 y FH(=)42 b FE(\000)917 -1 y FH(i)p 912 21 25 2 v
912 67 a(4)p 958 32 2 33 v 945 32 a(C)980 12 y Ft(\013\014)p
1034 -7 26 2 v 1034 32 a Fv(\020)1059 44 y Ft(\013)1084
32 y Fv(\015)1109 39 y Ft(\026\027)1161 32 y Fv(\020)1182
39 y Ft(\014)1760 32 y FH(\(8.36\))671 150 y Fv(U)709
129 y FC(+)704 162 y Ft(\026\027)788 150 y FH(=)g FE(\000)917
116 y FH(i)p 912 138 25 2 v 912 184 a(4)p 958 150 2 33
v 945 150 a(C)980 157 y Ft(\013\014)p 1034 110 26 2 v
1034 150 a Fv(\020)1059 120 y Ft(\013)1084 150 y Fv(\015)1109
157 y Ft(\026\027)1161 150 y Fv(\020)1186 129 y Ft(\014)1760
150 y FH(\(8.37\))329 354 y Fv(G)367 333 y Ft(i)p FB(\000)367
366 y Ft(\026\027)452 354 y FH(=)g FE(\000)p Fv(g)596
333 y Ft(ij)624 321 y Fm(?)p 644 314 30 2 v 644 354 a
Fv(f)673 324 y FC(\000)673 366 y Ft(j)689 357 y Fm(?)718
354 y FH(\(Im)14 b FE(N)7 b FH(\))878 368 y FC(\000\003)935
306 y Fs(\020)972 338 y(e)960 354 y Fv(F)999 333 y FC(\003)p
FB(\000)992 366 y Ft(\026\027)1063 354 y FH(+)1117 320
y(1)p 1117 342 25 2 v 1117 388 a(8)1147 354 y FE(r)1189
361 y Ft(k)1210 354 y Fv(f)1239 333 y FC(\003)1234 366
y Ft(`)p 1265 314 29 2 v 1265 354 a Fv(\025)1294 324
y Ft(k)q(A)1342 354 y Fv(\015)1367 361 y Ft(\026\027)1418
354 y Fv(\025)1446 333 y Ft(`B)1491 354 y Fv(\017)1511
361 y Ft(AB)727 470 y FE(\000)771 437 y FH(1)p 771 459
25 2 v 771 504 a(4)p 816 470 2 33 v 803 470 a(C)839 449
y Ft(\013\014)p 893 431 26 2 v 893 470 a Fv(\020)918
482 y Ft(\013)943 470 y Fv(\015)968 477 y Ft(\026\027)1019
470 y Fv(\020)1040 477 y Ft(\014)1073 470 y Fv(L)1106
450 y FC(\003)1132 422 y Fs(\021)1760 470 y FH(\(8.38\))313
587 y Fv(G)351 566 y Ft(i)363 555 y Fm(?)381 566 y FC(+)351
599 y Ft(\026\027)452 587 y FH(=)42 b FE(\000)p Fv(g)596
566 y Ft(i)608 555 y Fm(?)625 566 y Ft(j)644 587 y Fv(f)673
566 y FC(\000)668 599 y Ft(j)705 587 y FH(\(Im)15 b FE(N)7
b FH(\))866 601 y FC(\000\003)923 539 y Fs(\020)960 571
y(e)948 587 y Fv(F)987 566 y FC(\003+)980 599 y Ft(\026\027)1051
587 y FH(+)1105 553 y(1)p 1105 575 25 2 v 1105 621 a(8)1135
587 y FE(r)1177 594 y Ft(k)1196 585 y Fm(?)p 1215 547
30 2 v 1215 587 a Fv(f)1245 557 y FC(\003)1245 599 y
Ft(`)1259 590 y Fm(?)p 1279 547 29 2 v 1279 587 a Fv(\025)1308
557 y Ft(k)1327 545 y Fm(?)1308 599 y Ft(A)1347 587 y
Fv(\015)1372 594 y Ft(\026\027)1423 587 y Fv(\025)1451
566 y Ft(`)1465 555 y Fm(?)1451 599 y Ft(B)1486 587 y
Fv(\017)1506 566 y Ft(AB)727 703 y FE(\000)771 670 y
FH(1)p 771 692 25 2 v 771 738 a(4)p 816 703 2 33 v 803
703 a(C)839 710 y Ft(\013\014)p 893 664 26 2 v 893 703
a Fv(\020)918 674 y Ft(\013)943 703 y Fv(\015)968 710
y Ft(\026\027)1019 703 y Fv(\020)1044 683 y Ft(\014)p
1076 664 34 2 v 1076 703 a Fv(L)1110 674 y FC(\003)1136
655 y Fs(\021)1760 703 y FH(\(8.39\))458 908 y Fv(D)499
888 y Ft(iAB)610 908 y FH(=)700 874 y(i)p 694 897 25
2 v 694 942 a(2)724 908 y Fv(g)749 888 y Ft(ij)777 876
y Fm(?)797 908 y Fv(C)832 915 y Ft(j)848 906 y Fm(?)866
915 y Ft(k)885 906 y Fm(?)903 915 y Ft(`)917 906 y Fm(?)p
938 869 29 2 v 938 908 a Fv(\025)966 878 y Ft(k)985 867
y Fm(?)966 920 y Ft(C)1006 908 y Fv(\025)1034 888 y Ft(`)1048
876 y Fm(?)1034 920 y Ft(D)1069 908 y Fv(\017)1089 888
y Ft(AC)1144 908 y Fv(\017)1164 888 y Ft(B)r(D)1244 908
y FH(+)19 b Fv(W)1354 888 y Ft(iAB)1760 908 y FH(\(8.40\))-5
1042 y(In)j(eqs.)40 b(\(8.34)p
 (#equation.8.34) [[120 517 141 529] [1 1 1 [3 3]] [0 0 1]] pdfm (\),)
24 b(\(8.35)p
 (#equation.8.34) [[159 517 180 529] [1 1 1 [3 3]] [0 0 1]] pdfm (\),)g
(\(8.38)p
 (#equation.8.38) [[198 517 219 529] [1 1 1 [3 3]] [0 0 1]] pdfm (\),)g
(\(8.39)p
 (#equation.8.38) [[237 517 258 529] [1 1 1 [3 3]] [0 0 1]] pdfm (\))f
(w)o(e)f(ha)o(v)o(e)g(denoted)g(b)o(y)1289 1026 y Fs(e)1277
1042 y Fv(F)1309 1049 y Ft(\026\027)1374 1042 y FH(the)g(sup)q(erco)o
(v)m(arian)o(t)h(\014eld)-5 1103 y(strength)17 b(de\014ned)f(b)o(y:)26
1203 y Fs(e)15 1219 y Fv(F)54 1199 y FC(\003)47 1232
y Ft(\026\027)103 1219 y FH(=)e FE(F)196 1199 y FC(\003)191
1232 y Ft(\026\027)253 1219 y FH(+)19 b Fv(L)343 1199
y FC(\003)p 370 1180 34 2 v 370 1219 a Fv( )403 1190
y Ft(A)403 1232 y(\026)432 1219 y Fv( )466 1199 y Ft(B)464
1232 y(\027)504 1219 y Fv(\017)524 1226 y Ft(AB)600 1219
y FH(+)p 649 1180 V 11 w Fv(L)682 1190 y FC(\003)p 708
1180 V 708 1219 a Fv( )742 1231 y Ft(A\026)792 1219 y
Fv( )824 1226 y Ft(B)r(\027)873 1219 y Fv(\017)893 1199
y Ft(AB)969 1219 y FE(\000)11 b FH(i)d Fv(f)1070 1199
y FC(\003)1065 1232 y Ft(i)p 1105 1180 29 2 v 1105 1219
a Fv(\025)1133 1190 y Ft(iA)1174 1219 y Fv(\015)1199
1227 y FC([)p Ft(\027)1230 1219 y Fv( )1264 1199 y Ft(B)1262
1232 y(\026)p FC(])1304 1219 y Fv(\017)1324 1226 y Ft(AB)1399
1219 y FE(\000)j FH(i)p 1471 1180 30 2 v 8 w Fv(f)1500
1190 y FC(\003)1500 1232 y Ft(i)1512 1222 y Fm(?)p 1541
1180 29 2 v 1541 1219 a Fv(\025)1569 1190 y Ft(i)1581
1178 y Fm(?)1569 1232 y Ft(A)1601 1219 y Fv(\015)1626
1227 y FC([)p Ft(\027)1658 1219 y Fv( )1690 1227 y Ft(B)r(\026)p
FC(])1759 1219 y Fv(\017)1779 1199 y Ft(AB)1852 1219
y Fv(:)1760 1280 y FH(\(8.41\))68 1340 y(Let)k(us)f(mak)o(e)f(some)g
(observ)m(ation)i(ab)q(out)g(the)f(structure)g(of)h(the)f(Lagrangian)i
(and)f(of)f(the)g(trans-)-5 1400 y(formation)i(la)o(ws.)68
1460 y(i\))22 b(W)l(e)g(note)g(that)h(all)e(the)h(terms)f(of)h(the)g
(Lagrangian)i(are)e(giv)o(en)f(in)h(terms)f(of)h(purely)f(geo-)-5
1520 y(metric)c(ob)s(jects)j(p)q(ertaining)f(to)h(the)g(Sp)q(ecial)f
(and)h(quaternionic)f(geometries.)29 b(F)l(urthermore)18
b(the)-5 1580 y(Lagrangian)g(do)q(es)f(not)f(rely)f(on)i(the)e
(existence)g(of)h(a)g(prep)q(oten)o(tial)g(function)f
Fv(F)21 b FH(=)13 b Fv(F)i FH(\()p Fv(X)t FH(\))h(and)h(it)e(is)-5
1641 y(v)m(alid)h(for)h(an)o(y)f(c)o(hoice)f(of)h(the)g(quaternionic)g
(manifold.)68 1701 y(ii\))10 b(The)h(Lagrangian)j(is)c(not)i(in)o(v)m
(arian)o(t)e(under)h(symplectic)d(dualit)o(y)i(transformations.)19
b(Ho)o(w)o(ev)o(er,)-5 1761 y(in)f(absence)g(of)g(gauging)h(\()p
Fv(g)f FH(=)f(0\),)h(if)f(w)o(e)h(restrict)f(the)g(Lagrangian)j(to)f
(con\014gurations)g(where)e(the)-5 1821 y(v)o(ectors)d(are)h(on)g
(shell,)f(it)g(b)q(ecomes)g(symplectic)e(in)o(v)m(arian)o(t)i(\(ref)s
(\).)20 b(This)15 b(allo)o(ws)g(us)g(to)g(\014x)g(the)g(terms)-5
1881 y(app)q(earing)j(in)d FE(L)312 1863 y Ft(non)8 b(inv)312
1894 y FC(4)e Ft(f)t(er)q(m)449 1881 y FH(in)16 b(a)g(w)o(a)o(y)g
(indep)q(enden)o(t)g(from)f(sup)q(ersymmetry)e(argumen)o(ts.)68
1942 y(Here)i(w)o(e)g(rep)q(ort)g(only)h(the)f(results)g(of)g(the)h
(application)f(of)g(the)g(metho)q(d)g(of)h([4)p
 (#cite.CDFVP) [[436 301 442 313] [1 1 1 [3 3]] [0 0 1]] pdfm (],[67)p
 (#cite.ferscherzum) [[452 301 463 313] [1 1 1 [3 3]] [0 0 1]] pdfm 
-1 w(]in)f(our)h(case.)-5 2002 y(F)l(or)h(a)f(complete)e(treatmen)o(t)h
(see)g([4)p
 (#cite.CDFVP) [[228 287 233 299] [1 1 1 [3 3]] [0 0 1]] pdfm (],[67)p
 (#cite.ferscherzum) [[243 287 255 299] [1 1 1 [3 3]] [0 0 1]] pdfm 
(].)20 b(The)d(non-in)o(v)m(arian)o(t)f(part)h(of)f(the)g(Lagrangian)j
(is:)576 2112 y FE(L)k FH(=)f FE(L)727 2091 y Ft(v)q(ector)q(s)727
2124 y(K)r(in)862 2112 y FH(+)d FE(L)953 2091 y Ft(non)7
b(inv)953 2124 y(P)e(auli)1093 2112 y FH(+)19 b FE(L)1184
2091 y Ft(non)7 b(inv)1184 2124 y FC(4)p Ft(f)1760 2112
y FH(\(8.42\))-5 2234 y(where:)24 b FE(L)192 2216 y Ft(v)q(ector)q(s)
192 2247 y(K)r(in)331 2234 y FH(=)g(i)415 2186 y Fs(\020)p
440 2195 49 2 v 48 x FE(N)488 2241 y FC(\003\006)540
2234 y FE(F)581 2216 y FB(\000)p FC(\003)635 2234 y FE(F)676
2216 y FB(\000)p FC(\006)750 2234 y FE(\000)19 b Fv(h:c:)885
2186 y Fs(\021)909 2234 y FH(.)25 b(The)18 b(part)f FE(L)1190
2216 y Ft(non)8 b(inv)1190 2247 y FC(4)p Ft(f)1328 2234
y FH(of)18 b(the)f(4{fermi)f(Lagrangian)-5 2295 y(is)f(\014xed)g(b)o(y)
g(the)g(requiremen)o(t)d(of)k(on-shell)f(v)o(ector)g(in)o(v)m
(ariance.Indeed,)e(imp)q(osing)h(the)h(equation)h(of)-5
2355 y(m)e(motion)h(for)g(the)g(gauge)h(\014elds,with)f(straigh)o
(tforw)o(ard)h(calculations)f(one)g(\014nds)h(that)p
FE(L)1676 2337 y Ft(non)8 b(inv)1812 2355 y FH(can)-5
2415 y(b)q(e)17 b(written)e(as)i(follo)o(ws:)500 2535
y FE(L)534 2514 y Ft(non)7 b(inv)534 2547 y(on)g(shell)678
2535 y FH(=)743 2501 y(1)p 743 2523 25 2 v 743 2569 a(2)780
2487 y Fs(\020)805 2535 y FE(F)846 2514 y FB(\000)p FC(\003)900
2535 y FE(H)942 2514 y FB(\000)942 2547 y FC(\003)991
2535 y FH(+)20 b Fv(h:c:)1126 2487 y Fs(\021)1169 2535
y FH(+)f FE(L)1260 2514 y Ft(non)7 b(inv)1260 2547 y
FC(4)f Ft(f)t(er)q(m)1760 2535 y FH(\(8.43\))-5 2657
y(where:)665 2718 y FE(H)707 2697 y FB(\000)707 2732
y FC(\003)p FB(j)p Ft(\026\027)806 2718 y FH(=)866 2669
y Fs(\020)891 2718 y FE(N)18 b(\000)p 1000 2679 49 2
v 11 w(N)1048 2669 y Fs(\021)1073 2745 y FC(\003\006)1134
2718 y Fv(\034)1161 2697 y FB(\000)p FC(\006)1155 2730
y Ft(\026\027)1760 2718 y FH(\(8.44\))916 2892 y(42)p
eop
%%Page: 43 44
43 43 bop -5 15 a FH(with:)309 139 y Fv(\034)336 118
y FB(\000)p FC(\006)330 151 y Ft(\026\027)432 139 y FH(=)512
90 y Fs(h)531 139 y FE(\000)p FH(2i)8 b Fv(L)649 118
y FC(\006)685 78 y Fs(\022)p 716 99 34 2 v 61 x Fv( )749
109 y Ft(A)p FB(j)p Ft(\026)809 139 y Fv( )843 118 y
Ft(B)r FB(j)p Ft(\027)902 78 y Fs(\023)933 90 y FB(\000)971
139 y Fv(\017)991 146 y Ft(AB)1066 139 y FE(\000)19 b
FH(2)p 1148 99 30 2 v Fv(f)1178 109 y FC(\006)1178 151
y Ft(i)1190 141 y Fm(?)1227 90 y Fs(\020)p 1252 99 29
2 v 49 x Fv(\025)1280 109 y Ft(i)1292 97 y Fm(?)1280
151 y Ft(A)1312 139 y Fv(\015)1340 118 y Ft(\027)1362
139 y Fv( )1396 115 y Ft(\026)1394 151 y(B)1424 90 y
Fs(\021)1449 99 y FB(\000)1495 139 y Fv(\017)1515 118
y Ft(AB)512 259 y FE(\000)569 226 y FH(i)p 564 248 25
2 v 564 294 a(4)593 259 y FE(r)635 266 y Ft(i)649 259
y Fv(f)678 239 y FC(\006)673 272 y Ft(j)p 714 220 29
2 v 714 259 a Fv(\025)742 230 y Ft(iA)783 259 y Fv(\015)811
239 y Ft(\026\027)854 259 y Fv(\025)882 239 y Ft(j)r(B)937
259 y Fv(\017)957 266 y Ft(AB)1033 259 y FH(+)1101 226
y(i)p 1095 248 25 2 v 1095 294 a(2)1125 259 y Fv(L)1158
239 y FC(\006)p 1185 220 26 2 v 1185 259 a Fv(\020)1210
271 y Ft(\013)1235 259 y Fv(\015)1263 239 y Ft(\026\027)1306
259 y Fv(\020)1327 266 y Ft(\014)1359 259 y Fv(C)1398
239 y Ft(\013\014)1444 211 y Fs(i)1760 259 y FH(\(8.45\))-5
385 y(F)l(rom)e(dualit)o(y)f(argumen)o(ts)h(it)g(then)g(follo)o(ws)h
(\([4)p  (#cite.CDFVP) [[285 675 291 687] [1 1 1 [3 3]] [0 0 1]] pdfm 
(],[67)p
 (#cite.ferscherzum) [[301 675 312 687] [1 1 1 [3 3]] [0 0 1]] pdfm 
-1 w(]\))f(that)h(the)g(non)g(in)o(v)m(arian)o(t)f(4)h(fermion)e(terms)
-5 445 y(can)h(b)q(e)f(written)g(as)h(the)f(follo)o(wing)g(p)q(erfect)f
(square:)139 575 y FE(L)173 555 y Ft(noninv)173 588 y
FC(4)p Ft(f)t(er)q(m)301 575 y FH(=)f(+)401 542 y(i)p
396 564 25 2 v 396 610 a(4)425 575 y FE(H)467 555 y FB(\000)467
590 y FC(\003)p FB(j)p Ft(\026\027)553 575 y Fv(\034)580
555 y FB(\000)p FC(\003)p FB(j)p Ft(\026\027)704 575
y FH(+)19 b Fv(h:c:)13 b FH(=)h(+)951 542 y(i)p 946 564
V 946 610 a(4)983 527 y Fs(\020)1008 575 y FE(N)k(\000)p
1117 536 49 2 v 11 w(N)1165 527 y Fs(\021)1190 602 y
FC(\003\006)1250 575 y Fv(\034)1277 555 y FB(\000)p FC(\003)1271
588 y Ft(\026\027)1331 575 y Fv(\034)1358 555 y FB(\000)p
FC(\006)p FB(j)p Ft(\026\027)1483 575 y FH(+)h Fv(h:c:)143
b FH(\(8.46\))-5 698 y(This)24 b(result)f(w)o(as)h(in)f(fact)h(emplo)o
(y)o(ed)c(as)25 b(a)e(useful)h(consistency)e(c)o(hec)o(k)g(in)h(the)h
(calculations)f(to)-5 758 y(construct)17 b(the)f(Lagrangian.)68
819 y(iii\))g(W)l(e)g(note)h(that)f(the)h(\014eld)f(strengths)h
FE(F)887 800 y FC(\003)6 b FB(\000)882 831 y Ft(\026\027)963
819 y FH(originally)16 b(in)o(tro)q(duced)g(in)g(the)g(Lagrangian)j
(are)-5 879 y(the)i(free)f(gauge)i(\014eld)f(strengths.The)g(in)o
(teracting)f(\014eld)h(strengths)g(whic)o(h)g(are)g(sup)q(ersymmetry)-5
939 y(eigenstates)e(are)f(de\014ned)g(as)h(the)f(ob)s(jects)g(app)q
(earing)i(in)e(the)g(transformation)g(la)o(ws)h(of)g(the)f(gra)o(v-)-5
999 y(itinos)e(and)h(gauginos)g(\014elds,resp)q(ectiv)o(ely)l(,)o(name)
o(ly)c(the)i(b)q(osonic)i(part)f(of)h Fv(T)1429 981 y
FB(\000)1422 1011 y Ft(\026\027)1480 999 y FH(and)g Fv(G)1613
981 y FB(\000)7 b Ft(i)1613 1011 y(\026\027)1677 999
y FH(de\014ned)15 b(in)-5 1059 y(eq.s)32 b(8.34)p
 (#equation.8.34) [[98 513 119 525] [1 1 1 [3 3]] [0 0 1]] pdfm (,)17
b(8.38)p
 (#equation.8.38) [[126 513 147 525] [1 1 1 [3 3]] [0 0 1]] pdfm 
-5 1226 a Fw(9)81 b(Commen)n(ts)28 b(on)f(the)g(scalar)f(p)r(oten)n
(tial)-5 1335 y FH(A)12 b(general)g(W)l(ard)h(iden)o(tit)o(y[39)p
 (#cite.ward) [[196 447 208 459] [1 1 1 [3 3]] [0 0 1]] pdfm 
-2 w(])f(of)g Fv(N)5 b FH(-extended)12 b(sup)q(ergra)o(vit)o(y)g
(establishes)g(the)g(follo)o(wing)g(form)o(ulae)-5 1395
y(for)17 b(the)e(scalar)i(p)q(oten)o(tial)e Fv(V)d FH(\()p
Fv(\036)p FH(\))k(of)g(the)g(theory)g(\(in)f(appropriate)i
(normalizations)e(for)h(the)g(generic)-5 1456 y(fermionic)e(shifts)i
Fv(\016)r(\037)392 1438 y Ft(a)412 1456 y FH(\))330 1574
y Fv(Z)363 1581 y Ft(ab)399 1574 y Fv(\016)421 1581 y
Ft(A)449 1574 y Fv(\037)480 1553 y Ft(a)500 1574 y Fv(\016)524
1553 y Ft(B)p 554 1547 31 2 v 554 1574 a Fv(\037)585
1553 y Ft(b)613 1574 y FE(\000)11 b FH(3)p FE(M)747 1581
y Ft(AC)p 803 1535 60 2 v 803 1574 a FE(M)863 1545 y
Ft(C)r(B)934 1574 y FH(=)j Fv(\016)1010 1553 y Ft(A)1024
1586 y(B)1054 1574 y Fv(V)e FH(\()p Fv(\036)p FH(\))48
b Fv(A;)8 b(B)16 b FH(=)e(1)p Fv(;)8 b(:)g(:)g(:)g(;)g(N)214
b FH(\(9.47\))-5 1684 y(where)18 b Fv(\016)160 1691 y
Ft(A)189 1684 y Fv(\037)220 1666 y Ft(a)258 1684 y FH(is)h(the)f(extra)
g(con)o(tribution,)g(due)g(to)h(the)g(gauging,)g(to)g(the)f(spin)1517
1664 y FC(1)p 1517 1672 18 2 v 1517 1701 a(2)1558 1684
y FH(sup)q(ersymmetry)-5 1744 y(v)m(ariations)k(of)f(the)f(scalar)h(v)o
(ev's,)f Fv(Z)688 1751 y Ft(ab)745 1744 y FH(is)h(the)f(\(scalar)h(dep)
q(enden)o(t\))f(kinetic)f(term)g(normalization)-5 1804
y(and)j FE(M)155 1811 y Ft(AC)232 1804 y FH(is)f(the)g(\(scalar)g(dep)q
(enden)o(t\))g(gra)o(vitino)f(mass)h(matrix.)34 b(Since)20
b(in)h(the)g(case)g(at)g(hand)-5 1864 y(\()p Fv(N)e FH(=)14
b(2\))i(all)f(terms)f(in)h(question)g(are)g(expressed)g(in)g(terms)f
(of)h(Killing)f(v)o(ectors)h(and)h(prep)q(oten)o(tials,)-5
1925 y(con)o(tracted)c(with)h(the)f(symplectic)e(sections,)i(w)o(e)g
(will)g(b)q(e)h(able)f(to)h(deriv)o(e)e(a)i(completely)c(geometrical)-5
1985 y(form)o(ula)15 b(for)i Fv(V)11 b FH(\()p Fv(z)r(;)p
354 1958 25 2 v 8 w(z)q(;)d(q)r FH(\).)21 b(The)16 b(relev)m(an)o(t)f
(terms)g(in)h(the)g(fermionic)e(transformation)i(rules)g(are)695
2095 y Fv(\016)r( )751 2102 y Ft(A\026)841 2095 y FH(=)41
b Fv(ig)r(S)992 2102 y Ft(AB)1049 2095 y Fv(\015)1074
2102 y Ft(\026)1098 2095 y Fv(\017)1118 2074 y Ft(B)1164
2095 y Fv(;)707 2168 y(\016)r(\025)759 2147 y Ft(iA)841
2168 y FH(=)g Fv(g)r(W)998 2147 y Ft(iAB)1067 2168 y
Fv(\017)1087 2175 y Ft(B)1133 2168 y Fv(;)730 2240 y(\016)r(\020)775
2247 y Ft(\013)841 2240 y FH(=)g Fv(g)r(N)989 2220 y
Ft(A)984 2252 y(\013)1018 2240 y Fv(\017)1038 2247 y
Ft(A)1083 2240 y Fv(:)663 b FH(\(9.48\))-5 2350 y(In)16
b(our)h(normalization)e(the)h(previous)g(W)l(ard)h(iden)o(tit)o(y)d
(giv)o(es)312 2466 y Fv(V)25 b FH(=)14 b(\()p Fv(g)459
2473 y Ft(ij)487 2464 y Fm(?)508 2466 y Fv(k)535 2445
y Ft(i)533 2478 y FC(\003)560 2466 y Fv(k)587 2442 y
Ft(j)603 2430 y Fm(?)585 2478 y FC(\006)634 2466 y FH(+)d(4)p
Fv(h)735 2473 y Ft(uv)776 2466 y Fv(k)803 2445 y Ft(u)801
2478 y FC(\003)828 2466 y Fv(k)855 2445 y Ft(v)853 2478
y FC(\006)881 2466 y FH(\))p 900 2427 34 2 v Fv(L)933
2437 y FC(\003)960 2466 y Fv(L)993 2445 y FC(\006)1032
2466 y FH(+)g(\()p Fv(U)1138 2445 y FC(\003\006)1201
2466 y FE(\000)g FH(3)p 1275 2427 V Fv(L)1309 2437 y
FC(\003)1335 2466 y Fv(L)1368 2445 y FC(\006)1396 2466
y FH(\))p FE(P)1454 2445 y Ft(x)1450 2478 y FC(\003)1476
2466 y FE(P)1515 2445 y Ft(x)1511 2478 y FC(\006)1554
2466 y Fv(:)192 b FH(\(9.49\))-5 2576 y(with)19 b Fv(U)147
2558 y FC(\003\006)219 2576 y FH(is)g(de\014ned)g(in)g(\(4.40)p
 (#equation.4.38) [[197 149 218 161] [1 1 1 [3 3]] [0 0 1]] pdfm (\).)
30 b(Ab)q(o)o(v)o(e,)19 b(the)g(\014rst)g(t)o(w)o(o)g(terms)f(are)h
(related)g(to)g(the)g(gauging)i(of)-5 2636 y(isometries)15
b(of)i FE(S)t(K)11 b(\012)g(Q)p FH(.)22 b(F)l(or)17 b(an)g(ab)q(elian)f
(group,)h(the)g(\014rst)f(term)f(is)h(absen)o(t.)23 b(The)16
b(negativ)o(e)g(term)-5 2696 y(is)g(the)f(gra)o(vitino)g(mass)g(con)o
(tribution,)g(while)f(the)h(one)h(in)f Fv(U)1134 2678
y FC(\003\006)1202 2696 y FH(is)g(the)h(gaugino)g(shift)g(con)o
(tribution)-5 2756 y(due)g(to)h(the)f(quaternionic)f(prep)q(oten)o
(tial.)916 2892 y(43)p eop
%%Page: 44 45
44 44 bop 68 15 a FH(Eq.)22 b(\(9.49)p
 (#equation.9.49) [[116 763 136 775] [1 1 1 [3 3]] [0 0 1]] pdfm (\))16
b(can)h(b)q(e)f(rewritten)g(in)g(a)g(suggestiv)o(e)g(form)f(as)356
133 y Fv(V)25 b FH(=)14 b(\()p Fv(k)505 140 y FC(\003)532
133 y Fv(;)8 b(k)579 140 y FC(\006)607 133 y FH(\))p
626 94 34 2 v Fv(L)659 103 y FC(\003)685 133 y Fv(L)718
112 y FC(\006)757 133 y FH(+)j(\()p Fv(U)863 112 y FC(\003\006)927
133 y FE(\000)g FH(3)p 1001 94 V Fv(L)1034 103 y FC(\003)1061
133 y Fv(L)1094 112 y FC(\006)1121 133 y FH(\)\()p FE(P)1198
112 y Ft(x)1194 145 y FC(\003)1221 133 y FE(P)1260 112
y Ft(x)1256 145 y FC(\006)1294 133 y FE(\000)g(P)1379
140 y FC(\003)1405 133 y FE(P)1440 140 y FC(\006)1467
133 y FH(\))16 b Fv(;)244 b FH(\(9.50\))-5 241 y(where)354
345 y(\()p Fv(k)398 352 y FC(\003)424 345 y Fv(;)8 b(k)471
352 y FC(\006)499 345 y FH(\))14 b(=)g(\()8 b Fv(k)638
327 y Ft(i)636 357 y FC(\003)663 345 y Fv(;)48 b(k)752
327 y Ft(i)764 315 y Fm(?)750 357 y FC(\003)784 345 y
Fv(;)h(k)874 327 y Ft(u)872 357 y FC(\003)907 345 y FH(\))934
247 y Fs(0)934 320 y(B)934 347 y(@)1002 285 y FH(0)73
b Fv(g)1122 292 y Ft(ij)1150 283 y Fm(?)1254 285 y FH(0)979
345 y Fv(g)1002 352 y Ft(i)1014 343 y Fm(?)1032 352 y
Ft(j)1123 345 y FH(0)107 b(0)1002 405 y(0)97 b(0)73 b(2)p
Fv(h)1272 412 y Ft(uv)1321 247 y Fs(1)1321 320 y(C)1321
347 y(A)1366 247 y(0)1366 320 y(B)1366 347 y(@)1416 285
y Fv(k)1443 261 y Ft(j)1441 297 y FC(\006)1411 345 y
Fv(k)1438 322 y Ft(j)1454 310 y Fm(?)1436 357 y FC(\006)1416
405 y Fv(k)1443 387 y Ft(v)1441 418 y FC(\006)1482 247
y Fs(1)1482 320 y(C)1482 347 y(A)1760 345 y FH(\(9.51\))-5
488 y(is)16 b(the)g(scalar)h(pro)q(duct)g(of)f(the)g(Killing)f(v)o
(ector)g(and)i(w)o(e)f(ha)o(v)o(e)g(used)g(eq.)21 b(\(7.6)p
 (#equation.7.6) [[405 650 420 662] [1 1 1 [3 3]] [0 0 1]] pdfm (\))16
b(and)h(the)f(relation)546 605 y Fv(k)573 584 y Ft(i)571
617 y FC(\003)598 605 y Fv(L)631 584 y FC(\003)671 605
y FH(=)e Fv(k)750 584 y Ft(i)762 573 y Fm(?)748 617 y
FC(\003)p 782 566 V 782 605 a Fv(L)815 576 y FC(\003)856
605 y FH(=)f FE(P)942 612 y FC(\003)969 605 y Fv(L)1002
584 y FC(\003)1042 605 y FH(=)h FE(P)1129 612 y FC(\003)p
1155 566 V 1155 605 a Fv(L)1188 576 y FC(\003)1229 605
y FH(=)f(0)k Fv(:)425 b FH(\(9.52\))-5 714 y FE(P)34
696 y Ft(x)30 726 y FC(\003)73 714 y FH(are)16 b(the)g(quaternionic)f
(\(triplet\))g(prep)q(oten)o(tials)h(and)h Fv(U)1131
696 y FC(\003\006)1184 714 y Fv(;)8 b(L)1239 696 y FC(\003)1281
714 y FH(are)17 b(sp)q(ecial)e(geometry)g(data.)68 774
y(In)24 b(a)g(theory)f(with)h(only)f(ab)q(elian)h(v)o(ectors,)g(the)f
(p)q(oten)o(tial)h(ma)o(y)e(still)g(b)q(e)i(non-zero)g(due)g(to)-5
834 y(F)l(a)o(y)o(et-Iliop)q(oulos)16 b(terms:)553 943
y FE(P)592 922 y Ft(x)588 955 y FC(\003)628 943 y FH(=)e
Fv(\030)703 922 y Ft(x)701 955 y FC(\003)744 943 y FH(\(constan)o(t\);)
57 b Fv(\017)1053 922 y Ft(xy)q(z)1111 943 y Fv(\030)1134
919 y Ft(y)1132 955 y FC(\003)1159 943 y Fv(\030)1182
922 y Ft(z)1180 955 y FC(\006)1221 943 y FH(=)14 b(0)j
Fv(:)432 b FH(\(9.53\))-5 1052 y(In)16 b(this)g(case)603
1112 y Fv(V)11 b FH(\()p Fv(z)r(;)p 708 1085 25 2 v 8
w(z)r FH(\))i(=)h(\()p Fv(U)874 1091 y FC(\003\006)937
1112 y FE(\000)d FH(3)p 1011 1073 34 2 v Fv(L)1045 1083
y FC(\003)1071 1112 y Fv(L)1104 1091 y FC(\006)1132 1112
y FH(\))p Fv(\030)1174 1091 y Ft(x)1172 1124 y FC(\003)1199
1112 y Fv(\030)1222 1091 y Ft(x)1220 1124 y FC(\006)1264
1112 y Fv(:)482 b FH(\(9.54\))-5 1199 y(Examples)12 b(with)g
Fv(V)f FH(\()p Fv(z)r(;)p 426 1172 25 2 v 8 w(z)r FH(\))j(=)g(0)f(but)g
(non-v)m(anishing)h(gra)o(vitino)e(mass)g(\(with)h Fv(N)19
b FH(=)14 b(2)f(sup)q(ersymmetry)-5 1259 y(brok)o(en)18
b(to)g Fv(N)k FH(=)17 b(0\))h(w)o(ere)f(giv)o(en)g(in)h([36)p
 (#cite.flatpotn2) [[243 465 254 477] [1 1 1 [3 3]] [0 0 1]] pdfm (],)f
(then)h(generalizing)f(to)h Fv(N)k FH(=)17 b(2)h(the)g(no)g(scale)g(mo)
q(dels)f(of)-5 1319 y Fv(N)i FH(=)14 b(1)i(sup)q(ergra)o(vit)o(y)g([42)
p  (#cite.flatpotn1) [[178 450 189 462] [1 1 1 [3 3]] [0 0 1]] pdfm 
(].)k(These)c(mo)q(dels)f(w)o(ere)g(obtained)h(b)o(y)f(taking)h(a)g
Fv(\030)1433 1301 y Ft(x)1431 1331 y FC(\003)1472 1319
y FH(=)d(\()p Fv(\030)1563 1326 y FC(0)1583 1319 y Fv(;)8
b FH(0)p Fv(;)g FH(0\))17 b(.)k(In)15 b(this)-5 1379
y(case)i(the)f(expression)754 1499 y Fv(V)25 b FH(=)14
b Fv(U)897 1479 y FC(00)946 1499 y FE(\000)d FH(3)p 1020
1460 34 2 v Fv(L)1053 1470 y FC(0)1073 1499 y Fv(L)1106
1479 y FC(0)1760 1499 y FH(\(9.55\))-5 1586 y(reduces)16
b(to)665 1646 y Fv(V)25 b FH(=)14 b(\()p Fv(@)815 1653
y Ft(i)829 1646 y Fv(K)t(g)899 1626 y Ft(ij)927 1614
y Fm(?)947 1646 y Fv(@)973 1653 y Ft(j)989 1644 y Fm(?)1009
1646 y Fv(K)h FE(\000)c FH(3\))p Fv(e)1181 1626 y Ft(K)1760
1646 y FH(\(9.56\))-5 1733 y(whic)o(h)16 b(is)f(the)h
Fv(N)j FH(=)14 b(1)i(sup)q(ergra)o(vit)o(y)g(p)q(oten)o(tial,)f(with)h
(solution)g(\()g Fv(V)25 b FH(=)14 b(0\))i(the)g(cubic)f(holomorphic)-5
1793 y(prep)q(oten)o(tial)497 1932 y Fv(F)7 b FH(\()p
Fv(X)t FH(\))13 b(=)h Fv(d)708 1939 y Ft(AB)r(C)797 1898
y Fv(X)841 1880 y Ft(A)870 1898 y Fv(X)914 1880 y Ft(B)945
1898 y Fv(X)989 1880 y Ft(C)p 797 1920 222 2 v 876 1966
a Fv(X)920 1952 y FC(0)1089 1932 y Fv(A)f FH(=)h(1)p
Fv(;)8 b(:)g(:)g(:)g(;)g(n)16 b(:)376 b FH(\(9.57\))68
2045 y(Another)24 b(solution)g(is)g(obtained)g(b)o(y)f(taking)h(the)
1054 2022 y Ft(S)r(U)t FC(\(1)p Ft(;)p FC(1\))p 1054
2033 124 2 v 1079 2062 a Ft(U)t FC(\(1\))1198 2045 y
FE(\012)1258 2022 y Ft(S)r(O)q FC(\(2)p Ft(;n)p FC(\))p
1258 2033 128 2 v 1272 2062 a Ft(S)r(O)q FC(\()p Ft(n)p
FC(\))1414 2045 y FH(coset)g(in)g(the)f Fv(S)s(O)q FH(\(2)p
Fv(;)8 b(n)p FH(\))-5 2115 y(symmetric)k(parametrization)i(of)i(the)f
(symplectic)e(sections)i(\()p Fv(X)1208 2097 y FC(\003)1235
2115 y Fv(;)8 b(F)1289 2122 y FC(\003)1329 2115 y FH(=)13
b Fv(\021)1404 2122 y FC(\003\006)1457 2115 y Fv(S)s(X)1534
2097 y FC(\006)1577 2115 y FH(;)23 b Fv(X)1658 2097 y
FC(\003)1685 2115 y Fv(X)1729 2097 y FC(\006)1757 2115
y Fv(\021)1781 2122 y FC(\003\006)1847 2115 y FH(=)-5
2175 y(0)17 b Fv(;)8 b(\021)82 2182 y FC(\003\006)148
2175 y FH(=)13 b(\(1)p Fv(;)8 b FH(1)p Fv(;)g FE(\000)p
FH(1)p Fv(;)g(:)g(:)g(:)g(;)g FE(\000)p FH(1\)\))17 b(where)f(a)g(prep)
q(oten)o(tial)g Fv(F)22 b FH(do)q(es)17 b(not)g(exist.)k(In)16
b(this)g(case)606 2306 y Fv(U)644 2286 y FC(\003\006)708
2306 y FE(\000)11 b FH(3)p 782 2267 34 2 v Fv(L)815 2277
y FC(\003)842 2306 y Fv(L)875 2286 y FC(\006)916 2306
y FH(=)j FE(\000)1090 2273 y FH(1)p 1012 2295 182 2 v
1012 2342 a Fv(i)p FH(\()p Fv(S)f FE(\000)p 1141 2303
33 2 v 11 w Fv(S)s FH(\))1198 2306 y Fv(\021)1222 2313
y FC(\003\006)1760 2306 y FH(\(9.58\))-5 2442 y(where)j(w)o(e)g(ha)o(v)
o(e)f(used)i(the)f(fact)g(that)276 2569 y FE(N)317 2576
y FC(\003\006)383 2569 y FH(=)e(\()p Fv(S)g FE(\000)p
547 2530 V 10 w Fv(S)s FH(\)\(\010)653 2576 y FC(\003)p
680 2530 36 2 v 680 2569 a FH(\010)715 2576 y FC(\006)754
2569 y FH(+)p 803 2530 V 11 w(\010)838 2576 y FC(\003)865
2569 y FH(\010)900 2576 y FC(\006)927 2569 y FH(\))d(+)p
1006 2530 33 2 v 11 w Fv(S)s(\021)1063 2576 y FC(\003\006)1164
2569 y Fv(;)24 b FH(\010)1237 2549 y FC(\003)1278 2569
y FH(=)1417 2536 y Fv(X)1461 2517 y FC(\003)p 1335 2558
235 2 v 1335 2605 a FH(\()p Fv(X)1398 2591 y FC(\003)p
1425 2566 45 2 v 1425 2605 a Fv(X)1469 2612 y FC(\003)1495
2605 y FH(\))1514 2591 y FC(1)p Ft(=)p FC(2)1591 2569
y Fv(:)155 b FH(\(9.59\))-5 2707 y(The)11 b(iden)o(tit)o(y)e(\(9.58)p
 (#equation.9.58) [[140 117 161 129] [1 1 1 [3 3]] [0 0 1]] pdfm (\))j
(allo)o(ws)f(one)g(to)g(pro)o(v)o(e)f(that)i(the)f(tree)f(lev)o(el)f(p)
q(oten)o(tial)h(of)i(an)f(arbitrary)g(heterotic)-5 2768
y(string)j(compacti\014cation)f(\(including)g(orbifolds)h(with)g(t)o
(wisted)f(h)o(yp)q(erm)o(ultiplets\))e(is)i(semi-p)q(ositiv)o(e)916
2892 y(44)p eop
%%Page: 45 46
45 45 bop -5 15 a FH(de\014nite)12 b(pro)o(vided)g(w)o(e)h(don't)g
(gauge)h(the)e(gra)o(viphoton)i(and)f(the)g(gra)o(vidilaton)g(v)o
(ectors)f(\(i)p Fv(:)p FH(e)p Fv(:)f FE(P)1773 -3 y Ft(x)1769
28 y FC(\003)1809 15 y FH(=)j(0)-5 76 y(for)j(\003)d(=)g(0)p
Fv(;)8 b FH(1,)16 b FE(P)309 58 y Ft(x)305 88 y FC(\003)346
76 y FE(6)p FH(=)e(0)i(for)h(\003)d(=)g(2)p Fv(;)8 b(:)g(:)g(:)g(;)g(n)
776 83 y Ft(V)806 76 y FH(\).)22 b(On)16 b(the)g(other)h(hand,)f(it)g
(also)h(pro)o(v)o(es)f(that)h(tree)e(lev)o(el)-5 136
y(sup)q(ergra)o(vit)o(y)h(breaking)g(ma)o(y)e(only)i(o)q(ccurr)h(if)e
FE(P)921 118 y Ft(x)917 148 y FC(\003)957 136 y FE(6)p
FH(=)f(0)j(for)f(\003)e(=)f(0)p Fv(;)8 b FH(1.)22 b(This)16
b(instance)g(is)g(related)g(to)-5 196 y(mo)q(dels)f(with)i(Sc)o
(herk-Sc)o(h)o(w)o(arz)d(mec)o(hanism)f(studied)j(in)g(the)g
(literature)f([40)p
 (#cite.scsc) [[410 720 421 732] [1 1 1 [3 3]] [0 0 1]] pdfm (,)h(41)p
 (#cite.ant) [[428 720 440 732] [1 1 1 [3 3]] [0 0 1]] pdfm 
1 w(].)68 256 y(A)g(v)m(anishing)h(p)q(oten)o(tial)f(can)g(b)q(e)h
(obtained)f(if)g Fv(\030)967 238 y Ft(x)965 269 y FC(\003)1006
256 y FH(=)d(\()p Fv(\030)1097 263 y FC(\003)1124 256
y Fv(;)8 b FH(0)p Fv(;)g FH(0\))17 b(with)793 359 y Fv(\030)814
366 y FC(\003)841 359 y Fv(\030)862 366 y FC(\006)890
359 y Fv(\021)916 338 y FC(\003\006)981 359 y FH(=)d(0)j
Fv(:)672 b FH(\(9.60\))-5 461 y(In)13 b(this)f(case)h(w)o(e)f(ma)o(y)f
(also)i(consider)f(the)h(gauge)g(group)h(to)f(b)q(e)g
Fv(U)5 b FH(\(1\))1263 443 y Ft(p)p FC(+2)1332 461 y
FE(\012)t Fv(G)p FH(\()p Fv(n)1461 468 y Ft(V)1495 461
y FE(\000)t Fv(p)p FH(\))12 b(and)i(in)o(tro)q(duce)-5
522 y Fv(\030)16 529 y FC(\003)65 522 y FH(=)23 b(\()p
Fv(\030)166 529 y FC(0)186 522 y Fv(;)8 b(:)g(:)g(:)f(;)h(\030)316
529 y Ft(p)p FC(+1)381 522 y Fv(;)g FH(0)p Fv(;)g(:)g(:)g(:)g(;)g
FH(0\))16 b(suc)o(h)g(that)h Fv(\030)833 529 y FC(\003)860
522 y Fv(\030)881 529 y FC(\006)909 522 y Fv(\021)935
504 y FC(\003\006)1001 522 y FH(=)d(0)i(where)g Fv(\021)1260
504 y FC(\003\006)1328 522 y FH(is)h(the)f Fv(S)s(O)q
FH(\(2)p Fv(;)8 b(p)p FH(\))17 b(Loren)o(tzian)-5 582
y(metric.)i(The)d(p)q(oten)o(tial)g(is)g(no)o(w:)417
690 y Fv(V)25 b FH(=)14 b Fv(k)549 669 y Ft(i)547 702
y FC(\003)574 690 y Fv(g)597 697 y Ft(ij)625 688 y Fm(?)645
690 y Fv(k)672 666 y Ft(j)688 655 y Fm(?)670 702 y FC(\006)p
709 651 34 2 v 709 690 a Fv(L)742 661 y FC(\003)768 690
y Fv(L)801 669 y FC(\006)862 690 y FH(;)40 b(\()p Fv(U)973
669 y FC(\003\006)1036 690 y FE(\000)11 b FH(3)p 1110
651 V Fv(L)1144 661 y FC(\003)1170 690 y Fv(L)1203 669
y FC(\006)1231 690 y FH(\))p FE(P)1289 669 y Ft(x)1285
702 y FC(\003)1311 690 y FE(P)1350 669 y Ft(x)1346 702
y FC(\006)1387 690 y FH(=)j(0)297 b(\(9.61\))-5 793 y(where)16
b Fv(k)163 775 y Ft(i)161 805 y FC(\003)188 793 y Fv(L)221
775 y FC(\003)262 793 y FH(=)d(0)k(for)g(\003)c FE(\024)h
Fv(p)d FH(+)g(1.)22 b(The)16 b(gra)o(vitino)g(ha)o(v)o(e)g(equal)f
(mass)705 895 y FE(j)f Fv(m)776 903 y FC(3)p Ft(=)p FC(2)844
895 y FE(j')g Fv(e)934 875 y Ft(K=)p FC(2)1015 895 y
FE(j)f Fv(\030)1063 902 y FC(\003)1090 895 y Fv(X)1134
875 y FC(\003)1175 895 y FE(j)571 b FH(\(9.62\))-5 998
y(with)16 b Fv(\030)127 1005 y FC(\003)154 998 y Fv(\030)175
1005 y FC(\006)203 998 y Fv(\021)229 980 y FC(\003\006)295
998 y FH(=)e(0)i(,)g(\003)e(=)f(0)p Fv(;)8 b(:)g(:)g(:)g(;)g(p)k
FH(+)f(1.)68 1058 y(It)j(is)g(am)o(using)f(to)h(note)h(that)f(the)g
(gra)o(vitino)g(mass,)f(as)i(a)f(function)g(of)h(the)e
Fv(O)q FH(\(2)p Fv(;)8 b(p)p FH(\))p Fv(=O)q FH(\(2\))f
FE(\012)g Fv(O)q FH(\()p Fv(p)p FH(\))-5 1118 y(mo)q(duli)16
b(and)i(of)g(the)f(F-I)g(terms,)e(just)j(coincides)e(with)h(the)g(cen)o
(tral)g(c)o(harge)g(form)o(ula)f(for)h(the)g(lev)o(el)-5
1178 y Fv(N)34 1185 y Ft(L)74 1178 y FH(=)d(1)i(in)f(heterotic)g
(string)h(\(H-monop)q(oles\),)f(if)g(the)g(F-I)h(terms)e(are)i(iden)o
(ti\014ed)e(with)h(the)h Fv(O)q FH(\(2)p Fv(;)8 b(p)p
FH(\))-5 1239 y(lattice)15 b(electric)f(c)o(harges.)68
1299 y(Note)21 b(that,)h(b)q(ecause)f(of)h(the)e(sp)q(ecial)h(form)f
(of)h(the)g(gauged)1264 1283 y Fs(b)1253 1299 y Fv(Q)o
FH(,)1332 1295 y Fs(b)1327 1299 y Fv(!)1359 1281 y Ft(x)1381
1299 y FH(,)h(w)o(e)e(see)h(that)g(whenev)o(er)-5 1359
y FE(P)30 1366 y FC(\003)70 1359 y FE(6)p FH(=)14 b(0)h(the)g(gra)o
(vitino)g(is)f(c)o(harged)h(with)g(resp)q(ect)f(to)i(the)e
Fv(U)5 b FH(\(1\))16 b(factor)f(and)h(whenev)o(er)d FE(P)1690
1341 y Ft(x)1686 1371 y FC(\003)1726 1359 y FE(6)p FH(=)h(0)h(the)-5
1419 y(gra)o(vitino)g(is)h(c)o(harged)f(with)g(resp)q(ect)g(to)h(the)f
Fv(S)s(U)5 b FH(\(2\))16 b(factor)g(of)f(the)h Fv(U)5
b FH(\(1\))10 b FE(\012)f Fv(S)s(U)c FH(\(2\))16 b(automorphism)-5
1479 y(group)f(of)f(the)g(sup)q(ersymmetry)d(algebra.)20
b(In)14 b(the)g(case)f(of)i Fv(U)5 b FH(\(1\))1190 1461
y Ft(p)1224 1479 y FH(gauge)15 b(\014elds)e(with)h(non-v)m(anishing)-5
1540 y(F-I)20 b(terms)e Fv(\030)243 1521 y Ft(x)241 1552
y(p)286 1540 y FH(=)i(\(0)p Fv(;)8 b FH(0)p Fv(;)g(\030)476
1547 y Ft(p)497 1540 y FH(\))20 b(the)g(gauge)g(\014eld)g
Fv(A)912 1521 y FC(\003)912 1552 y Ft(\026)938 1540 y
Fv(\030)959 1547 y FC(\003)1006 1540 y FH(=)g Fv(A)1101
1547 y Ft(\026)1144 1540 y FH(gauge)h(a)f Fv(U)5 b FH(\(1\))21
b(subgroup)g(of)f Fv(S)s(U)5 b FH(\(2\))1858 1547 y Ft(L)-5
1600 y FH(susy)17 b(algebra.)68 1660 y(Mo)q(dels)i(with)f(breaking)g
(of)h Fv(N)j FH(=)17 b(2)i(to)f Fv(N)23 b FH(=)17 b(1)i([29)p
 (#cite.FGP1) [[313 369 325 381] [1 1 1 [3 3]] [0 0 1]] pdfm (])f
(necessarily)f(require)g Fv(k)1523 1642 y Ft(u)1521 1672
y FC(\003)1566 1660 y FH(not)i(to)f(b)q(e)h(zero.)-5
1720 y(The)e(minim)o(al)c(mo)q(del)i(where)h(this)g(happ)q(ens)i(with)e
Fv(V)25 b FH(=)13 b(0)k(is)f(the)g(one)h(based)f(on)581
1847 y FE(S)t(K)c(\012)e(Q)k FH(=)826 1814 y Fv(S)s(U)5
b FH(\(1)p Fv(;)j FH(1\))p 826 1836 180 2 v 865 1882
a Fv(U)d FH(\(1\))1021 1847 y FE(\012)1076 1814 y Fv(S)s(O)q
FH(\(4)p Fv(;)j FH(1\))p 1076 1836 181 2 v 1099 1882
a Fv(S)s(O)q FH(\(4\))1278 1847 y Fv(;)468 b FH(\(9.63\))-5
1978 y(where)17 b(a)g Fv(U)5 b FH(\(1\))12 b FE(\012)f
Fv(U)5 b FH(\(1\))17 b(isometry)e(of)i FE(Q)f FH(is)g(gauged.)24
b(In)16 b(this)g(case)h(the)f(v)m(anishing)h(of)g Fv(V)28
b FH(requires)16 b(a)-5 2038 y(comp)q(ensation)g(of)h(the)f
Fv(\016)r(\025;)8 b(\016)r(\020)19 b FH(v)m(ariations)e(with)f(the)g
(gra)o(vitino)g(con)o(tribution)522 2146 y(4)p Fv(k)573
2126 y Ft(u)571 2159 y FC(\003)599 2146 y Fv(k)626 2126
y Ft(v)624 2159 y FC(\006)652 2146 y Fv(h)680 2153 y
Ft(uv)732 2146 y FH(+)11 b Fv(U)819 2126 y FC(\003\006)871
2146 y FE(P)910 2126 y Ft(x)906 2159 y FC(\003)932 2146
y FE(P)971 2126 y Ft(x)967 2159 y FC(\006)1008 2146 y
FH(=)j(3)p 1084 2107 34 2 v Fv(L)1118 2117 y FC(\003)1144
2146 y Fv(L)1177 2126 y FC(\006)1205 2146 y FE(P)1244
2126 y Ft(x)1240 2159 y FC(\003)1266 2146 y FE(P)1305
2126 y Ft(x)1301 2159 y FC(\006)1344 2146 y Fv(:)402
b FH(\(9.64\))-5 2249 y(The)17 b(mo)q(duli)d(space)j(of)f(v)m(acua)h
(satisfying)g(\(9.64)p
 (#equation.9.64) [[269 227 289 239] [1 1 1 [3 3]] [0 0 1]] pdfm (\))f
(is)g(a)h(four)g(dimensional)d(subspace)j(of)g(\(9.63)p
 (#equation.9.63) [[475 227 496 239] [1 1 1 [3 3]] [0 0 1]] pdfm (\).)
68 2309 y(One)j(ma)o(y)f(w)o(onder)h(where)g(are)g(the)f(explicit)f
(mass)i(terms)f(for)h(h)o(yp)q(erm)o(ultiple)o(ts.)30
b(In)20 b Fv(N)25 b FH(=)c(2)-5 2369 y(sup)q(ergra)o(vit)o(y)l(,)h
(since)f(the)g(h)o(yp)q(erm)o(ultiple)o(t)e(mass)i(is)g(a)h(cen)o(tral)
f(c)o(harge,)h(whic)o(h)f(is)g(gauged,)i(suc)o(h)-5 2429
y(term)18 b(corresp)q(onds)i(to)f(the)g(gauging)h(of)g(a)f
Fv(U)5 b FH(\(1\))20 b(c)o(harge.)29 b(This)19 b(is)g(b)q(est)h(seen)e
(if)h(w)o(e)g(consider)f(the)-5 2490 y(case)13 b(where)g(no)g(v)o
(ector)g(m)o(ultiple)o(ts)e(\(and)i(then)g(gauginos\))i(are)e(presen)o
(t.)19 b(In)13 b(this)g(case)g Fv(L)1650 2472 y FC(\003)1690
2490 y FH(=)h Fv(L)1775 2472 y FC(0)1809 2490 y FH(=)g(1)-5
2550 y(and)j(the)f(p)q(oten)o(tial)g(b)q(ecomes)689 2610
y Fv(V)25 b FH(=)14 b(4)p Fv(h)846 2617 y Ft(uv)887 2610
y Fv(k)914 2589 y Ft(u)937 2610 y Fv(k)964 2589 y Ft(v)996
2610 y FE(\000)c FH(3)p FE(P)1108 2589 y Ft(x)1130 2610
y FE(P)1169 2589 y Ft(x)1760 2610 y FH(\(9.65\))-5 2694
y(where)17 b Fv(k)164 2676 y Ft(u)203 2694 y FH(is)g(the)g(Killing)e(v)
o(ector)h(of)h(a)g Fv(U)5 b FH(\(1\))18 b(symmetry)13
b(of)18 b FE(Q)p FH(,)e(gauged)i(b)o(y)e(the)h(gra)o(viphoton)g(and)-5
2759 y FE(P)34 2741 y Ft(x)71 2759 y FH(is)f(the)f(asso)q(ciated)i
(prep)q(oten)o(tial.)j(F)l(or)819 2736 y Ft(S)r(O)q FC(\(4)p
Ft(;)p FC(1\))p 819 2747 124 2 v 832 2776 a Ft(S)r(O)q
FC(\(4\))963 2759 y FH(this)15 b(repro)q(duces)h(the)f(Zac)o(hos)h(mo)q
(del)e([69)p
 (#cite.zachos) [[481 105 492 117] [1 1 1 [3 3]] [0 0 1]] pdfm 
1 w(].)20 b(The)916 2892 y(45)p eop
%%Page: 46 47
46 46 bop -5 15 a FH(gauged)20 b Fv(U)5 b FH(\(1\))20
b(in)e(this)h(mo)q(del)f(is)h(con)o(tained)f(in)h Fv(S)s(U)989
22 y Ft(R)1018 15 y FH(\(2\))g(whic)o(h)f(comm)o(utes)e(with)j(the)f
(symmetry)-5 76 y Fv(S)s(U)61 83 y Ft(L)87 76 y FH(\(2\))24
b(in)e(the)h(decomp)q(osition)f(of)h Fv(S)s(O)q FH(\(4\))j(=)f
Fv(S)s(U)1005 83 y Ft(L)1031 76 y FH(\(2\))16 b FE(\012)f
Fv(S)s(U)1229 83 y Ft(R)1258 76 y FH(\(2\).)42 b(This)23
b(mo)q(del)e(has)j(a)f(lo)q(cal)-5 136 y(minim)n(um)15
b(at)20 b(v)m(anishing)f(h)o(yp)q(erm)o(ultiplet)d(v)o(ev)i(at)h(whic)o
(h)g Fv(U)5 b FH(\(1\))20 b(is)e(un)o(brok)o(en,)h(and)h(the)f(extrema)
-5 196 y(\(at)d Fv(u)e FH(=)g(1\))i(\(maxima\))d(whic)o(h)i(break)h
Fv(U)5 b FH(\(1\).)22 b(The)15 b(extremal)f(mo)q(del)g(is)i(when)g(b)q
(oth)h Fv(n)1623 203 y Ft(H)1670 196 y FH(=)d Fv(n)1751
203 y Ft(V)1795 196 y FH(=)g(0.)-5 256 y(Still)h(w)o(e)h(ma)o(y)f(ha)o
(v)o(e)g(a)i(pure)f(F-I)g(term)688 366 y Fv(V)25 b FH(=)14
b FE(\000)p FH(3)p Fv(\030)879 346 y FC(2)949 366 y Fv(\030)i
FH(=)e(\()p Fv(\030)r(;)8 b FH(0)p Fv(;)g FH(0\))569
b(\(9.66\))-5 476 y(This)12 b(corresp)q(onds)g(to)g(the)f(gauging)i(of)
f(a)f Fv(U)5 b FH(\(1\))15 b FE(\032)e Fv(S)s(U)5 b FH(\(2\))1061
483 y Ft(L)1099 476 y FH(and)12 b(gra)o(vitinos)g(ha)o(v)o(e)e(c)o
(harged)i(coupling.)-5 536 y(This)17 b(mo)q(del)e(corresp)q(onds)i(to)g
(an)o(ti-De)f(Sitter)f Fv(N)k FH(=)14 b(2)j(sup)q(ergra)o(vit)o(y)e
([44)p  (#cite.fredas) [[392 638 403 650] [1 1 1 [3 3]] [0 0 1]] pdfm 
1 w(].)-5 703 y Fw(10)82 b(The)26 b(rigid)g(limit:)35
b(N=2)27 b(matter)h(coupled)d(Y)-7 b(ang{Mills)157 794
y(theory)-5 904 y FH(In)14 b(this)f(section)g(w)o(e)g(consider)h(the)f
(rigid)g(limit)e(of)j(matter)e(coupled)h(N=2)h(sup)q(ergra)o(vit)o(y)l
(.)19 b(The)14 b(aim)e(is)-5 964 y(that)k(of)f(obtaining)h(the)e(most)h
(general)f(form)g(of)i(matter)d(coupled)i(N=2)g(sup)q(er)g(Y)l
(ang{Mills)g(theory)l(.)-5 1024 y(By)20 b(this)h(w)o(e)f(mean)g(the)g
(rigid)h(sup)q(ersymmetri)o(c)d(N=2)i(theory)h(of)g Fv(n)g
FH(v)o(ector)f(m)o(ultiplet)o(s)e(coupled)-5 1084 y(to)i
Fv(m)e FH(h)o(yp)q(erm)o(ultiple)o(ts)f(in)o(teracting)g(through)j(a)g
(generic)e Fu(rigid)h(sp)n(e)n(cial)h(manifold)f FH(and)h(a)f(generic)
-5 1144 y Fu(hyp)n(erK\177)-25 b(ahler)17 b(manifold)p
FH(.)k(Suc)o(h)15 b(a)h(theory)l(,)f(in)g(general,)g(is)g(not)h
(renormalizable:)j(renormalizabilit)n(y)-5 1205 y(obtains)g(only)f(in)f
(the)h(case)g(of)g(a)h Fu(\015at)e FH(sp)q(ecial)h(manifold)e(and)j(a)f
Fu(\015at)g FH(h)o(yp)q(erK\177)-24 b(ahler)17 b(manifold.)25
b(Y)l(et)-5 1265 y(it)c(is)g(v)o(ery)e(in)o(teresting)h(as)i(an)f
(e\013ectiv)o(e)f(lo)o(w)g(energy)h(lagrangian.)37 b(Seib)q(erg)20
b(Witten)h(lagrangian)-5 1325 y([1)p
 (#cite.SW12) [[74 449 80 461] [1 1 1 [3 3]] [0 0 1]] pdfm (],)i(is)f
(just)h(an)g(instance)f(in)f(this)i(general)f(class.)39
b(One)22 b(could)g(deriv)o(e)f(this)h(t)o(yp)q(e)g(of)g(theory)h(b)o(y)
-5 1385 y(direct)e(metho)q(ds)g(solving)h(Bianc)o(hi)e(iden)o(tities)g
(in)i(\015at)g(sup)q(erspace)g(and)h(then)e(constructing)h(the)-5
1445 y(corresp)q(onding)13 b(rheonomic)d(action.)20 b(It)11
b(is)g(ho)o(w)o(ev)o(er)g(m)o(uc)o(h)e(simpler)h(to)i(deriv)o(e)e(it)h
(through)h(a)g(suitable)-5 1506 y Fu(sc)n(aling)20 b(limit)e
FH(from)e(the)h(N=2)g(sup)q(ergra)o(vit)o(y)g(theory)l(.)25
b(The)17 b(con)o(traction)g(parameter)f(is)i(ob)o(viously)-5
1566 y(the)k(Planc)o(k)g(mass)f Fv(\026)i FH(and)g(the)e(limit)f(m)o
(ust)h(b)q(e)h(p)q(erformed)f(in)h(suc)o(h)g(a)g(w)o(a)o(y)g(that)g(lo)
q(cal)h(sp)q(ecial)-5 1626 y(geometry)13 b(\015o)o(ws)i(to)g(rigid)e
(sp)q(ecial)h(geometry)f(and)i(quaternionic)f(geometry)e(\015o)o(ws)j
(to)g(h)o(yp)q(erK\177)-24 b(ahler)-5 1686 y(geometry)l(.)27
b(W)l(e)18 b(already)h(kno)o(w)f(ho)o(w)h(this)g(can)f(happ)q(en:)27
b(the)18 b(curv)m(ature)h(of)g(the)f(line)f(and)i Fv(S)s(U)5
b FH(\(2\))-5 1746 y(bundles)14 b(m)o(ust)f(\015o)o(w)h(to)g(zero)g(in)
g(the)f(limit.)18 b(In)c(the)f(next)h(subsection)g(w)o(e)f(describ)q(e)
h(the)f(appropriate)-5 1807 y(rescalings.)25 b(Then)17
b(in)g(a)h(further)f(subsection)h(w)o(e)e(rep)q(ort)i(the)f(\014nal)h
(result)f(written)g(in)g(space{time)-5 1867 y(comp)q(onen)o(t)d
(formalism)e(for)j(the)f(b)q(ene\014t)g(of)h(the)g(reader)f(who)h(do)q
(es)h(not)f(w)o(an)o(t)f(to)h(b)q(e)g(in)o(v)o(olv)o(ed)d(with)-5
1927 y(the)k(rheonom)o(y)f(formalism.)-5 2071 y Fk(10.1)66
b(Planc)n(k)24 b(mass)d(rescalings)-5 2164 y FH(W)l(e)14
b(b)q(egin)g(with)g(the)g(sp)q(ecial)f(geometry)g(sector.)20
b(Here)13 b(w)o(e)h(consider)f(the)h(co)o(v)m(arian)o(tly)f
(holomorphic)-5 2224 y(symplectic)g(section)32 b(4.26)p
 (#equation.4.26) [[171 233 192 245] [1 1 1 [3 3]] [0 0 1]] pdfm 
17 w(and)17 b(w)o(e)f(write:)101 2362 y Fv(V)34 b FE(\021)223
2302 y Fs(\022)270 2332 y Fv(L)303 2314 y FC(\003)262
2392 y Fv(M)309 2399 y FC(\006)345 2302 y Fs(\023)398
2362 y FE(\021)22 b FH(exp)8 b([)o FE(K)q Fv(=)p FH(2])673
2302 y Fs(\022)712 2332 y Fv(X)756 2314 y FC(\003)718
2392 y Fv(F)750 2399 y FC(\006)791 2302 y Fs(\023)844
2362 y FH(=)22 b(exp)987 2314 y Fs(h)1017 2346 y(b)1006
2362 y FE(K)q Fv(=)p FH(\(2)p Fv(\026)1141 2342 y FC(2)1162
2362 y FH(\))1181 2314 y Fs(i)1217 2289 y( )1250 2362
y FH(\012)1285 2369 y FC(0)1316 2362 y FH(+)1372 2329
y(1)p 1370 2351 30 2 v 1370 2396 a Fv(\026)1410 2346
y Fs(b)1404 2362 y FH(\012)11 b(+)1517 2329 y(1)p 1504
2351 50 2 v 1504 2396 a Fv(\026)1533 2382 y FC(3)1558
2362 y FH(\012)1593 2369 y FC(3)1613 2289 y Fs(!)1760
2362 y FH(\(10.1\))-5 2501 y(where:)397 2632 y(\012)432
2639 y FC(0)474 2632 y FH(=)534 2510 y Fs(0)534 2583
y(B)534 2608 y(B)534 2632 y(B)534 2659 y(@)618 2523 y
FC(1)p 603 2531 48 2 v 603 2535 a FB(p)p 633 2535 18
2 v 633 2563 a FC(2)613 2602 y FD(0)579 2663 y FE(\000)641
2643 y FC(i)p 623 2651 48 2 v 623 2656 a FB(p)p 652 2656
18 2 v 27 x FC(2)613 2723 y FD(0)683 2510 y Fs(1)683
2583 y(C)683 2608 y(C)683 2632 y(C)683 2659 y(A)831 2616
y(b)825 2632 y FH(\012)23 b(=)943 2510 y Fs(0)943 2583
y(B)943 2608 y(B)943 2632 y(B)943 2659 y(@)1005 2542
y FH(0)987 2602 y Fv(Y)1027 2584 y Ft(I)1005 2663 y FH(0)989
2723 y Fv(F)1021 2730 y Ft(J)1055 2510 y Fs(1)1055 2583
y(C)1055 2608 y(C)1055 2632 y(C)1055 2659 y(A)1197 2632
y FH(\012)1232 2639 y FC(3)1274 2632 y FH(=)1334 2510
y Fs(0)1334 2583 y(B)1334 2608 y(B)1334 2632 y(B)1334
2659 y(@)1388 2526 y(b)1380 2542 y Fv(Y)1408 2549 y FC(0)1390
2602 y FD(0)1390 2646 y Fs(b)1379 2663 y Fv(F)1411 2670
y FC(0)1390 2723 y FD(0)1438 2510 y Fs(1)1438 2583 y(C)1438
2608 y(C)1438 2632 y(C)1438 2659 y(A)1760 2632 y FH(\(10.2\))916
2892 y(46)p eop
%%Page: 47 48
47 47 bop -5 15 a FH(The)22 b(hatted)h(ob)s(jects)f(are)g(those)g(that)
h(surviv)o(e)e(in)h(the)f(in\014nite)h(Planc)o(k)f(mass)h(limit)d
Fv(\026)33 b FE(!)f(1)p FH(.)-5 76 y(Recalling)15 b(eq.)h(4.25)p
 (#equation.4.25) [[140 749 161 761] [1 1 1 [3 3]] [0 0 1]] pdfm 
16 w(w)o(e)g(obtain:)210 158 y Fs(b)200 174 y FE(K)42
b FH(=)f FE(\000)29 b FH(lim)415 199 y Ft(\026)p FB(!1)523
174 y Fv(\026)552 153 y FC(2)589 174 y FH(log)668 126
y Fs(h)688 174 y FH(i)8 b FE(h)p FH(\012)p FE(j)p 778
135 36 2 v FH(\012)p FE(i)840 126 y Fs(i)280 305 y FH(=)41
b FE(\000)29 b FH(lim)415 329 y Ft(\026)p FB(!1)523 305
y Fv(\026)552 284 y FC(2)589 305 y FH(log)660 231 y Fs(")684
305 y FH(1)12 b(+)791 271 y(i)p 774 293 50 2 v 774 339
a Fv(\026)803 324 y FC(2)844 256 y Fs(\020)p 869 266
40 2 v 49 x Fv(Y)908 275 y Ft(I)928 305 y Fv(F)960 312
y Ft(I)991 305 y FE(\000)p 1041 266 39 2 v 11 w Fv(F)1079
312 y Ft(J)1103 305 y Fv(Y)1143 284 y Ft(J)1167 256 y
Fs(\021)1203 305 y FH(+)1257 230 y FE(p)p 1298 230 25
2 v 1298 271 a FH(2)p 1257 293 66 2 v 1265 339 a Fv(\026)1294
324 y FC(3)1336 256 y Fs(\020)1361 305 y FH(Re)o Fv(Y)1458
284 y FC(0)1488 305 y FE(\000)f FH(Im)n Fv(F)1628 312
y FC(0)1648 256 y Fs(\021)359 446 y FH(+)428 412 y(i)p
410 434 50 2 v 410 480 a Fv(\026)439 465 y FC(6)473 398
y Fs(\020)p 498 407 40 2 v 48 x Fv(Y)537 416 y FC(0)556
446 y Fv(F)588 453 y FC(0)619 446 y FE(\000)p 669 407
39 2 v 11 w Fv(F)707 453 y FC(0)727 446 y Fv(Y)766 425
y FC(0)786 398 y Fs(\021)810 373 y(#)280 564 y FH(=)41
b FE(\000)8 b FH(i)436 516 y Fs(\020)p 461 525 40 2 v
48 x Fv(Y)500 535 y Ft(I)520 564 y Fv(F)552 571 y Ft(I)583
564 y FE(\000)p 633 525 39 2 v 11 w Fv(F)671 571 y Ft(J)696
564 y Fv(Y)735 543 y Ft(J)759 516 y Fs(\021)280 673 y
FH(=)41 b FE(\000)8 b FH(i)g FE(h)453 657 y Fs(b)447
673 y FH(\012)q FE(j)503 648 y Fs(b)p 497 634 36 2 v
497 673 a FH(\012)p FE(i)22 b(\021)g FH(i)654 657 y Fs(b)648
673 y FH(\012)683 652 y Ft(T)727 612 y Fs(\022)787 643
y FD(0)70 b FH(1)-17 b(1)766 703 y FE(\000)p FH(1)g(1)51
b FD(0)925 612 y Fs(\023)978 648 y(b)p 972 634 V 972
673 a FH(\012)753 b(\(10.3\))-5 792 y(whic)o(h)18 b(repro)q(duces)h
(eq.)f(4.49)p
 (#equation.4.49) [[184 577 204 589] [1 1 1 [3 3]] [0 0 1]] pdfm 
19 w(for)h(the)g(K\177)-24 b(ahler)18 b(p)q(oten)o(tial)h(of)g(rigid)f
(sp)q(ecial)g(geometry)l(.)27 b(An)18 b(obser-)-5 852
y(v)m(ation)g(here)e(is)h(in)g(order.)24 b(The)17 b(last)g(line)f(in)g
(eq.)g(10.3)p
 (#equation.10.3) [[295 563 316 575] [1 1 1 [3 3]] [0 0 1]] pdfm 
18 w(still)g(di\013ers)h(from)f(eq.)g(4.49)p
 (#equation.4.49) [[425 563 445 575] [1 1 1 [3 3]] [0 0 1]] pdfm 
18 w(in)h(one)g(resp)q(ect:)-5 913 y(the)e(symplectic)c(metric)i(and)i
(the)f(symplectic)e(sections)i(in)30 b(10.3)p
 (#equation.10.3) [[344 548 364 560] [1 1 1 [3 3]] [0 0 1]] pdfm 
15 w(are)15 b(\(2)p Fv(n)8 b FH(+)g(2\){dimensional)14
b(while)-5 973 y(those)21 b(in)f(eq.)f(4.48)p
 (#equation.4.48) [[137 533 157 545] [1 1 1 [3 3]] [0 0 1]] pdfm 
21 w(are)h(2)p Fv(n)p FH({dimensional.)32 b(Y)l(et)19
b(the)h(en)o(tries)f(of)i(the)f(symplectic)c(sections)k(in)g(the)-5
1033 y(t)o(w)o(o)f(additional)g(dimensions)f(are)h(alw)o(a)o(ys)f(zero)
h(so)h(that)f(w)o(e)f(can)i(safely)e(reduce)g(the)h(bundle)f(and)-5
1093 y(its)e(structural)g(group)i(from)d Fv(S)s(p)p FH(\(2)p
Fv(n)d FH(+)f(2)p Fv(;)d FH(I)-9 b(R\))16 b(to)h Fv(S)s(p)p
FH(\(2)p Fv(n;)8 b FH(I)-9 b(R\).)68 1153 y(Let)19 b(us)g(next)f
(consider)g(the)h(symplectic)c(v)o(ector)j Fv(U)1038
1160 y Ft(i)1071 1153 y FH(de\014ned)g(in)g(eq.)46 b(4.29)p
 (#equation.4.29) [[410 490 431 502] [1 1 1 [3 3]] [0 0 1]] pdfm (.)29
b(Using)19 b(the)f(ab)q(o)o(v)o(e)-5 1213 y(rescalings)e(w)o(e)g
(obtain:)485 1393 y Fv(U)518 1400 y Ft(i)555 1393 y FH(=)622
1359 y(1)p 620 1381 30 2 v 620 1427 a Fv(\026)671 1377
y Fs(b)662 1393 y Fv(U)695 1400 y Ft(i)729 1393 y FH(+)804
1359 y(1)p 791 1381 50 2 v 791 1427 a Fv(\026)820 1413
y FC(2)854 1270 y Fs(0)854 1343 y(B)854 1368 y(B)854
1393 y(B)854 1419 y(@)927 1283 y FC(1)p 903 1291 65 2
v 903 1323 a(2)921 1296 y FB(p)p 950 1296 18 2 v 27 x
FC(2)981 1303 y Fv(@)1007 1310 y Ft(i)1032 1286 y Fs(b)1021
1303 y FE(K)965 1363 y FD(0)917 1403 y FB(\000)p FC(i)p
903 1411 65 2 v 903 1444 a(2)921 1416 y FB(p)p 950 1416
18 2 v 28 x FC(2)981 1423 y Fv(@)1007 1430 y Ft(i)1032
1407 y Fs(b)1021 1423 y FE(K)965 1483 y FD(0)1068 1270
y Fs(1)1068 1343 y(C)1068 1368 y(C)1068 1393 y(C)1068
1419 y(A)1115 1393 y FH(+)1182 1359 y(1)p 1169 1381 50
2 v 1169 1427 a Fv(\026)1198 1413 y FC(3)1240 1270 y
Fs(0)1240 1343 y(B)1240 1368 y(B)1240 1393 y(B)1240 1419
y(@)1285 1303 y Fv(:)8 b(:)g(:)1285 1363 y(:)g(:)g(:)1285
1423 y(:)g(:)g(:)1285 1483 y(:)g(:)g(:)1350 1270 y Fs(1)1350
1343 y(C)1350 1368 y(C)1350 1393 y(C)1350 1419 y(A)1760
1393 y FH(\(10.4\))-5 1572 y(where)708 1688 y Fs(b)699
1704 y Fv(U)732 1711 y Ft(i)768 1704 y FH(=)828 1581
y Fs(0)828 1654 y(B)828 1679 y(B)828 1704 y(B)828 1731
y(@)910 1614 y FH(0)873 1674 y Fv(@)899 1681 y Ft(i)912
1674 y Fv(Y)952 1656 y Ft(I)910 1734 y FH(0)874 1794
y Fv(@)900 1801 y Ft(i)914 1794 y Fv(F)946 1801 y Ft(J)980
1581 y Fs(1)980 1654 y(C)980 1679 y(C)980 1704 y(C)980
1731 y(A)1038 1704 y FH(=)22 b Fv(@)1124 1711 y Ft(i)1153
1688 y Fs(b)1147 1704 y FH(\012)578 b(\(10.5\))-5 1867
y(So)16 b(w)o(e)e(ha)o(v)o(e)g(retriev)o(ed)f(eq.)h(4.50)p
 (#equation.4.50) [[197 319 218 331] [1 1 1 [3 3]] [0 0 1]] pdfm (,)i
(apart)g(from)d(the)i(iden)o(tically)e(zero)h(extra)h(en)o(tries.)20
b(Hence)13 b(w)o(e)i(can)-5 1928 y(set:)794 1997 y Fv(g)817
2004 y Ft(ij)845 1996 y Fm(?)888 1997 y FH(=)965 1964
y(1)p 953 1986 V 953 2032 a Fv(\026)982 2017 y FC(2)1017
1993 y Fs(b)1015 1997 y Fv(g)1038 2004 y Ft(ij)1066 1996
y Fm(?)1760 1997 y FH(\(10.6\))-5 2102 y(whic)o(h)h(is)g(consisten)o(t)
g(with)747 2158 y Fs(b)744 2162 y Fv(g)767 2169 y Ft(ij)795
2160 y Fm(?)838 2162 y FH(=)22 b FE(\000)8 b FH(i)g FE(h)995
2146 y Fs(b)986 2162 y Fv(U)1019 2169 y Ft(i)1034 2162
y FE(j)1056 2146 y Fs(b)1048 2162 y Fv(U)1081 2169 y
Ft(j)1097 2160 y Fm(?)1117 2162 y FE(i)624 b FH(\(10.7\))-5
2244 y(that)15 b(repro)q(duces)g(the)g(\014rst)g(of)g(eq.s)f(4.58)p
 (#equation.4.58) [[234 228 254 240] [1 1 1 [3 3]] [0 0 1]] pdfm (:)21
b(the)14 b(second)h(of)g(suc)o(h)f(equations)h(is)g(retriev)o(ed)d(b)o
(y)j(setting:)368 2371 y Fv(C)403 2378 y Ft(ij)r(k)475
2371 y FH(=)552 2337 y(1)p 540 2359 V 540 2405 a Fv(\026)569
2390 y FC(2)614 2354 y Fs(b)602 2371 y Fv(C)637 2378
y Ft(ij)r(k)706 2371 y FH(+)k FE(O)813 2298 y Fs( )863
2337 y FH(1)p 850 2359 V 850 2405 a Fv(\026)879 2390
y FC(3)904 2298 y Fs(!)1000 2371 y FH(=)-8 b FE(\))1154
2354 y Fs(b)1142 2371 y Fv(C)1177 2378 y Ft(ij)r(k)1249
2371 y FH(=)22 b FE(h)p Fv(@)1354 2378 y Ft(i)1377 2354
y Fs(b)1368 2371 y Fv(U)1406 2380 y Ft(j)1424 2371 y
FE(j)1447 2354 y Fs(b)1438 2371 y Fv(U)1471 2378 y Ft(k)1493
2371 y FE(i)248 b FH(\(10.8\))-5 2503 y(Finally)18 b(w)o(e)g(observ)o
(e)g(that)h(the)g(Levi{Civita)f(connection)g(\000)1151
2484 y Ft(i)1151 2515 y(j)r(k)1208 2503 y FH(is)h(not)g(rescaled)f(b)o
(y)g(an)o(y)h(p)q(o)o(w)o(er)g(of)-5 2563 y(the)i(Planc)o(k)f(mass)g
(since)g(it)g(con)o(tains)h(a)g(metric)d(and)k(an)f(in)o(v)o(erse)e
(metric)f(\(see)i(eq.)g(C.56)p
 (#equation.C.56) [[462 152 485 164] [1 1 1 [3 3]] [0 0 1]] pdfm (\).)
35 b(This)-5 2623 y(implies)14 b(the)i(follo)o(wing)g(rescaling)g(for)g
(the)g(Riemann)f(tensor)h(of)h(the)f(sp)q(ecial)g(manifold:)566
2740 y Fv(R)603 2747 y Ft(ij)631 2738 y Fm(?)649 2747
y Ft(k)q(`)682 2738 y Fm(?)725 2740 y FH(=)22 b Fv(g)808
2747 y Ft(ip)838 2738 y Fm(?)867 2740 y Fv(R)904 2717
y Ft(p)922 2705 y Fm(?)940 2753 y Ft(j)956 2744 y Fm(?)974
2753 y Ft(k)q(`)1007 2744 y Fm(?)1050 2740 y FH(=)1127
2707 y(1)p 1115 2729 V 1115 2775 a Fv(\026)1144 2760
y FC(2)1188 2724 y Fs(b)1177 2740 y Fv(R)1214 2747 y
Ft(ij)1242 2738 y Fm(?)1260 2747 y Ft(k)q(`)1293 2738
y Fm(?)1760 2740 y FH(\(10.9\))916 2892 y(47)p eop
%%Page: 48 49
48 48 bop -5 15 a FH(and)17 b(the)f(fundamen)o(tal)f(iden)o(tit)o(y)f
(of)j(lo)q(cal)f(sp)q(ecial)g(geometry)31 b(4.18)p
 (#equation.4.18) [[359 763 379 775] [1 1 1 [3 3]] [0 0 1]] pdfm 
17 w(b)q(ecomes)417 129 y Fs(b)406 145 y Fv(R)443 152
y Ft(ij)471 143 y Fm(?)489 152 y Ft(k)q(`)522 143 y Fm(?)565
145 y FH(=)643 111 y(1)p 630 133 50 2 v 630 179 a Fv(\026)659
165 y FC(2)693 145 y FH(\()714 141 y Fs(b)712 145 y Fv(g)735
152 y Ft(ij)763 143 y Fm(?)786 141 y Fs(b)783 145 y Fv(g)806
152 y Ft(k)q(`)839 143 y Fm(?)871 145 y FH(+)923 141
y Fs(b)920 145 y Fv(g)943 152 y Ft(k)q(j)978 143 y Fm(?)1002
141 y Fs(b)999 145 y Fv(g)1022 152 y Ft(i`)1048 143 y
Fm(?)1069 145 y FH(\))19 b(+)1176 129 y Fs(b)1165 145
y Fv(C)1200 152 y Ft(ik)q(s)1269 129 y Fs(b)1258 145
y Fv(C)1293 152 y Ft(t)1306 143 y Fm(?)1323 152 y Ft(j)1339
143 y Fm(?)1357 152 y Ft(`)1371 143 y Fm(?)1402 141 y
Fs(b)1400 145 y Fv(g)1425 124 y Ft(st)1454 113 y Fm(?)1736
145 y FH(\(10.10\))-5 277 y(that)f(in)g(the)f(limit)e
Fv(\026)25 b FE(!)f(1)17 b FH(repro)q(duces)h(the)g(fundamen)o(tal)e
(iden)o(tit)o(y)f(of)j(rigid)f(sp)q(ecial)h(geometry)-5
338 y(\(eq.)37 b(4.55)p
 (#equation.4.55) [[99 686 120 698] [1 1 1 [3 3]] [0 0 1]] pdfm (\).)68
398 y(Summarizing)14 b(w)o(e)i(ha)o(v)o(e:)506 482 y
Fu(R)n(esc)n(alings)i(in)f(the)h(Sp)n(e)n(cial)g(ge)n(ometry)g(se)n
(ctor)p 290 551 1301 2 v 315 661 a Fv(L)348 643 y FC(0)390
661 y FE(!)467 641 y FC(1)p 467 649 18 2 v 467 678 a(2)509
661 y FH(+)h FE(O)615 613 y Fs(\020)655 641 y FC(1)p
645 649 39 2 v 645 678 a Ft(\026)666 669 y Fr(2)689 613
y Fs(\021)1063 661 y Fv(L)1096 643 y Ft(I)1138 661 y
FE(!)1217 641 y FC(1)p 1215 649 22 2 v 1215 678 a Ft(\026)1250
661 y Fv(Y)1289 643 y Ft(I)1320 661 y FH(+)g FE(O)1426
613 y Fs(\020)1467 641 y FC(1)p 1456 649 39 2 v 1456
678 a Ft(\026)1477 669 y Fr(2)1500 613 y Fs(\021)315
736 y Fv(g)338 743 y Ft(ij)366 734 y Fm(?)408 736 y FE(!)496
716 y FC(1)p 485 724 V 485 753 a Ft(\026)506 743 y Fr(2)540
732 y Fs(b)537 736 y Fv(g)560 743 y Ft(ij)588 734 y Fm(?)628
736 y FH(+)g FE(O)735 688 y Fs(\020)775 716 y FC(1)p
765 724 V 765 753 a Ft(\026)786 743 y Fr(3)808 688 y
Fs(\021)1022 736 y Fv(C)1057 743 y Ft(ij)r(k)1128 736
y FE(!)1216 716 y FC(1)p 1205 724 V 1205 753 a Ft(\026)1226
743 y Fr(2)1269 720 y Fs(b)1257 736 y Fv(C)1292 743 y
Ft(ij)r(k)1361 736 y FH(+)g FE(O)1468 688 y Fs(\020)1508
716 y FC(1)p 1497 724 V 1497 753 a Ft(\026)1518 743 y
Fr(3)1541 688 y Fs(\021)315 871 y Fv(R)352 878 y Ft(ij)380
869 y Fm(?)398 878 y Ft(k)q(`)431 869 y Fm(?)474 871
y FE(!)570 851 y FC(1)p 559 859 V 559 888 a Ft(\026)580
878 y Fr(2)622 854 y Fs(b)611 871 y Fv(R)648 878 y Ft(ij)676
869 y Fm(?)694 878 y Ft(k)q(`)727 869 y Fm(?)767 871
y FH(+)h FE(O)874 822 y Fs(\020)914 851 y FC(1)p 904
859 V 904 888 a Ft(\026)925 878 y Fr(3)947 822 y Fs(\021)1208
871 y Fv(z)1233 853 y Ft(i)1269 871 y FE(!)1344 867 y
Fs(b)1341 871 y Fv(z)1366 853 y Ft(i)315 1006 y Fv(f)344
987 y FC(0)339 1018 y Ft(i)386 1006 y FE(!)473 986 y
FC(1)p 463 994 V 463 1023 a Ft(\026)484 1013 y Fr(2)526
989 y Fs(b)515 1006 y Fv(f)544 987 y FC(0)539 1018 y
Ft(i)575 1006 y FH(+)f FE(O)681 957 y Fs(\020)722 986
y FC(1)p 711 994 V 711 1023 a Ft(\026)732 1013 y Fr(3)755
957 y Fs(\021)1066 1006 y Fv(f)1095 987 y Ft(I)1090 1018
y(i)1137 1006 y FE(!)1216 986 y FC(1)p 1214 994 22 2
v 1214 1023 a Ft(\026)1260 989 y Fs(b)1248 1006 y Fv(f)1277
987 y Ft(I)1272 1018 y(i)1317 1006 y FH(+)g FE(O)1424
957 y Fs(\020)1464 986 y FC(1)p 1454 994 39 2 v 1454
1023 a Ft(\026)1475 1013 y Fr(3)1497 957 y Fs(\021)315
1137 y FH(\000)345 1119 y Ft(i)345 1149 y(j)r(k)405 1137
y FE(!)480 1121 y Fs(b)477 1137 y FH(\000)507 1119 y
Ft(i)507 1149 y(j)r(k)1178 1137 y FE(Q)i(!)1328 1117
y FC(1)p 1317 1125 V 1317 1154 a Ft(\026)1338 1145 y
Fr(2)1384 1121 y Fs(b)1369 1137 y FE(Q)p 290 1222 1301
2 v 1736 1318 a FH(\(10.11\))-5 1405 y(Next)15 b(w)o(e)h(consider)g
(the)g(rescalings)g(in)g(the)g(quaternionic)g(manifold)f(sector.)21
b(Here)15 b(w)o(e)h(set)449 1489 y Fu(R)n(esc)n(alings)h(in)h(the)g
(quaternionic)h(manifold)f(se)n(ctor)p 430 1558 1020
2 v 455 1665 a FE(U)491 1647 y Ft(\013A)565 1665 y FE(!)643
1645 y FC(1)p 642 1653 22 2 v 642 1682 a Ft(\026)687
1649 y Fs(b)676 1665 y FE(U)712 1647 y Ft(\013A)813 1665
y Fv(h)841 1672 y Ft(uv)904 1665 y FE(!)992 1645 y FC(1)p
981 1653 39 2 v 981 1682 a Ft(\026)1002 1673 y Fr(2)1034
1648 y Fs(b)1033 1665 y Fv(h)1061 1672 y Ft(uv)1239 1665
y Fv(q)1263 1647 y Ft(u)1307 1665 y FE(!)1383 1661 y
Fs(b)1379 1665 y Fv(q)1403 1647 y Ft(u)455 1796 y Fv(K)500
1778 y Ft(x)544 1796 y FE(!)632 1777 y FC(1)p 621 1785
V 621 1813 a Ft(\026)642 1804 y Fr(2)678 1780 y Fs(c)673
1796 y Fv(K)718 1778 y Ft(x)853 1796 y FH(\012)888 1778
y Ft(x)933 1796 y FE(!)1011 1780 y Fs(b)1005 1796 y FH(\012)1040
1778 y Ft(x)1152 1796 y FE(P)1191 1778 y Ft(x)1187 1809
y FC(\003)1235 1796 y FE(!)1323 1777 y FC(1)p 1312 1785
V 1312 1813 a Ft(\026)1333 1804 y Fr(2)1376 1780 y Fs(b)1364
1796 y FE(P)1403 1778 y Ft(x)1399 1809 y FC(\003)p 430
1882 1020 2 v 1736 1977 a FH(\(10.12\))-5 2064 y(Using)25
b(these)g(rescalings)f(the)h(quaternionic)f(algebra)50
b(5.22)p
 (#equation.5.22) [[333 272 354 284] [1 1 1 [3 3]] [0 0 1]] pdfm 
26 w(is)25 b(satis\014ed)g(b)o(y)f(the)h(rescaled)f(h)o(y-)-5
2125 y(p)q(erK\177)-24 b(ahler)19 b(structures)462 2108
y Fs(c)457 2125 y Fv(K)502 2106 y Ft(x)498 2137 y(uv)558
2125 y FH(as)h(m)o(uc)o(h)c(as)j(b)o(y)g(the)f(unrescaled)g(ones)h
Fv(K)1369 2106 y Ft(x)1365 2137 y(uv)1407 2125 y FH(:)26
b(ho)o(w)o(ev)o(er)17 b(the)h(relation)-5 2185 y(5.12)p
 (#equation.5.12) [[71 243 91 255] [1 1 1 [3 3]] [0 0 1]] pdfm 
17 w(b)q(et)o(w)o(een)e(the)g Fv(S)s(U)5 b FH(\(2\))16
b(curv)m(atures)h(and)g(the)f(h)o(yp)q(erK\177)-24 b(ahler)15
b(structures)1450 2169 y Fs(c)1445 2185 y Fv(K)1490 2167
y Ft(x)1486 2197 y(uv)1544 2185 y FH(b)q(ecomes:)809
2303 y Fs(b)803 2319 y FH(\012)838 2299 y Ft(x)883 2319
y FH(=)958 2286 y Fv(\025)p 948 2308 50 2 v 948 2354
a(\026)977 2339 y FC(2)1014 2303 y Fs(c)1010 2319 y Fv(K)1055
2299 y Ft(x)1736 2319 y FH(\(10.13\))-5 2463 y(and)25
b(in)f(the)g(limit)d Fv(\026)36 b FE(!)g(1)24 b FH(w)o(e)f(obtain)849
2447 y Fs(b)843 2463 y FH(\012)878 2445 y Ft(x)928 2463
y FH(=)k(0,)f(as)f(indeed)e(w)o(e)h(exp)q(ect)f(in)h(the)g(case)g(of)h
(a)-5 2524 y(h)o(yp)q(erK\177)-24 b(ahler)11 b(manifold.)19
b(Indeed)11 b(w)o(e)h(can)g(rephrase)g(this)g(result)f(b)o(y)h(sa)o
(ying)g(that,)g(up)q(on)h(restoration)-5 2584 y(of)k(ph)o(ysical)e
(units,)h(the)g Fv(S)s(U)5 b FH(\(2\){curv)m(ature)17
b(scale)f(is)855 2731 y Fv(\025)23 b FH(=)984 2680 y
Fs(b)981 2697 y Fv(\025)p 971 2719 V 971 2765 a(\026)1000
2750 y FC(2)1736 2731 y FH(\(10.14\))916 2892 y(48)p
eop
%%Page: 49 50
49 49 bop -5 15 a FH(and)14 b(in)g(the)f(in\014nite)g(Planc)o(k)f(mass)
i(limit)c(go)q(es)15 b(to)f(zero.)20 b(Indeed)13 b(when)h(w)o(e)f
(\014xed)g Fv(\025)h FH(=)g FE(\000)p FH(1)g(to)g(obtain)-5
76 y(canonical)21 b(kinetic)f(terms)g(this)h(v)m(alue)g(had)h(to)f(b)q
(e)h(in)o(terpreted)d(in)i(squared)h(Planc)o(k)e(mass)h(units)-5
136 y(\(namely)186 119 y Fs(b)184 136 y Fv(\025)14 b
FH(=)g FE(\000)p FH(1\).)21 b(Eq.s)16 b(10.12)p
 (#equation.10.12) [[193 734 219 746] [1 1 1 [3 3]] [0 0 1]] pdfm 
17 w(are)h(consisten)o(t)e(with)i(the)f(de\014nition)678
243 y FD(i)694 250 y FC(\003)725 227 y Fs(c)720 243 y
Fv(K)765 222 y Ft(x)787 243 y FE(P)826 222 y Ft(x)822
255 y FC(\003)871 243 y FH(=)22 b FE(r)984 227 y Fs(b)973
243 y FE(P)1012 222 y Ft(x)1008 255 y FC(\003)1056 243
y FH(=)g Fv(d)1153 227 y Fs(b)1141 243 y FE(P)1180 222
y Ft(x)1176 255 y FC(\003)1736 243 y FH(\(10.15\))-5
350 y(of)f(the)e(triholomorphic)f(momen)o(tum)e(map)j(on)i(h)o(yp)q
(erK\177)-24 b(ahler)19 b(manifolds.)31 b(The)20 b(last)g(equalit)o(y)e
(in)-5 410 y(eq.)c(10.15)p
 (#equation.10.15) [[89 669 115 681] [1 1 1 [3 3]] [0 0 1]] pdfm 
16 w(is)h(justi\014ed)g(b)o(y)f(the)h(v)m(anishing)g(of)g(the)g
Fv(S)s(U)5 b FH(\(2\))15 b(curv)m(ature)g(that)h(is)e(obtained)i(in)e
(the)h(limit)-5 470 y Fv(\026)23 b FE(!)f(1)p FH(.)f(Finally)15
b(the)h(rescaled)f(form)g(of)i(the)f(quaternionic)f(equiv)m(ariance)h
(eq.)f(7.54)p
 (#equation.7.54) [[439 654 460 666] [1 1 1 [3 3]] [0 0 1]] pdfm 
17 w(is)514 599 y FE(fP)574 606 y FC(\003)600 599 y Fv(;)8
b FE(P)657 606 y FC(\006)684 599 y FE(g)709 578 y Ft(x)744
599 y FE(\021)14 b FH(2)p Fv(K)866 578 y Ft(x)888 599
y FH(\(\003)p Fv(;)8 b FH(\006\))j FE(\000)1093 565 y
Fv(\025)p 1083 587 50 2 v 1083 633 a(\026)1112 619 y
FC(2)1145 599 y Fv(")1168 578 y Ft(xy)q(z)1235 599 y
FE(P)1274 575 y Ft(y)1270 611 y FC(\003)1305 599 y FE(P)1344
578 y Ft(z)1340 611 y FC(\006)1736 599 y FH(\(10.16\))-5
728 y(and)j(in)e(the)g(in\014nite)g(Planc)o(k)g(mass)h(limit)d(it)i
(\015o)o(ws)h(in)o(to)g(the)f(equiv)m(ariance)g(condition)g(of)h(momen)
o(tum)-5 788 y(maps)j(for)g(h)o(yp)q(erK\177)-24 b(ahler)16
b(manifolds,)f(that)h(is)g(eq.)f(7.50)p
 (#equation.7.50) [[299 578 319 590] [1 1 1 [3 3]] [0 0 1]] pdfm (.)68
849 y(T)l(o)k(complete)d(our)i(rigid)g(limit)d(programme)i(w)o(e)g(ha)o
(v)o(e)g(to)i(prescrib)q(e)e(the)h(appropriate)h(Planc)o(k)-5
909 y(mass)d(rescalings)g(for)h(the)f(space{time)e(\014elds)i(and)h
(the)f(fermions.)k(These)c(are)g(as)h(follo)o(ws:)469
993 y Fu(R)n(esc)n(alings)h(of)f(sp)n(ac)n(e{time)h(\014elds)g(and)g
(fermions)p 437 1058 1007 2 v 462 1165 a Fv(V)501 1147
y Ft(a)544 1165 y FE(!)623 1145 y FC(1)p 621 1153 22
2 v 621 1182 a Ft(\026)664 1149 y Fs(b)655 1165 y Fv(V)695
1147 y Ft(a)809 1165 y Fv(g)832 1172 y Ft(\026\027)897
1165 y FE(!)985 1145 y FC(1)p 974 1153 39 2 v 974 1182
a Ft(\026)995 1172 y Fr(2)1028 1161 y Fs(b)1026 1165
y Fv(g)1049 1172 y Ft(\026\027)1222 1165 y Fv(x)1250
1147 y Ft(\026)1296 1165 y FE(!)1371 1161 y Fs(b)1368
1165 y Fv(x)1396 1147 y Ft(\026)462 1295 y Fv(!)494 1277
y Ft(ab)552 1295 y FE(!)628 1291 y Fs(b)624 1295 y Fv(!)656
1277 y Ft(ab)832 1295 y Fv(A)869 1277 y FC(0)910 1295
y FE(!)989 1275 y FC(1)p 987 1283 22 2 v 987 1312 a Ft(\026)1027
1279 y Fs(b)1013 1295 y Fv(A)1050 1277 y FC(0)1163 1295
y Fv(A)1200 1277 y Ft(I)1242 1295 y FE(!)1329 1275 y
FC(1)p 1319 1283 39 2 v 1319 1312 a Ft(\026)1340 1302
y Fr(2)1376 1279 y Fs(b)1362 1295 y Fv(A)1399 1277 y
Ft(I)462 1425 y Fv( )494 1432 y Ft(A)544 1425 y FE(!)638
1406 y FC(1)p 621 1414 51 2 v 621 1422 a FB(p)p 650 1422
22 2 v 20 x Ft(\026)696 1409 y Fs(b)685 1425 y Fv( )717
1432 y Ft(A)795 1425 y Fv(\025)823 1407 y Ft(iA)886 1425
y FE(!)958 1394 y(p)p 1000 1394 30 2 v 31 x Fv(\026)1040
1409 y Fs(b)1037 1425 y Fv(\025)1065 1407 y Ft(iA)1156
1425 y Fv(\020)1181 1407 y Ft(\013)1228 1425 y FE(!)1321
1406 y FC(1)p 1305 1414 51 2 v 1305 1422 a FB(p)p 1334
1422 22 2 v 20 x Ft(\026)1374 1409 y Fs(b)1369 1425 y
Fv(\020)1394 1407 y Ft(\013)p 437 1515 1007 2 v 1736
1607 a FH(\(10.17\))-5 1693 y(Utilizing)13 b(the)i(rescalings)f(of)i
(eq.s)e(10.11)p
 (#equation.10.11) [[227 361 253 373] [1 1 1 [3 3]] [0 0 1]] pdfm (,)h
(10.12)p
 (#equation.10.12) [[260 361 286 373] [1 1 1 [3 3]] [0 0 1]] pdfm 
16 w(and)h(10.17)p
 (#equation.10.17) [[313 361 339 373] [1 1 1 [3 3]] [0 0 1]] pdfm 
16 w(in)e(the)h(curv)m(ature)g(de\014nitions)f(8.4)p
 (#equation.8.4) [[484 361 499 373] [1 1 1 [3 3]] [0 0 1]] pdfm (,)h
(8.5)p  (#equation.8.4) [[506 361 521 373] [1 1 1 [3 3]] [0 0 1]] pdfm 
(,)-5 1753 y(8.6)p
 (#equation.8.4) [[71 346 86 358] [1 1 1 [3 3]] [0 0 1]] pdfm (,)47
b(8.7)p  (#equation.8.4) [[100 346 115 358] [1 1 1 [3 3]] [0 0 1]] pdfm 
(,)23 b(8.9)p
 (#equation.8.9) [[124 346 139 358] [1 1 1 [3 3]] [0 0 1]] pdfm (,)f
(8.10)p  (#equation.8.9) [[148 346 168 358] [1 1 1 [3 3]] [0 0 1]] pdfm 
(,)h(8.11)p
 (#equation.8.9) [[177 346 198 358] [1 1 1 [3 3]] [0 0 1]] pdfm (,)g
(8.11)p  (#equation.8.9) [[207 346 227 358] [1 1 1 [3 3]] [0 0 1]] pdfm 
(,)47 b(8.11)p
 (#equation.8.9) [[242 346 263 358] [1 1 1 [3 3]] [0 0 1]] pdfm (,)23
b(8.12)p
 (#equation.8.12) [[271 346 292 358] [1 1 1 [3 3]] [0 0 1]] pdfm (,)g
(8.13)p
 (#equation.8.12) [[301 346 322 358] [1 1 1 [3 3]] [0 0 1]] pdfm (,)g
(8.14)p
 (#equation.8.12) [[330 346 351 358] [1 1 1 [3 3]] [0 0 1]] pdfm 
23 w(and)g(in)g(the)f(curv)m(ature)h(rheonomic)-5 1813
y(parametrization)c(giv)o(en)h(in)g(App)q(endix)g(B,)f(b)o(y)h(p)q
(erforming)g(the)g(limit)e Fv(\026)29 b FE(!)g(1)20 b
FH(w)o(e)g(obtain)h(the)-5 1874 y(rheonomic)c(parametrization)f(and)j
(curv)m(ature)e(de\014nition)h(of)g(the)g(rigid)f(theory)l(.)26
b(Indeed)17 b(the)h(\014rst)-5 1934 y(four)f(equations)f(A.23)p
 (#equation.A.23) [[148 303 171 315] [1 1 1 [3 3]] [0 0 1]] pdfm (,)g
(A.24)p
 (#equation.A.23) [[179 303 202 315] [1 1 1 [3 3]] [0 0 1]] pdfm (,)g
(A.25)p
 (#equation.A.23) [[210 303 233 315] [1 1 1 [3 3]] [0 0 1]] pdfm 
16 w(b)q(ecome:)567 2041 y Fv(T)603 2020 y Ft(a)665 2041
y FE(\021)41 b Fv(dV)810 2020 y Ft(a)850 2041 y FE(\000)19
b Fv(!)940 2020 y Ft(ab)995 2041 y FE(^)h Fv(V)1087 2020
y Ft(c)1113 2041 y Fv(\021)1137 2048 y Ft(bc)1191 2041
y FH(=)j(0)570 2133 y Fv(\032)595 2140 y Ft(A)665 2133
y FE(\021)41 b Fv(d )802 2140 y Ft(A)850 2133 y FE(\000)913
2099 y FH(1)p 913 2121 25 2 v 913 2167 a(4)951 2133 y
Fv(!)983 2112 y Ft(ab)1038 2133 y FE(^)20 b Fv(\015)1116
2140 y Ft(ab)1160 2133 y Fv( )1192 2140 y Ft(A)1243 2133
y FH(=)i(0)570 2249 y Fv(\032)595 2229 y Ft(A)665 2249
y FE(\021)41 b Fv(d )804 2229 y Ft(A)852 2249 y FE(\000)915
2216 y FH(1)p 915 2238 V 915 2283 a(4)952 2249 y Fv(!)984
2229 y Ft(ab)1040 2249 y FE(^)19 b Fv(\015)1117 2256
y Ft(ab)1162 2249 y Fv( )1196 2229 y Ft(A)1246 2249 y
FH(=)j(0)550 2344 y Fv(R)587 2323 y Ft(ab)665 2344 y
FE(\021)41 b Fv(d!)802 2323 y Ft(ab)858 2344 y FE(\000)19
b Fv(!)948 2323 y Ft(ac)1003 2344 y FE(^)h Fv(!)1088
2323 y Ft(cd)1132 2344 y Fv(\021)1156 2351 y Ft(cd)1214
2344 y FH(=)i(0)438 b(\(10.18\))-5 2451 y(that)17 b(are)f(the)g
(structural)g(equations)h(of)f(N=2)h(rigid)e(sup)q(erspace)i(if)f(they)
g(are)g(completed)e(with)348 2577 y Fv(F)387 2556 y FC(0)428
2577 y FE(\021)22 b Fv(dA)551 2556 y FC(0)590 2577 y
FH(+)673 2543 y(1)p 653 2565 66 2 v 653 2574 a FE(p)p
694 2574 25 2 v 694 2615 a FH(2)740 2529 y Fs(h)p 760
2537 34 2 v 48 x Fv( )793 2589 y Ft(A)841 2577 y FE(^)e
Fv( )926 2584 y Ft(B)964 2577 y Fv(")987 2556 y Ft(AB)1063
2577 y FH(+)p 1120 2537 V 19 w Fv( )1154 2547 y Ft(A)1202
2577 y FE(^)f Fv( )1288 2556 y Ft(B)1326 2577 y Fv(")1349
2584 y Ft(AB)1406 2529 y Fs(i)1448 2577 y FH(=)j(0)204
b(\(10.19\))-5 2707 y(Eq.)12 b(10.19)p
 (#equation.10.19) [[91 117 118 129] [1 1 1 [3 3]] [0 0 1]] pdfm 
14 w(is)h(precisely)e(what)i(w)o(e)f(obtain)h(in)g(the)f
Fv(\026)23 b FE(!)f(1)12 b FH(limit)e(from)i(the)g(case)h(\003)g(=)h(0)
f(of)g(eq.s)f(A.27)p
 (#equation.A.27) [[501 117 524 129] [1 1 1 [3 3]] [0 0 1]] pdfm 
-5 2768 a(and)27 b(8.11)p
 (#equation.8.9) [[96 103 117 115] [1 1 1 [3 3]] [0 0 1]] pdfm (.)21
b(Algebraically)11 b(eq.)i(10.19)p
 (#equation.10.19) [[213 103 240 115] [1 1 1 [3 3]] [0 0 1]] pdfm 
14 w(tells)f(us)i(that)f(the)g(gra)o(viphoton)h(one{form)f(is)g(the)g
(dual)g(of)g(the)916 2892 y(49)p eop
%%Page: 50 51
50 50 bop -5 15 a FH(cen)o(tral)18 b(c)o(harge)g(generator.)28
b(The)19 b(case)f(\003)f(=)h Fv(I)k FH(of)c(the)h(same)e(equations)i
(pro)o(vides)e(the)i(de\014nition)-5 76 y(and)e(rheonomic)e
(parametrization)g(of)h(the)g(Y)l(ang{Mills)g(curv)m(atures)g(in)g
(rigid)g(sup)q(erspace:)198 196 y Fv(F)237 176 y Ft(I)297
196 y FE(\021)42 b Fv(dA)440 176 y Ft(I)479 196 y FH(+)541
163 y(1)p 541 185 25 2 v 541 230 a(2)579 196 y Fv(g)10
b(f)641 176 y Ft(I)654 209 y(J)s(K)719 196 y Fv(A)756
176 y Ft(J)800 196 y FE(^)19 b Fv(A)889 176 y Ft(K)923
196 y Fv(;)8 b FH(+)p 991 157 40 2 v 8 w Fv(Y)1030 167
y Ft(I)p 1050 157 34 2 v 1050 196 a Fv( )1084 208 y Ft(A)1123
196 y FE(^)j Fv( )1199 203 y Ft(B)1229 196 y Fv(\017)1249
176 y Ft(AB)1317 196 y FH(+)g Fv(Y)1405 176 y Ft(I)p
1425 157 V 1425 196 a Fv( )1459 167 y Ft(A)1498 196 y
FE(^)g Fv( )1576 176 y Ft(B)1606 196 y Fv(\017)1626 203
y Ft(AB)298 300 y FH(=)42 b Fv(F)417 280 y Ft(I)410 312
y(ab)445 300 y Fv(V)484 280 y Ft(a)516 300 y FE(^)12
b Fv(V)600 280 y Ft(b)628 300 y FH(+)677 252 y Fs(\020)702
300 y FH(i)c Fv(f)753 280 y Ft(I)748 312 y(i)p 781 261
29 2 v 781 300 a Fv(\025)810 270 y Ft(iA)850 300 y Fv(\015)875
307 y Ft(a)896 300 y Fv( )930 280 y Ft(B)969 300 y Fv(\017)989
307 y Ft(AB)1056 300 y FH(+)j(i)p 1127 261 30 2 v 8 w
Fv(f)1156 270 y Ft(I)1156 312 y(i)1168 303 y Fm(?)p 1197
261 29 2 v 1197 300 a Fv(\025)1225 270 y Ft(i)1237 259
y Fm(?)1225 312 y Ft(A)1257 300 y Fv(\015)1282 307 y
Ft(a)1303 300 y Fv( )1335 307 y Ft(B)1374 300 y Fv(\017)1394
280 y Ft(AB)1450 252 y Fs(\021)1486 300 y FE(^)g Fv(V)1570
280 y Ft(a)1736 300 y FH(\(10.20\))-5 401 y(F)l(rom)g(the)g
Fv(\026)23 b FE(!)f(1)11 b FH(limit)e(of)j(eq.)f(A.28)p
 (#equation.A.27) [[221 671 244 683] [1 1 1 [3 3]] [0 0 1]] pdfm 
11 w(and)h(A.29)p
 (#equation.A.27) [[269 671 292 683] [1 1 1 [3 3]] [0 0 1]] pdfm 
12 w(w)o(e)f(obtain)h(the)g(gaugino)h(curv)m(ature)e(parametriza-)-5
462 y(tions:)292 563 y FE(r)p Fv(\025)362 542 y Ft(iA)444
563 y FH(=)42 b FE(r)566 570 y Ft(a)586 563 y Fv(\025)614
542 y Ft(iA)655 563 y Fv(V)694 542 y Ft(a)726 563 y FH(+)11
b(i)d Fv(Z)834 542 y Ft(i)830 575 y(a)851 563 y Fv(\015)879
542 y Ft(a)900 563 y Fv( )934 542 y Ft(A)973 563 y FH(+)j
Fv(G)1060 542 y FB(\000)p Ft(i)1060 575 y(ab)1102 563
y Fv(\015)1130 542 y Ft(ab)1166 563 y Fv( )1198 570 y
Ft(B)1228 563 y Fv(\017)1248 542 y Ft(AB)1315 563 y FH(+)g
Fv(D)1405 542 y Ft(i)p FB(j)p Ft(AB)1485 563 y Fv( )1517
570 y Ft(B)301 644 y FE(r)p Fv(\025)371 624 y Ft(i)383
612 y Fm(?)371 657 y Ft(A)444 644 y FH(=)42 b FE(r)566
651 y Ft(a)586 644 y Fv(\025)614 624 y Ft(i)626 612 y
Fm(?)614 657 y Ft(A)646 644 y Fv(V)686 624 y Ft(a)718
644 y FH(+)11 b(i)p 789 605 37 2 v 8 w Fv(Z)825 615 y
Ft(i)837 603 y Fm(?)825 657 y Ft(a)857 644 y Fv(\015)885
624 y Ft(a)906 644 y Fv( )938 651 y Ft(A)978 644 y FH(+)g
Fv(G)1065 624 y FC(+)p Ft(i)1104 612 y Fm(?)1065 657
y Ft(ab)1125 644 y Fv(\015)1153 624 y Ft(ab)1188 644
y Fv( )1222 624 y Ft(B)1252 644 y Fv(\017)1272 651 y
Ft(AB)1340 644 y FH(+)g Fv(D)1430 624 y Ft(i)1442 612
y Fm(?)1459 657 y Ft(AB)1524 644 y Fv( )1558 624 y Ft(B)1736
644 y FH(\(10.21\))-5 746 y(where)j Fv(Z)171 728 y Ft(i)167
758 y(a)202 746 y FH(and)g Fv(Z)331 728 y Ft(i)343 716
y Fm(?)327 758 y Ft(a)377 746 y FH(are)g(de\014ned)g(b)o(y)f(eq.)g
(A.30)p
 (#equation.A.27) [[255 588 279 600] [1 1 1 [3 3]] [0 0 1]] pdfm 
14 w(and)h(its)g(complex)d(conjugate)k(that)f(surviv)o(e)f(unmo)q(di-)
-5 806 y(\014ed)f(in)g(the)g(limit)d(while)j Fv(G)490
785 y FB(\006)p Ft(i)529 773 y Fm(?)490 818 y Ft(ab)562
806 y FH(and)h(the)e(auxiliary)h(\014elds)f Fv(D)1093
788 y Ft(i)p FB(j)p Ft(AB)1173 806 y FH(,)h Fv(D)1240
788 y Ft(i)1252 776 y Fm(?)1270 818 y Ft(AB)1339 806
y FH(are)g(giv)o(en)f(in)h(eq.s)f(10.35)p
 (#equation.10.35) [[476 574 503 586] [1 1 1 [3 3]] [0 0 1]] pdfm (.)21
b(As)-5 866 y(usual)e(the)f(rheonomic)f(parametrizations)g(corresp)q
(ond)j(to)e(the)h(sup)q(ersymmetry)c(transformation)-5
926 y(rules)j(that)h(w)o(e)f(ha)o(v)o(e)g(collected)e(in)j(the)f(next)g
(subsection)g(together)h(with)f(the)g(space{time)f(action)-5
986 y(for)f(the)g(b)q(ene\014t)g(of)g(those)g(readers)g(who)g(do)q(e)g
(not)h(w)o(an)o(t)e(to)i(get)e(in)o(v)o(olv)o(ed)f(with)i(the)f
(rheonom)o(y)g(for-)-5 1047 y(malism.)21 b(Also)c(the)g(rheonomic)f
(parametrizations)g(A.32)p
 (#equation.A.32) [[310 516 334 528] [1 1 1 [3 3]] [0 0 1]] pdfm (,)34
b(A.33)p
 (#equation.A.32) [[346 516 369 528] [1 1 1 [3 3]] [0 0 1]] pdfm (,)17
b(A.34)p
 (#equation.A.32) [[377 516 401 528] [1 1 1 [3 3]] [0 0 1]] pdfm 
17 w(man)o(tain)f(the)h(same)f(form)-5 1107 y(in)g(the)g(rigid)f
(limit,)e(but)j(the)g(h)o(yp)q(erino)f(shifts)h Fv(N)926
1089 y Ft(\013)921 1119 y(A)951 1107 y Fv(;)8 b(N)1017
1089 y Ft(A)1012 1119 y(\013)1062 1107 y FH(are)15 b(no)o(w)i(giv)o(en)
e(b)o(y)g(eq.s)g(10.35)p
 (#equation.10.35) [[440 501 467 513] [1 1 1 [3 3]] [0 0 1]] pdfm (.)23
b(Using)15 b(the)-5 1167 y(same)h(scaling)g(limit)d(one)k(obtains)g
(the)f(rigid)f(rheonomic)g(action)i(\(whic)o(h)e(w)o(e)h(do)h(not)f
(rep)q(ort\))h(from)-5 1227 y(whic)o(h)f(one)g(retriev)o(es)f(the)h
(space{time)e(action)j(rep)q(orted)f(in)g(the)g(next)g(subsection.)-5
1370 y Fk(10.2)66 b(Summary)24 b(of)e(the)g(rigid)i(N=2)e(Y)-6
b(ang{Mills)24 b(theory)-5 1463 y FH(Let)17 b(us)f(then)g(summarize)d
(our)j(results)g(b)o(y)g(writing)g(the)g(\014nal)g(most)f(general)h
(form)f(of)h(N=2)g(matter)-5 1523 y(coupled)f(Y)l(ang{Mills)f(theory)l
(.)21 b(Suc)o(h)14 b(a)i(theory)e(arises)h(from)f(a)h(generic)f(c)o
(hoice)g(of)h(the)g(rigid)g(sp)q(ecial)-5 1583 y(manifold)c
FE(S)t(M)287 1590 y Ft(r)q(ig)336 1583 y FH(,)h(a)h(generic)e(c)o
(hoice)g(of)h(the)g(Hyp)q(erk\177)-24 b(ahler)11 b(manifold)g
FE(HM)1407 1590 y Ft(r)q(ig)1468 1583 y FH(and)i(a)f(generic)f(c)o
(hoice)-5 1643 y(of)17 b(the)f Fu(gauging)p FH(.)68 1703
y(Let:)439 1773 y FE(F)480 1753 y Ft(I)521 1773 y FE(\021)22
b Fv(dA)644 1753 y Ft(I)683 1773 y FH(+)746 1740 y(1)p
746 1762 25 2 v 746 1808 a(2)783 1773 y Fv(f)812 1753
y Ft(I)825 1786 y(J)s(K)882 1773 y Fv(A)919 1753 y Ft(J)962
1773 y FE(^)12 b Fv(A)1044 1753 y Ft(K)1086 1773 y FH(=)c
FE(F)1173 1753 y Ft(I)1168 1786 y(\026\027)1219 1773
y Fv(dx)1272 1753 y Ft(\026)1315 1773 y FE(^)19 b Fv(dx)1420
1753 y Ft(\027)1736 1773 y FH(\(10.22\))-5 1875 y(b)q(e)c(the)g
(\014eld{strengths)h(of)f(the)g(gauge)h(group)g FE(G)s
FH(.)21 b(Let)15 b Fv(z)1058 1857 y Ft(i)1087 1875 y
FH(b)q(e)g(the)g(co)q(ordinates)h(of)f(the)g(rigid)g(sp)q(ecial)-5
1935 y(manifold)22 b FE(S)t(M)298 1942 y Ft(r)q(ig)347
1935 y FH(,)i(whose)g(complex)d(dimension)h Fv(n)h FH(equals)g(the)g
(real)g(dimension)f(of)h(the)g(gauge)-5 1995 y(group)16
b(and)f(let)f Fv(q)318 1977 y Ft(u)355 1995 y FH(b)q(e)g(the)h(4)8
b Fv(m)15 b FH(co)q(ordinates)g(of)g(the)g(Hyp)q(erk\177)-24
b(ahler)13 b(manifold)g FE(HM)1566 2002 y Ft(r)q(ig)1615
1995 y FH(.)21 b(In)14 b(addition)-5 2055 y(let)21 b
Fv(\025)99 2037 y Ft(iA)140 2055 y Fv(;)8 b(\025)190
2037 y Ft(i)202 2026 y Fm(?)190 2068 y Ft(A)243 2055
y FH(b)q(e)22 b(the)f(t)o(w)o(o)g(c)o(hiral)f(pro)s(jections)h(of)g
(the)g(gaugino)i(\014eld)d(and)i Fv(\020)1467 2037 y
Ft(\013)1492 2055 y Fv(;)8 b(\020)1535 2062 y Ft(\013)1581
2055 y FH(the)21 b(t)o(w)o(o)g(c)o(hiral)-5 2116 y(pro)s(jections)16
b(of)h(the)f(h)o(yp)q(erino)g(\014eld.)k(Let)d(us)f(moreo)o(v)o(er)e
(de\014ne)i(:)487 2217 y Fu(the)i(c)n(ovariant)f(derivatives)i(of)e
(the)h(Bose)g(\014elds)262 2290 y FE(r)304 2297 y Ft(\026)327
2290 y Fv(z)352 2269 y Ft(i)407 2290 y FH(=)42 b Fv(@)513
2297 y Ft(\026)536 2290 y Fv(z)561 2269 y Ft(i)594 2290
y FH(+)19 b Fv(g)11 b(A)722 2269 y Ft(I)722 2302 y(\026)753
2290 y Fv(k)780 2269 y Ft(i)778 2302 y(I)262 2369 y FE(r)304
2376 y Ft(\026)327 2369 y Fv(z)352 2348 y Ft(i)407 2369
y FH(=)42 b Fv(@)513 2376 y Ft(\026)p 536 2342 V 536
2369 a Fv(z)561 2348 y Ft(i)594 2369 y FH(+)19 b Fv(g)g(A)730
2348 y Ft(I)730 2381 y(\026)761 2369 y Fv(k)788 2348
y Ft(i)800 2336 y Fm(?)786 2381 y Ft(I)255 2447 y FE(r)297
2454 y Ft(\026)320 2447 y Fv(q)344 2427 y Ft(u)407 2447
y FH(=)42 b Fv(@)513 2454 y Ft(\026)536 2447 y Fv(q)560
2427 y Ft(u)601 2447 y FH(+)19 b Fv(g)g(A)737 2427 y
Ft(I)737 2460 y(\026)768 2447 y Fv(k)795 2427 y Ft(u)793
2460 y(I)877 2520 y FH(and)487 2593 y Fu(the)f(c)n(ovariant)f
(derivatives)i(of)e(the)h(F)l(ermi)f(\014elds)232 2665
y FE(r)274 2672 y Ft(\026)297 2665 y Fv(\025)325 2645
y Ft(iA)407 2665 y FH(=)42 b Fv(@)513 2672 y Ft(\026)536
2665 y Fv(\025)564 2645 y Ft(iA)624 2665 y FH(+)681 2617
y Fs(\020)706 2665 y FH(\000)736 2645 y Ft(i)736 2678
y(j)r(k)783 2665 y FE(r)825 2672 y Ft(\026)847 2665 y
Fv(z)872 2645 y Ft(j)910 2665 y FH(+)19 b Fv(g)11 b(A)1038
2645 y Ft(I)1038 2678 y(\026)1069 2665 y Fv(@)1095 2672
y Ft(j)1113 2665 y Fv(k)1140 2645 y Ft(i)1138 2678 y(I)1158
2617 y Fs(\021)1200 2665 y Fv(\025)1228 2645 y Ft(j)r(A)240
2759 y FE(r)282 2766 y Ft(\026)305 2759 y Fv(\025)333
2739 y Ft(i)345 2727 y Fm(?)333 2772 y Ft(A)407 2759
y FH(=)42 b Fv(@)513 2766 y Ft(\026)536 2759 y Fv(\025)564
2739 y Ft(i)576 2727 y Fm(?)564 2772 y Ft(A)616 2759
y FH(+)673 2711 y Fs(\020)p 698 2720 31 2 v 48 x FH(\000)728
2730 y Ft(i)740 2718 y Fm(?)728 2772 y Ft(j)744 2762
y Fm(?)762 2772 y Ft(k)781 2762 y Fm(?)810 2759 y FE(r)852
2766 y Ft(\026)p 875 2733 25 2 v 875 2759 a Fv(z)900
2739 y Ft(j)916 2727 y Fm(?)955 2759 y FH(+)20 b Fv(g)10
b(A)1083 2739 y Ft(I)1083 2772 y(\026)1114 2759 y Fv(@)1140
2766 y Ft(j)1156 2757 y Fm(?)1176 2759 y Fv(k)1203 2739
y Ft(i)1215 2727 y Fm(?)1201 2772 y Ft(I)1235 2711 y
Fs(\021)1277 2759 y Fv(\025)1305 2736 y Ft(j)1321 2724
y Fm(?)1305 2772 y Ft(A)916 2892 y FH(50)p eop
%%Page: 51 52
51 51 bop 251 15 a FE(r)293 22 y Ft(\026)316 15 y Fv(\020)341
-5 y Ft(\013)407 15 y FH(=)42 b Fv(@)513 22 y Ft(\026)536
15 y Fv(\020)561 -5 y Ft(\013)605 15 y FH(+)662 -33 y
Fs(\020)687 15 y FH(\001)728 -5 y Ft(\013\014)728 28
y(u)782 15 y FE(r)824 22 y Ft(\026)847 15 y Fv(q)871
-5 y Ft(u)912 15 y FH(+)20 b Fv(g)10 b(A)1040 -5 y Ft(I)1040
28 y(\026)1071 15 y Fv(@)1097 22 y Ft(u)1120 15 y Fv(k)1147
-5 y Ft(v)1145 28 y(I)1175 15 y FE(U)1211 -5 y Ft(u)p
FB(j)p Ft(\013A)1301 15 y FE(U)1337 -5 y Ft(\014)r(B)1332
28 y(v)1397 15 y Fv(")1420 22 y Ft(AB)1477 -33 y Fs(\021)p
1527 15 2 33 v 1514 15 a FH(C)1549 22 y Ft(\014)r(\015)1601
15 y Fv(\020)1626 -5 y Ft(\015)258 107 y FE(r)300 114
y Ft(\026)322 107 y Fv(\020)343 114 y Ft(\015)407 107
y FH(=)42 b Fv(@)513 114 y Ft(\026)536 107 y Fv(\020)557
114 y Ft(\015)599 107 y FH(+)p 664 107 V 14 w(C)687 114
y Ft(\015)r(\013)740 59 y Fs(\020)765 107 y FH(\001)806
86 y Ft(\013\014)806 119 y(u)860 107 y FE(r)902 114 y
Ft(\026)925 107 y Fv(q)949 86 y Ft(u)990 107 y FH(+)19
b Fv(g)11 b(A)1118 86 y Ft(I)1118 119 y(\026)1149 107
y Fv(@)1175 114 y Ft(u)1197 107 y Fv(k)1224 86 y Ft(v)1222
119 y(I)1253 107 y FE(U)1289 86 y Ft(u)p FB(j)p Ft(\013A)1379
107 y FE(U)1415 86 y Ft(\014)r(B)1410 119 y(v)1475 107
y Fv(")1498 114 y Ft(AB)1554 59 y Fs(\021)1596 107 y
Fv(\020)1617 114 y Ft(\014)1736 107 y FH(\(10.23\))-5
217 y(In)h(terms)e(of)i(these)f(\014eld)g(strengths)h(and)h(deriv)m
(ativ)o(es)d(and)i(of)g(all)f(the)h(geometric)d(structures)j(p)q
(ertain-)-5 277 y(ing)i(to)g(rigid)g(sp)q(ecial)f(manifolds)f(and)j(to)
f(h)o(yp)q(erK\177)-24 b(ahler)13 b(manifolds)g(discussed)g(in)h
(previous)f(sections)-5 337 y(the)j(most)g(general)g(N=2)g(sup)q
(ersymmetric)d(in)o(v)m(arian)o(t)i(lagrangian)j(has)f(the)f(follo)o
(wing)g(form:)p 502 454 877 2 v 527 557 a Fu(Matter)h(c)n(ouple)n(d)h
(N=2)g(Y)l(ang)g(Mil)r(ls)h(action)p 502 637 V 342 743
a FE(L)k FH(=)f FE(L)493 750 y Ft(k)q(in)567 743 y FH(+)d
FE(L)658 750 y Ft(P)5 b(auli)770 743 y FH(+)19 b FE(L)861
750 y Ft(massmatr)q(ix)1077 743 y FH(+)g FE(L)1168 750
y Ft(potential)1330 743 y FH(+)g FE(L)1421 750 y FC(4)p
Ft(f)t(er)q(mi)1736 743 y FH(\(10.24\))-5 830 y(where)167
940 y FE(L)201 947 y Ft(k)q(in)278 940 y FH(=)j(i)360
892 y Fs(\020)p 385 901 49 2 v 48 x FE(N)433 947 y Ft(I)s(J)484
940 y FE(F)525 920 y Ft(I)s FB(\000)520 953 y Ft(\026\027)580
940 y FE(F)621 920 y Ft(J)s FB(\000j)p Ft(\026\027)743
940 y FE(\000)d(N)842 947 y Ft(I)s(J)892 940 y FE(F)933
920 y Ft(I)s FC(+)928 953 y Ft(\026\027)989 940 y FE(F)1030
920 y Ft(J)s FC(+)p FB(j)p Ft(\026\027)1132 892 y Fs(\021)269
1026 y FH(+)h Fv(g)350 1033 y Ft(ij)378 1024 y Fm(?)406
1026 y FE(r)448 1005 y Ft(\026)471 1026 y Fv(z)496 1005
y Ft(i)519 1026 y FE(r)561 1033 y Ft(\026)p 583 999 25
2 v 583 1026 a Fv(z)608 1005 y Ft(j)624 994 y Fm(?)664
1026 y FH(+)f Fv(h)749 1033 y Ft(uv)798 1026 y FE(r)840
1005 y Ft(\026)863 1026 y Fv(q)887 1005 y Ft(u)917 1026
y FE(r)959 1033 y Ft(\026)982 1026 y Fv(q)1006 1005 y
Ft(v)269 1123 y FE(\000)338 1089 y FH(i)p 332 1112 V
332 1157 a(2)370 1123 y Fv(g)393 1130 y Ft(ij)421 1121
y Fm(?)450 1075 y Fs(\020)p 475 1084 29 2 v 48 x Fv(\025)503
1093 y Ft(iA)552 1123 y Fv(\015)580 1103 y Ft(\026)612
1123 y FE(r)654 1130 y Ft(\026)676 1123 y Fv(\025)704
1100 y Ft(j)720 1088 y Fm(?)704 1135 y Ft(A)761 1123
y FH(+)p 818 1084 V 19 w Fv(\025)846 1093 y Ft(j)862
1082 y Fm(?)846 1135 y Ft(A)891 1123 y Fv(\015)919 1103
y Ft(\026)950 1123 y FE(r)992 1130 y Ft(\026)1015 1123
y Fv(\025)1043 1103 y Ft(iA)1084 1075 y Fs(\021)269 1224
y FE(\000)g FH(i)341 1176 y Fs(\020)p 366 1184 26 2 v
48 x Fv(\020)391 1194 y Ft(\013)424 1224 y Fv(\015)452
1203 y Ft(\026)483 1224 y FE(r)525 1231 y Ft(\026)548
1224 y Fv(\020)569 1231 y Ft(\013)614 1224 y FH(+)p 671
1184 V 19 w Fv(\020)696 1235 y Ft(\013)729 1224 y Fv(\015)757
1203 y Ft(\026)789 1224 y FE(r)831 1231 y Ft(\026)854
1224 y Fv(\020)879 1203 y Ft(\013)903 1176 y Fs(\021)1736
1224 y FH(\(10.25\))167 1331 y FE(L)201 1338 y Ft(P)5
b(auli)315 1331 y FH(=)22 b(i)394 1297 y(1)p 394 1319
25 2 v 394 1365 a(2)431 1331 y Fv(C)466 1338 y Ft(ij)r(k)524
1283 y Fs(\020)549 1331 y Fv(g)574 1310 y Ft(k)q(`)607
1299 y Fm(?)p 627 1291 30 2 v 627 1331 a Fv(f)657 1301
y Ft(J)657 1343 y(`)671 1334 y Fm(?)700 1331 y FH(Im)n
FE(N)799 1338 y Ft(I)s(J)849 1331 y FE(F)890 1310 y FB(\000)p
Ft(I)885 1343 y(\026\027)938 1283 y Fs(\021)p 971 1291
29 2 v 971 1331 a Fv(\025)999 1301 y Ft(iA)1048 1331
y Fv(\015)1076 1310 y Ft(\026\027)1127 1331 y Fv(\025)1155
1310 y Ft(j)r(B)1210 1331 y Fv(")1233 1338 y Ft(AB)269
1448 y FE(\000)d FH(i)346 1414 y(1)p 346 1436 25 2 v
346 1482 a(2)p 384 1409 39 2 v 384 1448 a Fv(C)422 1455
y Ft(i)434 1446 y Fm(?)452 1455 y Ft(j)468 1446 y Fm(?)486
1455 y Ft(k)505 1446 y Fm(?)534 1399 y Fs(\020)559 1448
y Fv(g)584 1427 y Ft(k)603 1415 y Fm(?)621 1427 y Ft(`)638
1448 y Fv(f)667 1427 y Ft(J)662 1460 y(`)700 1448 y FH(Im)n
FE(N)799 1455 y Ft(I)s(J)849 1448 y FE(F)890 1427 y FC(+)p
Ft(I)885 1460 y(\026\027)946 1399 y Fs(\021)p 979 1408
29 2 v 979 1448 a Fv(\025)1007 1418 y Ft(i)1019 1406
y Fm(?)1007 1460 y Ft(A)1048 1448 y Fv(\015)1076 1427
y Ft(\026\027)1127 1448 y Fv(\025)1155 1424 y Ft(j)1171
1412 y Fm(?)1155 1460 y Ft(B)1200 1448 y Fv(")1223 1427
y Ft(AB)1736 1448 y FH(\(10.26\))167 1544 y FE(L)201
1551 y Ft(massmatr)q(ix)419 1544 y FH(=)k FE(M)540 1523
y Ft(\013)p FB(j)p Ft(\014)p 604 1504 26 2 v 604 1544
a Fv(\020)629 1556 y Ft(\013)662 1544 y Fv(\020)683 1551
y Ft(\014)726 1544 y FH(+)c FE(M)843 1552 y Ft(\013)p
FB(j)p Ft(\014)p 908 1504 V 908 1544 a Fv(\020)933 1514
y Ft(\013)966 1544 y Fv(\020)991 1523 y Ft(\014)269 1627
y FH(+)h FE(M)387 1601 y Ft(\013)p FB(j)409 1641 y(j)p
Ft(iB)p 469 1587 V 469 1627 a Fv(\020)495 1639 y Ft(\013)528
1627 y Fv(\025)556 1606 y Ft(iB)618 1627 y FH(+)f FE(M)758
1601 y FB(j)29 b Ft(B)735 1641 y(\013)p FB(j)p Ft(i)780
1632 y Fm(?)p 836 1587 V 836 1627 a Fv(\020)861 1597
y Ft(\013)894 1627 y Fv(\025)922 1606 y Ft(i)934 1595
y Fm(?)922 1639 y Ft(B)269 1719 y FH(+)20 b FE(M)387
1727 y Ft(iA)p FB(j)p Ft(`B)p 488 1680 29 2 v 488 1719
a Fv(\025)516 1689 y Ft(iA)557 1719 y Fv(\025)585 1699
y Ft(`B)649 1719 y FH(+)g FE(M)796 1694 y Ft(A)p FB(j)33
b Ft(B)767 1734 y(i)779 1724 y Fm(?)823 1734 y FB(j)p
Ft(`)847 1724 y Fm(?)p 904 1680 V 904 1719 a Fv(\025)932
1689 y Ft(i)944 1678 y Fm(?)932 1732 y Ft(A)964 1719
y Fv(\025)992 1699 y Ft(`)1006 1687 y Fm(?)992 1732 y
Ft(B)1736 1719 y FH(\(10.27\))167 1792 y FE(L)201 1799
y Ft(potential)365 1792 y FH(=)22 b FE(\000)8 b FH(V)q(\()p
Fv(z)r(;)p 576 1765 25 2 v 8 w(z)q(;)g(q)r FH(\))1071
b(\(10.28\))167 1888 y FE(L)201 1895 y FC(4)p Ft(f)t(er)q(mi)340
1888 y FH(=)405 1855 y(1)p 405 1877 V 405 1922 a(4)443
1888 y Fv(R)480 1895 y Ft(ij)508 1886 y Fm(?)526 1895
y Ft(`k)559 1886 y Fm(?)p 588 1849 29 2 v 588 1888 a
Fv(\025)617 1858 y Ft(iA)666 1888 y Fv(\025)694 1868
y Ft(`B)p 747 1849 V 747 1888 a Fv(\025)775 1858 y Ft(j)791
1847 y Fm(?)775 1901 y Ft(A)820 1888 y Fv(\025)848 1868
y Ft(k)867 1856 y Fm(?)848 1901 y Ft(B)269 2005 y FH(+)332
1971 y(1)p 332 1993 25 2 v 332 2039 a(2)369 2005 y(I)-9
b(R)414 1984 y Ft(\013)437 2017 y(\014)r FB(j)p Ft(ts)507
2005 y FE(U)543 1984 y Ft(t)538 2017 y(A\015)595 2005
y FE(U)631 1984 y Ft(s)626 2017 y(B)r(\016)682 2005 y
Fv(")705 1984 y Ft(AB)p 778 2005 2 33 v 765 2005 a FH(C)801
1984 y Ft(\016)q(\021)p 847 1965 26 2 v 847 2005 a Fv(\020)872
2017 y Ft(\013)905 2005 y Fv(\020)926 2012 y Ft(\021)p
955 1965 V 955 2005 a Fv(\020)980 1975 y Ft(\014)1012
2005 y Fv(\020)1037 1984 y Ft(\015)269 2121 y FE(\000)345
2088 y FH(1)p 332 2110 49 2 v 332 2156 a(32)394 2121
y(Im)o FE(N)494 2128 y Ft(I)s(J)544 2121 y Fv(C)579 2128
y Ft(ij)r(k)637 2121 y Fv(C)672 2128 y Ft(`mn)758 2121
y Fv(g)783 2101 y Ft(k)q(r)819 2089 y Fm(?)839 2121 y
Fv(g)864 2101 y Ft(ns)901 2089 y Fm(?)p 930 2082 30 2
v 930 2121 a Fv(f)959 2092 y Ft(I)959 2134 y(r)976 2124
y Fm(?)p 996 2082 V 996 2121 a Fv(f)1026 2092 y Ft(J)1026
2134 y(s)1042 2124 y Fm(?)p 1062 2082 29 2 v 1062 2121
a Fv(\025)1091 2092 y Ft(iA)1131 2121 y Fv(\015)1156
2128 y Ft(\026\027)1199 2121 y Fv(\025)1227 2101 y Ft(j)r(B)p
1283 2082 V 1283 2121 a Fv(\025)1311 2092 y Ft(`C)1355
2121 y Fv(\015)1383 2101 y Ft(\026\027)1426 2121 y Fv(\025)1454
2101 y Ft(mD)1526 2121 y Fv(")1549 2128 y Ft(AB)1605
2121 y Fv(")1628 2128 y Ft(C)r(D)269 2238 y FE(\000)345
2204 y FH(1)p 332 2226 49 2 v 332 2272 a(32)394 2238
y(Im)o FE(N)494 2245 y Ft(I)s(J)p 544 2199 39 2 v 544
2238 a Fv(C)583 2245 y Ft(i)595 2236 y Fm(?)613 2245
y Ft(j)629 2236 y Fm(?)647 2245 y Ft(k)666 2236 y Fm(?)p
686 2199 V 686 2238 a Fv(C)725 2245 y Ft(`)739 2236 y
Fm(?)757 2245 y Ft(m)788 2236 y Fm(?)806 2245 y Ft(n)827
2236 y Fm(?)864 2238 y Fv(g)889 2217 y Ft(k)908 2206
y Fm(?)927 2217 y Ft(r)946 2238 y Fv(g)971 2217 y Ft(n)992
2206 y Fm(?)1010 2217 y Ft(s)1029 2238 y Fv(f)1058 2217
y Ft(I)1053 2250 y(r)1078 2238 y Fv(f)1107 2217 y Ft(J)1102
2250 y(s)p 1140 2198 29 2 v 1140 2238 a Fv(\025)1169
2208 y Ft(i)1181 2196 y Fm(?)1169 2250 y Ft(A)1201 2238
y Fv(\015)1226 2245 y Ft(\026\027)1269 2238 y Fv(\025)1297
2214 y Ft(j)1313 2203 y Fm(?)1297 2250 y Ft(B)p 1342
2198 V 1342 2238 a Fv(\025)1370 2208 y Ft(k)1389 2196
y Fm(?)1370 2250 y Ft(C)1409 2238 y Fv(\015)1437 2217
y Ft(\026\027)1480 2238 y Fv(\025)1508 2217 y Ft(`)1522
2206 y Fm(?)1508 2250 y Ft(D)1552 2238 y Fv(")1575 2217
y Ft(AB)1631 2238 y Fv(")1654 2217 y Ft(C)r(D)1736 2238
y FH(\(10.29\))1736 2326 y(\(10.30\))-5 2436 y(where)16
b(the)g(mass{matrices)e(and)j(the)f(scalar)h(p)q(oten)o(tial)f(are)g
(giv)o(en)f(b)o(y:)p 366 2553 1149 2 v 391 2656 a Fu(N=2)j(Y)l(ang)g
(Mil)r(ls)h(mass)e(matric)n(es)g(and)h(sc)n(alar)f(p)n(otential)p
366 2735 V 916 2892 a FH(51)p eop
%%Page: 52 53
52 52 bop 408 16 a FE(M)468 -5 y Ft(\013)p FB(j)p Ft(\014)565
16 y FH(=)41 b FE(\000)8 b Fv(g)j FE(U)761 -5 y Ft(\013A)756
28 y(u)820 16 y FE(U)856 -5 y Ft(\014)r(B)851 28 y(v)917
16 y Fv(")940 23 y Ft(AB)1005 16 y FE(r)1047 -5 y FC([)p
Ft(u)1087 16 y Fv(k)1114 -9 y Ft(v)q FC(])1112 28 y Ft(I)1152
16 y Fv(Y)1191 -5 y Ft(I)408 97 y FE(M)468 105 y Ft(\013)p
FB(j)p Ft(\014)565 97 y FH(=)41 b FE(\000)8 b Fv(g)j
FE(U)756 105 y Ft(\013A)p FB(j)p Ft(u)846 97 y FE(U)877
105 y Ft(\014)r(B)r FB(j)p Ft(v)965 97 y Fv(")988 76
y Ft(AB)1053 97 y FE(r)1095 76 y FC([)p Ft(u)1135 97
y Fv(k)1162 71 y Ft(v)q FC(])1160 109 y Ft(I)p 1201 58
40 2 v 1201 97 a Fv(Y)1240 68 y Ft(I)389 180 y FE(M)449
154 y Ft(\013)p FB(j)471 194 y(j)p Ft(iB)565 180 y FH(=)50
b(4)8 b Fv(g)j FE(U)755 159 y Ft(\013A)750 192 y(u)814
180 y Fv(k)841 159 y Ft(u)839 192 y(I)872 180 y Fv(f)901
159 y Ft(I)896 192 y(i)930 180 y Fv(")953 187 y Ft(AB)371
272 y FE(M)453 246 y FB(j)30 b Ft(B)431 286 y(\013)p
FB(j)p Ft(i)476 277 y Fm(?)565 272 y FH(=)41 b FE(\000)8
b FH(4)g Fv(g)k FE(U)789 279 y Ft(\013A)p FB(j)p Ft(u)878
272 y Fv(k)905 251 y Ft(u)903 284 y(I)p 936 232 30 2
v 936 272 a Fv(f)966 242 y Ft(I)966 284 y(i)978 274 y
Fm(?)1006 272 y Fv(")1029 251 y Ft(AB)371 377 y FE(M)431
384 y Ft(iA)p FB(j)p Ft(`B)565 377 y FH(=)649 343 y(1)p
649 365 25 2 v 649 411 a(3)687 377 y Fv(g)720 329 y Fs(\020)745
377 y Fv(")768 384 y Ft(AB)833 377 y Fv(g)856 384 y Ft(ij)884
375 y Fm(?)905 377 y Fv(k)932 353 y Ft(j)948 341 y Fm(?)930
389 y Ft(I)968 377 y Fv(f)997 356 y Ft(I)992 389 y(`)1028
377 y FH(+)f(i\()p Fv(\033)1138 384 y Ft(x)1160 377 y
FH(\))1205 356 y Ft(C)1179 389 y(A)1235 377 y Fv(\017)1255
384 y Ft(B)r(C)1320 377 y FE(P)1359 356 y Ft(x)1355 389
y(I)1389 377 y FE(r)1431 384 y Ft(`)1447 377 y Fv(f)1476
356 y Ft(I)1471 389 y(i)1497 329 y Fs(\021)335 493 y
FE(M)424 468 y Ft(A)p FB(j)33 b Ft(B)395 508 y(i)407
498 y Fm(?)451 508 y FB(j)p Ft(`)475 498 y Fm(?)565 493
y FH(=)649 460 y(1)p 649 482 V 649 527 a(3)687 493 y
Fv(g)720 445 y Fs(\020)745 493 y Fv(")768 473 y Ft(AB)833
493 y Fv(g)856 500 y Ft(i)868 491 y Fm(?)886 500 y Ft(j)905
493 y Fv(k)932 470 y Ft(j)930 505 y(I)p 950 454 30 2
v 950 493 a Fv(f)979 464 y Ft(I)979 506 y(`)993 496 y
Fm(?)1025 493 y FE(\000)11 b FH(i)p Fv(\017)1109 473
y Ft(AC)1164 493 y FH(\()p Fv(\033)1211 500 y Ft(x)1233
493 y FH(\))1279 473 y Ft(B)1252 506 y(C)1318 493 y FE(P)1357
473 y Ft(x)1353 506 y(I)1387 493 y FE(r)1429 500 y Ft(`)1443
491 y Fm(?)p 1463 454 V 1463 493 a Fv(f)1492 464 y Ft(I)1492
506 y(i)1504 496 y Fm(?)1524 445 y Fs(\021)1736 493 y
FH(\(10.31\))331 596 y(V)q(\()p Fv(z)r(;)p 435 570 25
2 v 8 w(z)q(;)d(q)r FH(\))41 b(=)g Fv(g)669 575 y FC(2)706
548 y Fs(\020)739 596 y Fv(g)762 603 y Ft(ij)790 594
y Fm(?)811 596 y Fv(k)838 575 y Ft(i)836 608 y(I)864
596 y Fv(k)891 572 y Ft(j)907 561 y Fm(?)889 608 y Ft(J)947
596 y FH(+)19 b(4)8 b Fv(h)1064 603 y Ft(uv)1114 596
y Fv(k)1141 575 y Ft(u)1139 608 y(I)1164 596 y Fv(k)1191
575 y Ft(v)1189 608 y(J)1213 548 y Fs(\021)p 1255 557
40 2 v 1255 596 a Fv(Y)1294 567 y Ft(I)1322 596 y Fv(Y)1361
575 y Ft(J)644 717 y FH(+)g Fv(g)715 696 y Ft(ij)743
685 y Fm(?)772 717 y Fv(f)801 696 y Ft(I)796 729 y(i)p
830 677 30 2 v 830 717 a Fv(f)859 687 y Ft(J)859 729
y(j)875 720 y Fm(?)936 663 y FC(3)915 675 y Fs(X)912
766 y Ft(x)p FC(=1)994 717 y FE(P)1033 696 y Ft(x)1029
729 y(I)1063 717 y FE(P)1102 696 y Ft(x)1098 729 y(J)1736
717 y FH(\(10.32\))-5 859 y(The)13 b(coupling)f(constan)o(t)i(in)e
(fron)o(t)h(of)g(the)f(mass{matrices)f(and)i(of)g(the)f(p)q(oten)o
(tial)h(is)f(just)h(a)g(sym)o(b)q(olic)-5 919 y(notation)i(to)g(remind)
d(the)h(reader)h(that)h(these)e(terms)g(are)h(en)o(tirely)e(due)i(to)g
(the)g(gauging)h(and)g(v)m(anish)-5 979 y(in)f(the)g(ungauged)h(theory)
l(.)20 b(In)14 b(general)g(there)f(is)h(not)g(a)h(single)e(coupling)h
(constan)o(t)h(rather)f(there)f(are)-5 1039 y(as)k(man)o(y)d(indep)q
(enden)o(t)h(coupling)h(constan)o(ts)h(as)g(m)o(utually)c(comm)o(uting)
g(subgroups)18 b(in)d(the)h(gauge)-5 1100 y(group.)22
b(F)l(or)16 b(instance)f(if)h FE(G)i FH(is)d(a)h(pro)q(duct)h(or)f
Fv(r)h(U)5 b FH(\(1\){factors,)17 b(there)e(are)g Fv(r)i
FH(indep)q(enden)o(t)e(coupling)-5 1160 y(constan)o(ts)i(that)g(can)f
(b)q(e)h(reabsorb)q(ed)g(in)o(to)f(the)g(de\014nition)g(of)g(the)g
(killing)f(v)o(ectors)g Fv(k)1600 1142 y Ft(i)1598 1172
y(I)1619 1160 y Fv(;)8 b(k)1668 1142 y Ft(u)1666 1172
y(I)1690 1160 y FH(.)68 1220 y(The)16 b(sup)q(ersymmetry)d
(transformation)j(rules)g(with)g(resp)q(ect)f(to)i(whic)o(h)e(the)h
(lagrangian)33 b(10.24)p
 (#equation.10.24) [[498 474 524 486] [1 1 1 [3 3]] [0 0 1]] pdfm 
-5 1280 a(is)16 b(in)o(v)m(arian)o(t)g(are)g(the)g(follo)o(wing)g
(ones:)916 2892 y(52)p eop
%%Page: 53 54
53 53 bop 432 28 1016 2 v 457 130 a Fu(N=2)18 b(rigid)f(tr)n
(ansformation)g(rules)h(of)f(Bose)h(\014elds)p 432 210
V 429 342 a Fv(\016)9 b(A)497 322 y Ft(I)497 355 y(\026)562
342 y FH(=)41 b(+)8 b(i)718 294 y Fs(\020)751 342 y Fv(f)780
322 y Ft(I)775 355 y(i)p 808 303 29 2 v 808 342 a Fv(\025)837
312 y Ft(iA)886 342 y Fv(\015)911 349 y Ft(\026)943 342
y Fv(\017)963 322 y Ft(B)1001 342 y Fv(")1024 349 y Ft(AB)1100
342 y FH(+)p 1157 303 30 2 v 19 w Fv(f)1186 312 y Ft(I)1186
355 y(i)1198 345 y Fm(?)p 1219 303 29 2 v 1219 342 a
Fv(\025i)1264 322 y Ft(?)1313 349 y(A)1350 342 y Fv(\015)1375
349 y Ft(\026)1407 342 y Fv(\017)1427 349 y Ft(B)1465
342 y Fv(")1488 322 y Ft(AB)1553 294 y Fs(\021)458 436
y Fv(\016)r(z)507 416 y Ft(i)562 436 y FH(=)41 b(+)p
687 397 V 8 w Fv(\025)716 406 y Ft(iA)765 436 y Fv(\017)785
443 y Ft(A)440 513 y Fv(\016)p 464 487 25 2 v 2 w(z)488
493 y Ft(i)500 481 y Fm(?)562 513 y FH(=)g(+)p 687 474
29 2 v 8 w Fv(\025)716 484 y Ft(i)728 472 y Fm(?)716
526 y Ft(A)756 513 y Fv(\017)776 493 y Ft(A)294 586 y
FE(U)330 565 y Ft(\013A)325 598 y(u)381 586 y FH(\()p
Fv(q)r FH(\))8 b Fv(\016)r(q)499 565 y Ft(u)562 586 y
FH(=)41 b Fv(")664 565 y Ft(AB)p 737 586 2 33 v 724 586
a FH(C)760 565 y Ft(\013\014)p 814 560 20 2 v 814 586
a Fv(\017)834 593 y Ft(B)864 586 y Fv(\020)885 593 y
Ft(\014)920 586 y FH(+)p 969 560 V 11 w Fv(\017)989 565
y Ft(A)1017 586 y Fv(\020)1042 565 y Ft(\013)1736 586
y FH(\(10.33\))p 420 692 1040 2 v 445 794 a Fu(N=2)18
b(rigid)f(tr)n(ansformation)g(rules)h(of)f(F)l(ermi)g(\014elds)p
420 874 V 368 994 a Fv(\016)r(\025)420 973 y Ft(iA)502
994 y FH(=)41 b(i)8 b FE(r)645 1001 y Ft(\026)668 994
y Fv(z)693 973 y Ft(i)715 994 y Fv(\015)743 973 y Ft(\026)775
994 y Fv(\017)795 973 y Ft(A)842 994 y FH(+)19 b Fv(G)937
973 y FB(\000)p Ft(i)937 1006 y(\026\027)989 994 y Fv(\015)1017
973 y Ft(\026\027)1068 994 y Fv(\017)1088 1001 y Ft(B)1126
994 y Fv(")1149 973 y Ft(AB)1225 994 y FH(+)h Fv(D)1324
973 y Ft(i)p FB(j)p Ft(AB)1411 994 y Fv(\017)1431 1001
y Ft(B)376 1073 y Fv(\016)r(\025)428 1052 y Ft(i)440
1041 y Fm(?)428 1085 y Ft(A)502 1073 y FH(=)41 b(i)8
b FE(r)645 1080 y Ft(\026)p 668 1047 25 2 v 668 1073
a Fv(z)692 1052 y Ft(i)704 1041 y Fm(?)733 1073 y Fv(\015)761
1052 y Ft(\026)792 1073 y Fv(\017)812 1080 y Ft(A)860
1073 y FH(+)19 b Fv(G)955 1052 y FC(+)p Ft(i)994 1041
y Fm(?)955 1085 y Ft(\026\027)1024 1073 y Fv(\015)1052
1052 y Ft(\026\027)1103 1073 y Fv(\017)1123 1052 y Ft(B)1161
1073 y Fv(")1184 1080 y Ft(AB)1260 1073 y FH(+)g Fv(D)1358
1052 y Ft(i)1370 1041 y Fm(?)1388 1085 y FB(j)p Ft(AB)1463
1073 y Fv(\017)1483 1052 y Ft(B)390 1154 y Fv(\016)r(\020)435
1161 y Ft(\013)502 1154 y FH(=)41 b(i)8 b FE(U)639 1133
y Ft(\014)r(B)634 1166 y(u)699 1154 y FE(r)741 1161 y
Ft(\026)764 1154 y Fv(q)788 1133 y Ft(u)818 1154 y Fv(\015)846
1133 y Ft(\026)869 1154 y Fv(\017)889 1133 y Ft(A)926
1154 y Fv(")949 1161 y Ft(AB)p 1022 1154 2 33 v 1009
1154 a FH(C)1044 1161 y Ft(\013\014)1110 1154 y FH(+)19
b Fv(N)1211 1133 y Ft(A)1206 1166 y(\013)1248 1154 y
Fv(\017)1268 1161 y Ft(A)387 1226 y Fv(\016)r(\020)436
1206 y Ft(\013)502 1226 y FH(=)41 b(i)8 b FE(U)634 1234
y Ft(\014)r(B)r FB(j)p Ft(u)724 1226 y FE(r)766 1233
y Ft(\026)789 1226 y Fv(q)813 1206 y Ft(u)843 1226 y
Fv(\015)871 1206 y Ft(\026)895 1226 y Fv(\017)915 1233
y Ft(A)951 1226 y Fv(")974 1206 y Ft(AB)p 1047 1226 V
1034 1226 a FH(C)1070 1206 y Ft(\013\014)1135 1226 y
FH(+)20 b Fv(N)1237 1206 y Ft(\013)1232 1239 y(A)1270
1226 y Fv(\017)1290 1206 y Ft(A)1736 1226 y FH(\(10.34\))-5
1312 y(where:)p 503 1399 875 2 v 528 1502 a Fu(N=2)e(rigid)f(values)i
(of)e(the)h(auxiliary)f(\014elds)p 503 1582 V 363 1722
a Fv(G)401 1701 y FB(\000)p Ft(i)401 1734 y(\026\027)486
1722 y FH(=)41 b(i)8 b Fv(g)612 1701 y Ft(ij)640 1690
y Fm(?)p 661 1682 30 2 v 661 1722 a Fv(f)690 1692 y Ft(I)690
1734 y(j)706 1725 y Fm(?)735 1722 y FH(Im)n FE(N)834
1729 y Ft(I)s(J)893 1661 y Fs(\022)923 1722 y FE(F)964
1701 y FB(\000)p Ft(J)959 1734 y(\026\027)1027 1722 y
FH(+)1081 1688 y(1)p 1081 1710 25 2 v 1081 1756 a(8)1110
1722 y FE(r)1152 1729 y Ft(k)1173 1722 y Fv(f)1202 1701
y Ft(J)1197 1734 y(`)p 1235 1682 29 2 v 1235 1722 a Fv(\025)1264
1692 y Ft(k)q(A)1320 1722 y Fv(\015)1345 1729 y Ft(\026\027)1396
1722 y Fv(\025)1424 1701 y Ft(`B)1478 1722 y Fv(")1501
1729 y Ft(AB)1566 1661 y Fs(\023)347 1842 y Fv(G)385
1821 y FC(+)p Ft(i)424 1809 y Fm(?)385 1854 y Ft(\026\027)486
1842 y FH(=)50 b(i)8 b Fv(g)621 1821 y Ft(i)633 1809
y Fm(?)651 1821 y Ft(j)669 1842 y Fv(f)698 1821 y Ft(I)693
1854 y(j)727 1842 y FH(Im)n FE(N)826 1849 y Ft(I)s(J)885
1781 y Fs(\022)915 1842 y FE(F)956 1821 y FC(+)p Ft(J)951
1854 y(\026\027)1019 1842 y FH(+)1073 1808 y(1)p 1073
1830 25 2 v 1073 1876 a(8)1102 1842 y FE(r)1144 1849
y Ft(k)1163 1840 y Fm(?)p 1183 1802 30 2 v 1183 1842
a Fv(f)1213 1812 y Ft(J)1213 1854 y(`)1227 1844 y Fm(?)p
1255 1802 29 2 v 1255 1842 a Fv(\025)1284 1812 y Ft(k)1303
1800 y Fm(?)1284 1854 y Ft(A)1331 1842 y Fv(\015)1356
1849 y Ft(\026\027)1408 1842 y Fv(\025)1436 1821 y Ft(`)1450
1809 y Fm(?)1436 1854 y Ft(B)1479 1842 y Fv(")1502 1821
y Ft(AB)1567 1781 y Fs(\023)324 1941 y Fv(D)365 1920
y Ft(i)p FB(j)p Ft(AB)486 1941 y FH(=)41 b Fv(Y)605 1920
y Ft(i)p FB(j)p Ft(AB)694 1941 y FH(+)11 b Fv(W)796 1920
y Ft(i)p FB(j)p FC([)p Ft(AB)r FC(])905 1941 y FH(+)g
Fv(W)1007 1920 y Ft(i)p FB(j)p FC(\()p Ft(AB)r FC(\))307
2014 y Fv(D)348 1993 y Ft(i)360 1981 y Fm(?)378 2026
y FB(j)p Ft(AB)486 2014 y FH(=)41 b Fv(Y)605 1993 y Ft(i)617
1981 y Fm(?)624 2026 y FB(j)p Ft(AB)701 2014 y FH(+)11
b Fv(W)803 1993 y Ft(i)815 1981 y Fm(?)826 2026 y FB(j)p
FC([)p Ft(AB)r FC(])924 2014 y FH(+)g Fv(W)1026 1993
y Ft(i)1038 1981 y Fm(?)1049 2026 y FB(j)p FC(\()p Ft(AB)r
FC(\))327 2117 y Fv(Y)366 2096 y Ft(i)p FB(j)p Ft(AB)486
2117 y FH(=)41 b(i)584 2083 y(1)p 584 2105 25 2 v 584
2151 a(2)622 2117 y Fv(g)647 2096 y Ft(ij)675 2084 y
Fm(?)p 703 2078 39 2 v 703 2117 a Fv(C)742 2124 y Ft(j)758
2115 y Fm(?)776 2124 y Ft(k)795 2115 y Fm(?)813 2124
y Ft(`)827 2115 y Fm(?)p 856 2077 29 2 v 856 2117 a Fv(\025)885
2087 y Ft(k)904 2075 y Fm(?)885 2129 y Ft(C)932 2117
y Fv(\025)960 2096 y Ft(`)974 2084 y Fm(?)960 2129 y
Ft(D)995 2117 y Fv(")1018 2096 y Ft(AC)1082 2117 y Fv(")1105
2096 y Ft(B)r(D)320 2233 y Fv(Y)359 2213 y Ft(i)371 2201
y Fm(?)378 2246 y FB(j)p Ft(AB)486 2233 y FH(=)g FE(\000)p
FH(i)623 2200 y(1)p 623 2222 25 2 v 623 2267 a(2)660
2233 y Fv(g)685 2213 y Ft(i)697 2201 y Fm(?)716 2213
y Ft(j)742 2233 y Fv(C)777 2240 y Ft(j)r(k)q(`)p 837
2194 29 2 v 837 2233 a Fv(\025)866 2203 y Ft(k)q(C)923
2233 y Fv(\025)951 2213 y Ft(`D)998 2233 y Fv(")1021
2240 y Ft(AC)1085 2233 y Fv(")1108 2240 y Ft(B)r(D)294
2336 y Fv(W)347 2315 y Ft(i)p FB(j)p FC([)p Ft(AB)r FC(])486
2336 y FH(=)g Fv(")588 2315 y Ft(AB)653 2336 y Fv(k)680
2315 y Ft(i)678 2348 y(I)p 699 2297 40 2 v 699 2336 a
Fv(Y)738 2307 y Ft(I)282 2409 y Fv(W)335 2388 y Ft(i)347
2376 y Fm(?)358 2421 y FB(j)p FC([)p Ft(AB)r FC(])486
2409 y FH(=)g Fv(")588 2416 y Ft(AB)653 2409 y Fv(k)680
2388 y Ft(i)692 2376 y Fm(?)678 2421 y Ft(I)712 2409
y Fv(Y)752 2388 y Ft(I)286 2498 y Fv(W)339 2478 y Ft(i)p
FB(j)p FC(\()p Ft(AB)r FC(\))486 2498 y FH(=)g FE(\000)p
FH(i)8 b Fv(\017)646 2478 y Ft(AC)702 2498 y FH(\()p
Fv(\033)749 2505 y Ft(x)770 2498 y FH(\))817 2478 y Ft(B)789
2511 y(C)855 2498 y FE(P)894 2478 y Ft(x)890 2511 y(I)916
2498 y Fv(g)941 2478 y Ft(ij)969 2466 y Fm(?)p 990 2459
30 2 v 990 2498 a Fv(f)1019 2468 y Ft(I)1019 2511 y(j)1035
2501 y Fm(?)274 2577 y Fv(W)327 2557 y Ft(i)339 2545
y Fm(?)351 2590 y FB(j)p FC(\()p Ft(AB)r FC(\))486 2577
y FH(=)41 b(i)8 b(\()p Fv(\033)634 2584 y Ft(x)656 2577
y FH(\))701 2557 y Ft(C)675 2590 y(A)731 2577 y Fv(\017)751
2584 y Ft(B)r(C)817 2577 y FE(P)856 2557 y Ft(x)852 2590
y(I)877 2577 y Fv(g)902 2557 y Ft(i)914 2545 y Fm(?)933
2557 y Ft(j)951 2577 y Fv(f)980 2557 y Ft(I)975 2590
y(j)372 2667 y Fv(N)416 2646 y Ft(A)411 2679 y(\013)486
2667 y FH(=)41 b(2)8 b FE(U)633 2646 y Ft(A)628 2679
y(\013)p FB(j)p Ft(u)693 2667 y Fv(k)720 2646 y Ft(u)718
2679 y(I)p 750 2628 40 2 v 750 2667 a Fv(Y)790 2637 y
Ft(I)376 2747 y Fv(N)420 2726 y Ft(\013)415 2759 y(A)486
2747 y FH(=)41 b FE(\000)p FH(2)8 b FE(U)672 2726 y Ft(\013)667
2759 y(A)p FB(j)p Ft(u)735 2747 y Fv(k)762 2726 y Ft(u)760
2759 y(I)793 2747 y Fv(Y)832 2726 y Ft(I)1736 2747 y
FH(\(10.35\))916 2892 y(53)p eop
%%Page: 54 55
54 54 bop -5 15 a Fk(10.3)66 b(The)22 b(renormalizable)j(microscopic)e
(theory)-5 108 y FH(As)15 b(an)g(exempli\014cation)d(of)j(the)f
(general)h(formalism)d(and)j(for)g(the)g(sak)o(e)f(of)h(its)g(in)o
(trinsic)e(in)o(terest,)g(in)-5 168 y(this)j(subsection)g(w)o(e)f
(consider)h(the)g(case)f(of)i(the)e(renormalizable)f(microscopic)f(N=2)
j(\(matter)f(cou-)-5 228 y(pled\))e(Y)l(ang{Mills)f(theory)l(.)20
b(The)13 b(theory)f(is)h(sp)q(eci\014ed)f(b)o(y)h(the)f(c)o(hoice)g(of)
h(the)g(follo)o(wing)f(geometrical)-5 288 y(data:)55
390 y(1.)24 b(A)16 b(\015at)h(rigid)f(sp)q(ecial)f(manifold)g
FE(S)t(M)825 397 y Ft(f)t(lat)906 390 y FH(describing)h(the)g(v)o
(ector)f(m)o(ultiplet)e(couplings)55 492 y(2.)24 b(A)16
b(\015at)h(Hyp)q(erk\177)-24 b(ahler)15 b(manifold)g
FE(HM)840 499 y Ft(f)t(lat)921 492 y FH(describing)h(the)g(h)o(yp)q
(erm)o(ultiple)o(t)e(couplings)-5 594 y(Let)j(us)f(brie\015y)g(discuss)
g(these)g(geometries)e(and)j(the)f(corresp)q(onding)h(form)f(of)g(the)g
(Lagrangian.)-5 677 y Fu(Flat)i(rigid)f(sp)n(e)n(cial)h(ge)n(ometry)p
-5 694 563 2 v 68 761 a FH(In)e(the)g(v)o(ector)g(m)o(ultiple)o(t)e
(sector)i(the)g(appropriate)g(geometry)f(is)h(describ)q(ed)g(as)h
(follo)o(ws.)k(Let)16 b Fv(\022)-5 821 y FH(b)q(e)g(the)g(theta{angle,)
g(1)p Fv(=g)494 803 y FC(2)530 821 y FH(the)g(in)o(v)o(erse)e(of)i(the)
g(squared)g(gauge)h(coupling)f(constan)o(t,)g(and)g FD(g)1759
828 y Ft(I)s(J)1817 821 y FH(the)-5 882 y(constan)o(t)h(Killing)e
(metric)f(on)i(the)g(gauge)i(Lie)e(algebra.)21 b(De\014ne)16
b(the)g(complex)e(parameter:)797 1011 y Fv(\034)28 b
FH(=)22 b Fv(\022)e FH(+)g(i)1044 977 y(1)p 1034 999
45 2 v 1034 1045 a Fv(g)1059 1031 y FC(2)1736 1011 y
FH(\(10.36\))-5 1143 y(and)d(c)o(ho)q(ose)g(as)g(holomorphic)e(section)
h(of)g(the)g(\015at)h(symplectic)c(bundle)j(the)g(follo)o(wing)g(one:)
415 1258 y Fs(b)409 1274 y FH(\012)22 b(=)526 1214 y
Fs(\022)624 1244 y Fv(Y)663 1226 y Ft(I)565 1305 y Fv(\034)14
b FD(g)628 1312 y Ft(I)s(J)679 1305 y Fv(Y)718 1287 y
Ft(J)751 1214 y Fs(\023)985 1274 y Fv(I)t(;)8 b(J)17
b FH(=)d(1)p Fv(;)8 b(:)g(:)g(:)g(;)g(n)14 b FH(=)g(dim)n
FE(G)267 b FH(\(10.37\))-5 1406 y(In)16 b(this)g(case)g(the)f(upp)q(er)
h(half)g(of)g(the)g(holomorphic)f(section)31 b(10.37)p
 (#equation.10.37) [[352 430 379 442] [1 1 1 [3 3]] [0 0 1]] pdfm 
17 w(can)16 b(b)q(e)g(tak)o(en)g(as)g(co)q(ordinates)-5
1466 y(on)h(the)f(manifold)f(\(the)h(sp)q(ecial)g(co)q(ordinates\):)839
1576 y Fv(z)864 1555 y Ft(i)900 1576 y FE(\021)22 b Fv(Y)1000
1555 y Ft(I)1028 1576 y Fv(:)694 b FH(\(10.38\))-5 1686
y(The)17 b(action)f(of)g(the)g(gauge)i(group)f(on)g(these)e(co)q
(ordinates)j(is)e(ob)o(viously)f(the)h(adjoin)o(t)h(action:)749
1796 y Fv(\016)771 1803 y Ft(I)799 1796 y Fv(Y)838 1775
y Ft(J)885 1796 y FH(=)22 b Fv(f)974 1775 y Ft(J)997
1808 y(I)s(K)1058 1796 y Fv(Y)1097 1775 y Ft(K)1736 1796
y FH(\(10.39\))-5 1906 y(where)16 b Fv(f)165 1888 y Ft(J)189
1918 y(I)s(K)257 1906 y FH(are)g(the)g(structure)g(constan)o(ts)h(of)g
(the)f(gauge)h(Lie)f(algebra:)751 2016 y([)p Fv(t)783
2023 y Ft(I)811 2016 y Fv(;)g(t)859 2023 y Ft(J)883 2016
y FH(])22 b(=)g Fv(f)1008 1995 y Ft(K)1035 2028 y(I)s(J)1086
2016 y Fv(t)1104 2023 y Ft(K)1736 2016 y FH(\(10.40\))-5
2126 y Fv(t)13 2133 y Ft(I)49 2126 y FH(b)q(eing)17 b(a)f(basis)h(of)f
(generators.)22 b(Hence)15 b(using)i(eq.s)f(4.58)p
 (#equation.4.58) [[317 257 338 269] [1 1 1 [3 3]] [0 0 1]] pdfm 
16 w(and)34 b(4.57)p
 (#equation.4.57) [[368 257 389 269] [1 1 1 [3 3]] [0 0 1]] pdfm 
17 w(w)o(e)15 b(obtain)475 2227 y FE(N)516 2234 y Ft(I)s(J)636
2227 y FH(=)p 775 2200 27 2 v 101 w Fv(\034)f FD(g)838
2234 y Ft(I)s(J)1031 2227 y Fv(g)1054 2234 y Ft(ij)1082
2225 y Fm(?)1151 2227 y FH(=)49 b(2)8 b(Im)o Fv(\034)14
b FD(g)1392 2234 y Ft(I)s(J)446 2287 y FH(Im)n FE(N)545
2294 y Ft(I)s(J)636 2287 y FH(=)49 b FE(\000)8 b FH(Im)n
Fv(\034)14 b FD(g)891 2294 y Ft(I)s(J)1042 2287 y Fv(f)1071
2269 y Ft(I)1066 2299 y(i)1151 2287 y FH(=)126 b Fv(\016)1339
2269 y Ft(I)1337 2299 y(i)474 2347 y Fv(C)509 2354 y
Ft(ij)r(k)636 2347 y FH(=)142 b(0)204 b Fv(k)1071 2324
y Ft(j)1069 2359 y(I)1151 2347 y FH(=)54 b Fv(f)1272
2329 y Ft(J)1296 2360 y(I)s(K)1356 2347 y Fv(Y)1395 2329
y Ft(K)1736 2287 y FH(\(10.41\))-5 2472 y Fu(Flat)18
b(Hyp)n(erK\177)-25 b(ahler)17 b(ge)n(ometry)p -5 2488
579 2 v 68 2560 a FH(In)k(the)f(h)o(yp)q(erm)o(ultiple)o(t)e(sector)j
(w)o(e)f(arrange)h(the)f(4)p Fv(m)h FH(co)q(ordinates)h
Fv(q)1423 2542 y Ft(u)1465 2560 y FH(of)f FE(HM)1627
2567 y Ft(f)t(lat)1722 2560 y FH(=)29 b(I)-9 b(R)1834
2539 y FC(4)p Ft(m)-5 2620 y FH(in)o(to)16 b(a)h(4)p
Fv(m)f FH(column)f(v)o(ector:)576 2737 y FD(q)22 b FE(\021)g
Fv(q)713 2717 y Ft(a)p FB(j)p Ft(t)959 2677 y Fs(\032)999
2706 y Fv(a)13 b FH(=)h(0)p Fv(;)8 b FH(1)p Fv(;)g FH(2)p
Fv(;)g FH(3)999 2766 y Fv(t)13 b FH(=)h(1)p Fv(;)8 b
FH(2)p Fv(;)g(:)g(:)g(:)16 b(m)1736 2737 y FH(\(10.42\))916
2892 y(54)p eop
%%Page: 55 56
55 55 bop -5 15 a FH(that)17 b(is)f(regarded)h(as)f(an)h(elemen)o(t)c
(of)k(the)f(tensor)g(pro)q(duct)h(I)-9 b(R)1172 -5 y
FC(4)1203 15 y FE(\012)11 b FH(I)-9 b(R)1297 -5 y Ft(m)1353
15 y FE(\030)22 b FH(I)-9 b(R)1458 -5 y FC(4)p Ft(m)1509
15 y FH(.)22 b(Let)158 201 y Fv(J)190 182 y FC(+)p FB(j)p
FC(1)295 201 y FH(=)382 78 y Fs(0)382 151 y(B)382 176
y(B)382 201 y(B)382 227 y(@)446 110 y FH(0)68 b(1)h(0)f(0)426
170 y FE(\000)p FH(1)49 b(0)69 b(0)f(0)446 231 y(0)g(0)h(0)f(1)446
291 y(0)g(0)50 b FE(\000)p FH(1)e(0)756 78 y Fs(1)756
151 y(C)756 176 y(C)756 201 y(C)756 227 y(A)939 201 y
Fv(J)971 182 y FB(\000j)p FC(1)1076 201 y FH(=)1163 78
y Fs(0)1163 151 y(B)1163 176 y(B)1163 201 y(B)1163 227
y(@)1227 110 y FH(0)68 b(1)50 b(0)68 b(0)1207 170 y FE(\000)p
FH(1)49 b(0)h(0)68 b(0)1227 231 y(0)g(0)50 b(0)f FE(\000)p
FH(1)1227 291 y(0)68 b(0)50 b(1)68 b(0)1537 78 y Fs(1)1537
151 y(C)1537 176 y(C)1537 201 y(C)1537 227 y(A)158 439
y Fv(J)190 421 y FC(+)p FB(j)p FC(2)295 439 y FH(=)382
316 y Fs(0)382 389 y(B)382 414 y(B)382 439 y(B)382 466
y(@)426 349 y FH(0)h(0)g FE(\000)p FH(1)48 b(0)426 409
y(0)69 b(0)88 b(0)68 b(1)426 469 y(1)h(0)88 b(0)68 b(0)426
530 y(0)50 b FE(\000)p FH(1)68 b(0)g(0)756 316 y Fs(1)756
389 y(C)756 414 y(C)756 439 y(C)756 466 y(A)939 439 y
Fv(J)971 421 y FB(\000j)p FC(2)1076 439 y FH(=)1163 316
y Fs(0)1163 389 y(B)1163 414 y(B)1163 439 y(B)1163 466
y(@)1207 349 y FH(0)50 b(0)f FE(\000)p FH(1)68 b(0)1207
409 y(0)50 b(0)68 b(0)h FE(\000)p FH(1)1207 469 y(1)50
b(0)68 b(0)88 b(0)1207 530 y(0)50 b(1)68 b(0)88 b(0)1537
316 y Fs(1)1537 389 y(C)1537 414 y(C)1537 439 y(C)1537
466 y(A)158 678 y Fv(J)190 660 y FC(+)p FB(j)p FC(3)295
678 y FH(=)382 555 y Fs(0)382 628 y(B)382 653 y(B)382
678 y(B)382 704 y(@)446 588 y FH(0)g(0)68 b(0)49 b(1)446
648 y(0)88 b(0)68 b(1)49 b(0)446 708 y(0)68 b FE(\000)p
FH(1)49 b(0)g(0)426 768 y FE(\000)p FH(1)69 b(0)f(0)49
b(0)756 555 y Fs(1)756 628 y(C)756 653 y(C)756 678 y(C)756
704 y(A)939 678 y Fv(J)971 660 y FB(\000j)p FC(3)1076
678 y FH(=)1163 555 y Fs(0)1163 628 y(B)1163 653 y(B)1163
678 y(B)1163 704 y(@)1227 588 y FH(0)68 b(0)h(0)f(1)1227
648 y(0)g(0)50 b FE(\000)p FH(1)e(0)1227 708 y(0)68 b(1)h(0)f(0)1207
768 y FE(\000)p FH(1)49 b(0)69 b(0)f(0)1537 555 y Fs(1)1537
628 y(C)1537 653 y(C)1537 678 y(C)1537 704 y(A)1736 439
y FH(\(10.43\))-5 863 y(b)q(e)18 b(the)f(t)o(w)o(o)g(triplets)f(of)i
(self{dual)f(and)h(an)o(tiself)e(dual)i('t)e(Ho)q(oft)i(matrices)e
(satisfying)h(the)g(quater-)-5 923 y(nionic)f(algebra:)550
1033 y Fv(J)582 1013 y FB(\006j)p Ft(x)649 1033 y Fv(J)681
1013 y FB(\006j)p Ft(y)780 1033 y FH(=)42 b FE(\000)8
b Fv(\016)931 1013 y Ft(xy)979 1033 y FH(1)-17 b(1)1011
1040 y FC(4)p FB(\002)p FC(4)1095 1033 y FH(+)19 b Fv(")1175
1013 y Ft(xy)q(z)1242 1033 y Fv(J)1274 1013 y FB(\006j)p
Ft(z)648 1127 y Fv(J)680 1101 y FB(\006j)p Ft(x)675 1139
y(ab)780 1127 y FH(=)42 b FE(\006)912 1093 y FH(1)p 912
1115 25 2 v 912 1161 a(2)949 1127 y Fv(")972 1134 y Ft(abcd)1050
1127 y Fv(J)1082 1101 y FB(\006j)p Ft(x)1077 1139 y(cd)714
1227 y FH(0)g(=)860 1179 y Fs(h)879 1227 y Fv(J)911 1207
y FC(+)p FB(j)p Ft(x)978 1227 y Fv(;)16 b(J)1040 1207
y FB(\000j)p Ft(y)1098 1179 y Fs(i)1223 1227 y FE(8)p
Fv(x;)8 b(y)410 b FH(\(10.44\))-5 1337 y(Let,)16 b(furthermore)582
1590 y Fv(e)605 1597 y Ft(a)647 1590 y FH(=)707 1353
y Fs(8)707 1390 y(>)707 1403 y(>)707 1415 y(>)707 1428
y(>)707 1440 y(>)707 1453 y(>)707 1465 y(>)707 1478 y(>)707
1490 y(>)707 1502 y(>)707 1515 y(>)707 1527 y(>)707 1540
y(<)707 1615 y(>)707 1627 y(>)707 1639 y(>)707 1652 y(>)707
1664 y(>)707 1677 y(>)707 1689 y(>)707 1702 y(>)707 1714
y(>)707 1727 y(>)707 1739 y(>)707 1752 y(>)707 1764 y(:)753
1418 y Fv(e)776 1425 y FC(0)817 1418 y FH(=)877 1358
y Fs(\022)916 1388 y FH(1)49 b(0)916 1449 y(0)g(1)1022
1358 y Fs(\023)753 1647 y Fv(e)776 1654 y Ft(x)819 1647
y FH(=)879 1472 y Fs(8)879 1510 y(>)879 1522 y(>)879
1535 y(>)879 1547 y(>)879 1560 y(>)879 1572 y(>)879 1584
y(>)879 1597 y(<)879 1672 y(>)879 1684 y(>)879 1697 y(>)879
1709 y(>)879 1721 y(>)879 1734 y(>)879 1746 y(>)879 1759
y(:)925 1533 y Fv(e)948 1540 y FC(1)989 1533 y FH(=)1049
1472 y Fs(\022)1102 1502 y FH(0)63 b FE(\000)p FH(i)1088
1563 y FE(\000)p FH(i)f(0)1250 1472 y Fs(\023)925 1647
y Fv(e)948 1654 y FC(2)989 1647 y FH(=)1049 1586 y Fs(\022)1088
1617 y FH(0)49 b FE(\000)p FH(1)1088 1677 y(1)69 b(0)1233
1586 y Fs(\023)925 1761 y Fv(e)948 1768 y FC(3)989 1761
y FH(=)1049 1700 y Fs(\022)1088 1731 y FE(\000)p FH(i)48
b(0)1102 1791 y(1)68 b(i)1222 1700 y Fs(\023)1736 1590
y FH(\(10.45\))-5 1869 y(b)q(e)17 b(a)f(complete)e(basis)j(of)g(t)o(w)o
(o)f(matrices)e(for)j(the)f(expansion)g(of)h(a)f(generic)g(quaternion:)
831 1979 y Fv(Q)22 b FE(\021)g Fv(q)977 1959 y Ft(a)1006
1979 y Fv(e)1029 1986 y Ft(a)1736 1979 y FH(\(10.46\))-5
2089 y Fv(e)18 2096 y Ft(x)40 2089 y FH(,)16 b(b)q(eing)g(the)g(three)f
(imaginary)g(units.)22 b(The)16 b(\015at)g(Hyp)q(erK\177)-24
b(ahler)16 b(metric)d(and)k(the)f(corresp)q(onding)-5
2149 y(triplet)f(of)i(Hyp)q(erK\177)-24 b(ahler)15 b(2{forms)h(are)h
(giv)o(en)e(b)o(y:)446 2259 y Fv(ds)494 2239 y FC(2)556
2259 y FE(\021)41 b Fv(h)664 2266 y Ft(uv)713 2259 y
Fv(dq)762 2239 y Ft(u)793 2259 y Fv(dq)842 2239 y Ft(v)884
2259 y FH(=)22 b Fv(d)p FD(q)999 2239 y Ft(T)1043 2259
y FH(\(1)-17 b(1)1094 2266 y FC(4)p FB(\002)p FC(4)1170
2259 y FE(\012)11 b FH(1)-17 b(1)1252 2266 y Ft(m)p FB(\002)p
Ft(m)1343 2259 y FH(\))17 b Fv(d)p FD(q)447 2338 y Fv(K)492
2318 y Ft(x)556 2338 y FH(=)42 b Fv(d)p FD(q)691 2318
y Ft(T)738 2338 y FE(^)791 2290 y Fs(\020)815 2338 y
Fv(J)847 2318 y FC(+)p FB(j)p Ft(x)917 2338 y FE(\012)11
b FH(1)-17 b(1)999 2345 y Ft(m)p FB(\002)p Ft(m)1091
2290 y Fs(\021)1132 2338 y Fv(d)p FD(q)549 b FH(\(10.47\))-5
2448 y(Alternativ)o(ely)11 b(in)i(the)g(ab)q(o)o(v)o(e)g(form)o(ula)f
(one)i(can)f(use)h(the)f(triplet)f(of)i(an)o(tiself)e(dual)h(t'Ho)q
(oft)h(matrices)-5 2508 y(to)j(de\014ne)f(the)g(Hyp)q(erK\177)-24
b(ahler)15 b(structure.)21 b(Using)16 b(the)g(iden)o(tities:)678
2580 y Fs(\()732 2622 y Fv(J)764 2597 y FC(+)p FB(j)p
Ft(x)759 2635 y(ab)837 2622 y FH(=)894 2603 y FC(1)p
894 2611 18 2 v 894 2640 a(2)929 2622 y FH(tr\()p Fv(e)1009
2629 y Ft(a)p 1029 2596 23 2 v 1029 2622 a Fv(e)1052
2629 y Ft(b)1069 2622 y Fv(e)1092 2604 y Ft(T)1092 2635
y(x)1119 2622 y FH(\))732 2691 y Fv(J)764 2665 y FB(\000j)p
Ft(x)759 2703 y(ab)837 2691 y FH(=)e FE(\000)941 2671
y FC(1)p 941 2679 18 2 v 941 2708 a(2)976 2691 y FH(tr\()p
Fv(e)1056 2698 y Ft(a)1076 2691 y Fv(e)1099 2673 y Ft(T)1099
2703 y(x)p 1126 2664 23 2 v 1126 2691 a Fv(e)1149 2698
y Ft(b)1166 2691 y FH(\))1736 2653 y(\(10.48\))916 2892
y(55)p eop
%%Page: 56 57
56 56 bop -5 15 a FH(and)17 b(rearranging)g(the)f(4)p
Fv(m)h FH(co)q(ordinates)g Fv(q)801 -3 y Ft(a)p FB(j)p
Ft(t)860 15 y FH(in)o(to)f(an)g Fv(m)p FH(-v)o(ector)g(of)g
(quaternions:)697 237 y FD(Q)22 b FH(=)822 89 y Fs(0)822
162 y(B)822 187 y(B)822 212 y(B)822 237 y(B)822 262 y(B)822
288 y(@)866 116 y Fv(Q)905 98 y FC(1)947 116 y FH(=)g
Fv(q)1031 98 y Ft(a)p FB(j)p FC(1)1087 116 y Fv(e)1110
123 y Ft(a)866 177 y Fv(Q)905 159 y FC(2)947 177 y FH(=)g
Fv(q)1031 159 y Ft(a)p FB(j)p FC(2)1087 177 y Fv(e)1110
184 y Ft(a)970 237 y Fv(:)8 b(:)g(:)871 297 y(Q)910 279
y Ft(t)947 297 y FH(=)22 b Fv(q)1031 279 y Ft(a)p FB(j)p
Ft(t)1082 297 y Fv(e)1105 304 y Ft(a)970 357 y Fv(:)8
b(:)g(:)1138 89 y Fs(1)1138 162 y(C)1138 187 y(C)1138
212 y(C)1138 237 y(C)1138 262 y(C)1138 288 y(A)1736 237
y FH(\(10.49\))-5 458 y(eq.s)16 b(10.47)p
 (#equation.10.47) [[94 657 120 669] [1 1 1 [3 3]] [0 0 1]] pdfm 
17 w(can)h(b)q(e)f(rewritten)f(as)i(follo)o(ws:)516 588
y Fv(ds)564 567 y FC(2)626 588 y FH(=)710 554 y(1)p 710
576 25 2 v 710 622 a(2)752 588 y(tr)806 540 y Fs(\020)831
588 y Fv(d)p FD(Q)898 567 y FB(y)925 588 y FH(1)-17 b(1)956
595 y Ft(m)p FB(\002)p Ft(m)1048 588 y Fv(d)p FD(Q)1115
540 y Fs(\021)539 704 y Fv(K)46 b FH(=)718 671 y(1)p
718 693 V 718 738 a(2)756 704 y Fv(d)p FD(Q)823 684 y
Ft(T)870 704 y FE(^)20 b FH(1)-17 b(1)955 711 y Ft(m)p
FB(\002)p Ft(m)1047 704 y Fv(d)p 1072 665 43 2 v FD(Q)22
b FH(=)1201 671 y(1)p 1201 693 25 2 v 1201 738 a(2)1239
704 y Fv(K)1284 684 y Ft(x)1314 704 y Fv(e)1337 684 y
Ft(T)1337 717 y(x)1736 704 y FH(\(10.50\))-5 827 y(The)c(action)g(of)g
(the)g(gauge)h(group)f FE(G)j FH(on)d(the)g(h)o(yp)q(erm)o(ultiple)o
(ts)d(is)j(assumed)f(to)h(b)q(e)g(linear)f(and)i(b)q(e)-5
887 y(generated)d(b)o(y)g(a)h(set)f(of)h(4)p Fv(m)11
b FE(\002)f FH(4)p Fv(m)17 b FH(matrices)d Fv(T)893 894
y Ft(I)913 887 y FH(.)21 b(Namely)14 b(w)o(e)i(set:)554
997 y Fv(\016)576 1004 y Ft(I)595 997 y FD(q)22 b FH(=)g
Fv(T)736 1004 y Ft(I)764 997 y FD(q)70 b FE(\000)-8 b(!)62
b Fv(k)1034 977 y Ft(u)1032 1010 y(I)1079 997 y FH(=)22
b(\()p Fv(T)1187 1004 y Ft(I)1206 997 y FH(\))1225 973
y Ft(u)1246 1012 y(v)1283 997 y Fv(q)1307 977 y Ft(v)1736
997 y FH(\(10.51\))-5 1107 y(In)d(order)h(for)g(this)f(action)h(to)g(b)
q(e)f(an)h(isometry)e(of)i(the)f(Euclidean)g(diagonal)h(metric)37
b(10.47)p
 (#equation.10.47) [[473 501 499 513] [1 1 1 [3 3]] [0 0 1]] pdfm 
20 w(it)19 b(is)-5 1167 y(necessary)11 b(and)i(su\016cien)o(t)d(that)i
(the)f(matrices)e Fv(T)896 1174 y Ft(I)928 1167 y FH(b)q(elong)j(to)f
(the)h(orthogonal)h(Lie)e(algebra)h Fv(S)s(O)q FH(\(4)p
Fv(m)p FH(\),)-5 1228 y(namely:)832 1288 y Fv(T)868 1267
y Ft(T)861 1300 y(I)909 1288 y FH(=)i FE(\000)p Fv(T)1029
1295 y Ft(I)1736 1288 y FH(\(10.52\))-5 1375 y(The)i(action)g(of)g
FE(G)i FH(ho)o(w)o(ev)o(er)c(is)i(not)g(only)f(required)g(to)h(b)q(e)g
(isometrical)d(but)j(also)g(to)g(b)q(e)g(triholomor-)-5
1435 y(phic.)21 b(This)16 b(means:)495 1495 y Fv(`)515
1502 y Ft(I)544 1495 y Fv(K)589 1475 y Ft(x)633 1495
y FE(\021)22 b FD(i)710 1502 y Ft(I)738 1495 y Fv(dK)808
1475 y Ft(x)850 1495 y FH(+)d Fv(d)8 b FD(i)956 1502
y Ft(I)985 1495 y Fv(K)1030 1475 y Ft(x)1074 1495 y FH(=)22
b Fv(d)8 b FD(i)1183 1502 y Ft(I)1211 1495 y Fv(K)1256
1475 y Ft(x)1300 1495 y FH(=)22 b(0)352 b(\(10.53\))-5
1583 y(A)16 b(straigh)o(tforw)o(ard)h(calculation)f(yields:)494
1693 y Fv(d)8 b FD(i)543 1700 y Ft(I)571 1693 y Fv(K)616
1672 y Ft(x)660 1693 y FH(=)14 b FE(\000)8 b Fv(d)p FD(q)814
1672 y Ft(T)861 1693 y FE(^)914 1644 y Fs(h)933 1693
y Fv(T)962 1700 y Ft(I)990 1693 y Fv(;)16 b(J)1052 1672
y FC(+)p FB(j)p Ft(x)1122 1693 y FE(\012)11 b FH(1)-17
b(1)1204 1700 y Ft(m)p FB(\002)p Ft(m)1295 1644 y Fs(i)1332
1693 y Fv(d)p FD(q)349 b FH(\(10.54\))-5 1803 y(so)20
b(that)g(the)g(triholomorphicit)o(y)d(condition)i(is)g(that)h(the)f
(generators)i Fv(T)1380 1810 y Ft(I)1419 1803 y FH(should)f(comm)o(ute)
c(with)-5 1863 y(the)f(tensor)g(pro)q(duct)g(of)g(the)g('t)f(Ho)q(oft)i
(matrices)d(with)h(the)h(unit)f(matrix)f(in)i Fv(m)p
FH({dimensions.)k(When)-5 1923 y(this)d(last)h(condition)f(is)g(v)o
(eri\014ed)f(w)o(e)g(can)i(write)e(the)h(momen)o(tum)d(maps)i(as:)651
2033 y FE(P)690 2012 y Ft(x)686 2045 y(I)734 2033 y FH(=)22
b FD(q)824 2012 y Ft(T)859 2033 y Fv(J)891 2012 y FC(+)p
FB(j)p Ft(x)961 2033 y FE(\012)11 b FH(1)-17 b(1)1043
2040 y Ft(m)p FB(\002)p Ft(m)1143 2033 y Fv(T)1172 2040
y Ft(I)1200 2033 y FD(q)506 b FH(\(10.55\))-5 2143 y(Alternativ)o(ely)
14 b(using)i(the)g(quaternionic)g(notation)h(w)o(e)f(ha)o(v)o(e:)572
2272 y FD(P)610 2279 y Ft(I)653 2272 y FH(=)718 2239
y(1)p 718 2261 V 718 2307 a(2)755 2272 y FE(P)794 2252
y Ft(x)790 2285 y(I)824 2272 y Fv(e)847 2252 y Ft(T)847
2285 y(x)897 2272 y FH(=)970 2239 y(1)p 970 2261 V 970
2307 a(2)1008 2272 y FD(Q)1050 2252 y Ft(T)1077 2272
y FH(1)-17 b(1)1109 2279 y Ft(m)p FB(\002)p Ft(m)1209
2272 y Fv(T)1238 2279 y Ft(I)p 1266 2233 43 2 v 1266
2272 a FD(Q)428 b FH(\(10.56\))-5 2419 y Fu(The)18 b(lagr)n(angian)p
-5 2435 320 2 v 68 2503 a FH(Using)d(these)f(ingredien)o(ts)f(the)i
(lagrangian)g(of)g(the)f(microscopic)f(renormalizable)f(theory)i(is)h
(im-)-5 2563 y(mediately)d(retriev)o(ed)g(from)i(the)g(general)g(form)o
(ulae)f(of)i(the)f(previous)g(subsection.)21 b(It)14
b(is)g(con)o(v)o(enien)o(t)-5 2623 y(to)j(set:)539 2673
y FD(Y)67 b FE(\021)57 b Fv(Y)783 2655 y Ft(I)811 2673
y Fv(t)829 2680 y Ft(I)p 1014 2634 44 2 v 1014 2673 a
FD(Y)110 b FE(\021)p 1254 2634 40 2 v 49 w Fv(Y)1293
2644 y Ft(I)1321 2673 y Fv(t)1339 2680 y Ft(I)522 2733
y FD(F)557 2740 y Ft(\026\027)648 2733 y FE(\021)49 b
Fv(F)775 2715 y Ft(I)768 2745 y(\026\027)819 2733 y Fv(t)837
2740 y Ft(I)954 2733 y FH(tr)8 b(\()p Fv(t)1037 2740
y Ft(I)1056 2733 y Fv(t)1074 2740 y Ft(J)1099 2733 y
FH(\))48 b FE(\021)66 b FD(g)1299 2740 y Ft(I)s(J)1736
2699 y FH(\(10.57\))916 2892 y(56)p eop
%%Page: 57 58
57 57 bop -5 15 a Fv(t)13 22 y Ft(I)52 15 y FH(denoting)19
b(a)g(basis)g(of)g(generators)g(of)g(the)g(gauge)g(group)h(and)f(in)g
(this)f(condensed)h(notation)g(w)o(e)-5 76 y(obtain:)527
136 y FE(L)561 112 y Ft(micr)q(oscopic)561 148 y(N)t
FC(=2)p Ft(Y)8 b(M)772 136 y FH(=)22 b FE(L)866 112 y
Ft(micr)q(oscopic)866 148 y(bosonic)1074 136 y FH(+)d
FE(L)1165 112 y Ft(micr)q(oscopic)1165 148 y(f)t(er)q(mionic)1736
136 y FH(\(10.58\))-5 223 y(where)d(the)g(b)q(osonic)h(lagrangian)h
(is:)242 352 y FE(L)276 329 y Ft(micr)q(oscopic)276 365
y(bosonic)506 352 y FH(=)42 b FE(\000)8 b FH(Im)n Fv(\034)14
b FH(tr)i(\()p FD(F)834 359 y Ft(\026\027)886 352 y FD(F)921
359 y Ft(\026\027)964 352 y FH(\))j(+)1064 318 y(1)p
1064 341 25 2 v 1064 386 a(2)1102 352 y(Re)p Fv(\034)14
b FH(tr)i(\()p FD(F)1303 359 y Ft(\026\027)1355 352 y
FD(F)1390 359 y Ft(\032\033)1431 352 y FH(\))h Fv(")1490
332 y Ft(\026\027)r(\032\033)586 453 y FH(+2)8 b(Im)n
Fv(\034)14 b FH(tr)804 405 y Fs(\020)829 453 y FE(r)871
460 y Ft(\026)894 453 y FD(Y)c FE(r)988 460 y Ft(\026)p
1010 414 44 2 v 1010 453 a FD(Y)1054 405 y Fs(\021)1098
453 y FH(+)20 b FE(r)1198 460 y Ft(\026)1220 453 y FD(q)1250
432 y Ft(T)1294 453 y FE(r)1336 460 y Ft(\026)1359 453
y FD(q)f FE(\000)g Fv(V)11 b FH(\()p FD(Y)q Fv(;)d FD(q)p
FH(\))98 b(\(10.59\))292 598 y Fv(V)11 b FH(\()p FD(Y)q
Fv(;)d FD(q)p FH(\))42 b(=)g(2)8 b(Im)n Fv(\034)15 b
FH(tr)766 550 y Fs(\020h)810 598 y FD(Y)10 b Fv(;)p 893
559 V 17 w FD(Y)936 550 y Fs(i\021)981 561 y FC(2)1020
598 y FE(\000)19 b FH(2)8 b FD(q)1140 577 y Ft(T)1184
550 y Fs(n)1212 598 y FD(Y)i Fv(;)p 1294 559 V 16 w FD(Y)1346
550 y Fs(o)1382 598 y FD(q)586 719 y FH(+)679 685 y(1)p
637 707 110 2 v 637 753 a(2Im)n Fv(\034)791 665 y FC(3)770
678 y Fs(X)768 768 y Ft(x)p FC(=1)849 719 y FE(P)888
698 y Ft(x)884 731 y(I)918 719 y FE(P)957 698 y Ft(x)953
731 y(J)987 719 y FD(g)1016 698 y Ft(I)s(J)1736 719 y
FH(\(10.60\))-5 861 y(The)i(form)o(ula)e(for)i(the)f(scalar)h(p)q(oten)
o(tial)f(exhibits)g(in)g(a)h(clear)f(fashion)h(the)f(\015at)h
(directions)f(asso)q(ciated)-5 921 y(with)17 b(the)f(mo)q(duli)f
(\014elds)h FD(Y)i FH(in)e(the)h(Cartan)g(subalgebra)h
FE(H)f FH(of)f(the)h(gauge)g(algebra.)22 b(Actually)15
b(the)-5 981 y(p)q(oten)o(tial)23 b(is)g(just)h(homogeneous)f(of)g
(degree)g(four)g(in)g(all)g(the)g(scalar)g(\014elds)g(as)h(exp)q(ected)
e(from)-5 1041 y(renormalizabilit)o(y)l(.)68 1101 y(The)d(fermionic)e
(part)i(of)g(the)f(lagrangian)i(also)g(simpli\014es)c(v)o(ery)i(m)o(uc)
o(h)f(since)h(it)g(just)h(con)o(tains)-5 1162 y(the)g(kinetic)e(part)j
(and)g(the)e(mass)h(terms)f(induced)g(b)o(y)h(the)f(gauging.)31
b(The)20 b(P)o(auli)e(terms)g(and)h(the)-5 1222 y(4{fermi)c(terms)f
(are)i(all)g(zero,)f(since)h(the)f(tensor)i Fv(C)955
1229 y Ft(ij)r(k)1020 1222 y FH(v)m(anishes)g(and)f(the)g(Riemann)e
(tensors)j(of)f(the)-5 1282 y(sp)q(ecial)j(and)g(Hyp)q(erK\177)-24
b(ahler)17 b(manifolds)h(also)h(v)m(anish.)29 b(The)19
b(ev)m(aluation)g(of)g(the)f(mass)g(matrices)f(is)-5
1342 y(straigh)o(tforw)o(ard)e(b)o(y)e(inserting)g(the)h(explicit)e
(form)g(of)i(the)g(Killing)e(v)o(ectors)h(and)i(of)f(the)f(momen)o(tum)
-5 1402 y(maps)f(in)o(to)g(eq.s)f(10.31)p
 (#equation.10.31) [[145 431 172 443] [1 1 1 [3 3]] [0 0 1]] pdfm (.)21
b(The)13 b(only)f(item)e(that)j(is)f(still)f(missing)g(in)h(suc)o(h)g
(a)g(calculation)g(is)g(the)g(explicit)-5 1462 y(form)j(of)i(the)f
(quaternionic)f(vielb)q(ein.)20 b(This)c(is)g(v)o(ery)f(easily)h(giv)o
(en.)k(W)l(e)c(set:)526 1572 y FE(U)562 1552 y Ft(A\013)635
1572 y FE(\021)22 b(U)732 1552 y Ft(A\013)727 1585 y(b)p
FB(j)p Ft(s)792 1572 y Fv(dq)841 1552 y Ft(b)p FB(j)p
Ft(s)906 1572 y FH(=)g Fv(d)p FD(Q)h FH(=)f Fv(dq)1165
1552 y Ft(a)p FB(j)p Ft(t)1216 1572 y FH(\()p Fv(e)1258
1579 y Ft(a)1279 1572 y FH(\))1298 1552 y Ft(A)1324 1585
y(B)1736 1572 y FH(\(10.61\))-5 1682 y(and)16 b(w)o(e)e(iden)o(tify)f
(the)h(symplectic)e(index)h Fv(\013)i FH(running)g(on)h(2)p
Fv(m)e FH(v)m(alues)h(with)f(the)h(pair)f(of)h(indices)f
Fv(B)s(;)8 b(t)-5 1742 y FH(\()17 b Fv(B)f FH(=)e(1)p
Fv(;)8 b FH(2;)16 b Fv(t)e FH(=)f(1)p Fv(;)8 b(:)g(:)g(:)g(;)g(m)p
FH(\).)21 b(In)16 b(this)g(w)o(a)o(y)g(w)o(e)g(obtain:)738
1859 y FE(U)774 1833 y Ft(A)29 b FB(j)p Ft(t)796 1873
y(B)r FB(j)p Ft(b)p FB(j)p Ft(s)899 1859 y FH(=)22 b
Fv(\016)983 1838 y Ft(t)981 1871 y(s)1008 1859 y FH(\()p
Fv(e)1050 1866 y Ft(b)1066 1859 y FH(\))1085 1838 y Ft(A)1112
1871 y(B)1736 1859 y FH(\(10.62\))-5 2025 y Fw(App)r(endix)c(A:)h(The)f
(solution)h(of)g(the)g(Bianc)n(hi)e(iden)n(tities)g(and)-5
2116 y(the)27 b(sup)r(ersymmetry)f(transformation)i(la)n(ws)-5
2226 y FH(In)c(this)f(App)q(endix)g(w)o(e)h(describ)q(e)f(the)g
(geometric)f(approac)o(h)j(for)f(the)f(deriv)m(ation)h(of)g(the)f
Fv(N)32 b FH(=)-5 2286 y(2)23 b(sup)q(ersymmetry)d(transformation)j(la)
o(ws)g(of)g(the)f(ph)o(ysical)g(\014elds.)40 b(As)22
b(it)h(will)e(app)q(ear)j(in)e(the)-5 2346 y(follo)o(wing)16
b(this)g(requires)g(the)g(preliminary)d(solution)k(of)f(Bianc)o(hi)f
(iden)o(tities)f(in)i(sup)q(erspace.)68 2407 y(The)23
b(\014rst)g(step)g(to)g(p)q(erform)f(is)h(to)g(extend)f(the)h(ph)o
(ysical)e(\014elds)i(to)g(sup)q(er\014elds)g(in)f Fv(N)31
b FH(=)25 b(2)-5 2467 y(sup)q(erspace:)d(that)17 b(means)e(that)i(the)f
(space{time)e(1-forms)i Fv(!)1161 2449 y Ft(a)6 b(b)1203
2467 y FH(,)16 b Fv(V)1272 2449 y Ft(a)1293 2467 y FH(,)p
Fv( )1341 2449 y Ft(A)1369 2467 y FH(,)f Fv( )1430 2474
y Ft(A)1459 2467 y FH(,)g Fv(A)1525 2449 y FC(\003)1568
2467 y FH(and)i(the)f(space{)-5 2527 y(time)c(0{forms)h
Fv(\025)312 2509 y Ft(iA)353 2527 y FH(,)h Fv(\025)409
2509 y Ft(i)421 2497 y Fm(?)409 2539 y Ft(A)442 2527
y FH(,)f Fv(z)494 2509 y Ft(i)508 2527 y FH(,)h Fv(z)561
2509 y Ft(i)573 2497 y Fm(?)593 2527 y FH(,)g Fv(\020)646
2509 y Ft(\013)671 2527 y FH(,)f Fv(\020)719 2534 y Ft(\013)744
2527 y FH(,)h Fv(q)796 2509 y Ft(u)832 2527 y FH(de\014ned)f(in)h
(section)f(8)h(are)g(promoted)f(to)h(1{sup)q(erforms)-5
2587 y(and)j(0{sup)q(erforms)g(in)f Fv(N)j FH(=)14 b(2)i(sup)q
(erspace,)g(resp)q(ectiv)o(ely)l(.)68 2647 y(The)26 b(de\014nition)f
(of)g(the)g(sup)q(erspace)h(curv)m(atures)g(actually)f(coincides)f
(with)h(that)h(giv)o(en)e(in)-5 2707 y(eq.s)d(8.4)p
 (#equation.8.4) [[95 117 110 129] [1 1 1 [3 3]] [0 0 1]] pdfm ({8.14)p
 (#equation.8.12) [[116 117 137 129] [1 1 1 [3 3]] [0 0 1]] pdfm 
23 w(pro)o(vided)g(all)g(the)g Fv(p)p FH({forms)h(\()p
Fv(p)h FH(=)f(0)p Fv(;)8 b FH(1)p Fv(;)g FH(2\))23 b(are)e(though)o(t)i
(as)f Fv(p)p FH({sup)q(erforms)g(\(here)-5 2768 y(and)g(in)e(the)g
(follo)o(wing)h(b)o(y)f("curv)m(atures")i(w)o(e)e(mean)f(not)j(only)e
(2{forms,)h(but)g(also)h(the)e(1{forms)916 2892 y(57)p
eop
%%Page: 58 59
58 58 bop -5 15 a FH(de\014ned)16 b(as)h(co)o(v)m(arian)o(t)f
(di\013eren)o(tials)f(of)i(the)f(0{form)g(sup)q(er\014elds\).)-5
76 y(W)l(e)g(note)h(that)f(the)g(de\014nition)g(of)h(sup)q(erspace)f
(curv)m(atures)h(in)f(the)g(gra)o(vitational)g(sector,)g(namely:)296
186 y Fv(T)332 165 y Ft(a)394 186 y FE(\021)41 b(D)q
Fv(V)553 165 y Ft(a)585 186 y FE(\000)11 b FH(i)p 657
146 34 2 v 8 w Fv( )690 197 y Ft(A)730 186 y FE(^)g Fv(\015)802
165 y Ft(a)823 186 y Fv( )857 165 y Ft(A)1773 186 y FH(\(A.1\))299
281 y Fv(\032)324 288 y Ft(A)394 281 y FE(\021)41 b Fv(d )531
288 y Ft(A)571 281 y FE(\000)626 248 y FH(1)p 626 270
25 2 v 626 316 a(4)655 281 y Fv(\015)680 288 y Ft(ab)725
281 y Fv(!)757 261 y Ft(ab)804 281 y FE(^)11 b Fv( )880
288 y Ft(A)919 281 y FH(+)979 248 y(i)p 973 270 V 973
316 a(2)1017 265 y Fs(b)1003 281 y FE(Q)f(^)i Fv( )1131
288 y Ft(A)1170 281 y FH(+)1223 277 y Fs(b)1219 281 y
Fv(!)1267 261 y Ft(B)1249 294 y(A)1309 281 y FE(^)f Fv( )1385
288 y Ft(B)1429 281 y FE(\021)i(r)p Fv( )1555 288 y Ft(A)1773
281 y FH(\(A.2\))299 399 y Fv(\032)324 378 y Ft(A)394
399 y FE(\021)41 b Fv(d )533 378 y Ft(A)573 399 y FE(\000)627
365 y FH(1)p 627 387 V 627 433 a(4)657 399 y Fv(\015)682
406 y Ft(ab)726 399 y Fv(!)758 378 y Ft(ab)805 399 y
FE(^)12 b Fv( )884 378 y Ft(A)923 399 y FE(\000)983 365
y FH(i)p 978 387 V 978 433 a(2)1021 383 y Fs(b)1007 399
y FE(Q)f(^)g Fv( )1137 378 y Ft(A)1176 399 y FH(+)1230
395 y Fs(b)1225 399 y Fv(!)1257 378 y Ft(A)1282 411 y(B)1323
399 y FE(^)h Fv( )1402 378 y Ft(B)1445 399 y FE(\021)i(r)p
Fv( )1574 378 y Ft(A)1773 399 y FH(\(A.3\))279 493 y
Fv(R)316 473 y Ft(ab)394 493 y FE(\021)41 b Fv(d!)531
473 y Ft(ab)579 493 y FE(\000)11 b Fv(!)661 473 y Ft(a)678
506 y(c)706 493 y FE(^)g Fv(!)782 473 y Ft(cb)1773 493
y FH(\(A.4\))294 575 y Fv(F)333 554 y FC(0)394 575 y
FE(\021)41 b Fv(dA)536 554 y FC(0)575 575 y FH(+)p 633
536 34 2 v 20 w Fv(L)666 546 y FC(0)p 685 535 V 685 575
a Fv( )719 587 y Ft(A)759 575 y FE(^)11 b Fv( )835 582
y Ft(B)865 575 y Fv(\017)885 554 y Ft(AB)952 575 y FH(+)g
Fv(L)1034 554 y FC(0)p 1054 535 V 1054 575 a Fv( )1088
545 y Ft(A)1127 575 y FE(^)h Fv( )1206 554 y Ft(B)1235
575 y Fv(\017)1255 582 y Ft(AB)1773 575 y FH(\(A.5\))-5
685 y(where)17 b Fv(F)176 667 y FC(0)211 685 y FH(denotes)g(the)f(gra)o
(viphoton,)h(has)h(b)q(een)e(c)o(hosen)h(in)f(suc)o(h)g(a)h(w)o(a)o(y)g
(that)g(b)o(y)f(setting)g Fv(R)1796 667 y Ft(ab)1847
685 y FH(=)-5 745 y Fv(T)31 727 y Ft(a)71 745 y FH(=)k
Fv(\032)154 727 y Ft(A)203 745 y FH(=)f Fv(\032)285 752
y Ft(A)334 745 y FH(=)h Fv(F)431 727 y FC(0)469 745 y
FH(=)g(0)g(,)h(deleting)d(the)i(comp)q(osite)f(connections)1395
729 y Fs(b)1380 745 y FE(Q)8 b Fv(;)1464 741 y Fs(b)1459
745 y Fv(!)1491 727 y Ft(A)1489 757 y(B)1540 745 y FH(and)20
b(normalising)-5 805 y Fv(L)28 787 y FC(0)56 805 y FH(\(0)p
Fv(;)8 b FH(0\))15 b(=)f(1)h(w)o(e)f(obtain)h(the)f(Maurer{Cartan)i
(equations)e(of)h(the)f Fv(N)19 b FH(=)14 b(2)h(P)o(oincar)o(\023)-23
b(e)14 b(sup)q(eralgebra)-5 866 y(where)k(the)g(one)h(forms)e
Fv(!)484 847 y Ft(ab)520 866 y Fv(;)8 b(V)581 847 y Ft(a)602
866 y Fv(;)g( )658 847 y Ft(A)686 866 y Fv(;)g( )740
873 y Ft(A)768 866 y Fv(;)g(A)827 847 y FC(0)865 866
y FH(are)18 b(dual)h(to)f(the)g(corresp)q(onding)i(generators)f(of)f
(the)-5 926 y(group.)68 986 y(The)j(next)g(step)f(is)h(to)g(write)f(do)
o(wn)i(the)e(Bianc)o(hi)g(iden)o(tities)e(for)j(all)g(the)f(curv)m
(atures)h(and)h(to)-5 1046 y(solv)o(e)17 b(them)f(in)h(sup)q(erspace.)
25 b(Applying)17 b(the)g Fv(d)g FH(op)q(erator)i(to)f(eq.s)34
b(A.1)p  (#equation.A.1) [[380 516 398 528] [1 1 1 [3 3]] [0 0 1]] pdfm 
({)17 b(A.4)p
 (#equation.A.1) [[408 516 426 528] [1 1 1 [3 3]] [0 0 1]] pdfm 
17 w(and)36 b(8.9)p
 (#equation.8.9) [[457 516 472 528] [1 1 1 [3 3]] [0 0 1]] pdfm ({)18
b(8.14)p
 (#equation.8.12) [[482 516 503 528] [1 1 1 [3 3]] [0 0 1]] pdfm 
18 w(one)-5 1106 y(\014nds:)234 1216 y FE(D)q Fv(T)309
1198 y Ft(a)389 1216 y FH(+)49 b Fv(R)513 1196 y Ft(ab)560
1216 y FE(^)12 b Fv(V)644 1196 y Ft(b)672 1216 y FE(\000)f
FH(i)p 736 1177 V Fv( )769 1187 y Ft(A)809 1216 y FE(^)g
Fv(\015)881 1196 y Ft(a)902 1216 y Fv(\032)927 1223 y
Ft(A)966 1216 y FH(+)g(i)p 1029 1190 26 2 v Fv(\032)1054
1196 y Ft(A)1094 1216 y FE(^)g Fv(\015)1166 1196 y Ft(a)1187
1216 y Fv( )1219 1223 y Ft(A)1261 1216 y FH(=)j(0)436
b(\(A.6\))235 1312 y FE(r)p Fv(\032)302 1319 y Ft(A)389
1312 y FH(+)481 1278 y(1)p 481 1300 25 2 v 481 1346 a(4)510
1312 y Fv(\015)535 1319 y Ft(ab)580 1312 y Fv(R)617 1292
y Ft(ab)664 1312 y FE(^)11 b Fv( )740 1319 y Ft(A)780
1312 y FE(\000)840 1278 y FH(i)p 835 1300 V 835 1346
a(2)868 1296 y Fs(c)864 1312 y Fv(K)k FE(^)c Fv( )996
1319 y Ft(A)1036 1312 y FE(\000)1096 1278 y FH(i)p 1090
1300 V 1090 1346 a(2)1131 1296 y Fs(b)1120 1312 y Fv(R)1174
1292 y Ft(B)1157 1324 y(A)1215 1312 y FE(^)g Fv( )1291
1319 y Ft(B)1335 1312 y FH(=)j(0)362 b(\(A.7\))235 1430
y FE(r)p Fv(\032)302 1412 y Ft(A)389 1430 y FH(+)481
1396 y(1)p 481 1418 V 481 1464 a(4)510 1430 y Fv(\015)535
1437 y Ft(ab)580 1430 y Fv(R)617 1409 y Ft(ab)664 1430
y FE(^)11 b Fv( )742 1409 y Ft(A)782 1430 y FH(+)841
1396 y(i)p 836 1418 V 836 1464 a(2)869 1413 y Fs(c)865
1430 y Fv(K)k FE(^)c Fv( )999 1409 y Ft(A)1038 1430 y
FE(\000)1099 1413 y Fs(b)1088 1430 y Fv(R)1125 1409 y
Ft(A)1152 1442 y(B)1193 1430 y FE(^)g Fv( )1271 1409
y Ft(B)1315 1430 y FH(=)j(0)382 b(\(A.8\))226 1522 y
FE(D)q Fv(R)302 1503 y Ft(ab)389 1522 y FH(=)63 b(0)1259
b(\(A.9\))232 1603 y FE(r)274 1585 y FC(2)294 1603 y
Fv(z)319 1585 y Ft(i)389 1603 y FE(\000)49 b Fv(g)510
1555 y Fs(\020)535 1603 y Fv(F)574 1582 y FC(\003)611
1603 y FE(\000)p 661 1564 34 2 v 11 w Fv(L)694 1574 y
FC(\003)p 729 1563 V 729 1603 a Fv( )762 1615 y Ft(A)802
1603 y FE(^)11 b Fv( )878 1610 y Ft(B)908 1603 y Fv(\017)928
1582 y Ft(AB)996 1603 y FE(\000)p 1045 1564 V 10 w Fv(L)1079
1574 y FC(\003)p 1113 1563 V 1113 1603 a Fv( )1147 1573
y Ft(A)1186 1603 y FE(^)h Fv( )1265 1582 y Ft(B)1295
1603 y Fv(\017)1315 1610 y Ft(AB)1371 1555 y Fs(\021)1412
1603 y Fv(k)1439 1582 y Ft(i)1437 1615 y FC(\003)1464
1603 y FH(\()p Fv(z)r FH(\))i(=)g(0)131 b(\(A.10\))223
1697 y FE(r)265 1679 y FC(2)285 1697 y Fv(z)310 1679
y Ft(i)322 1667 y Fm(?)389 1697 y FE(\000)49 b Fv(g)510
1649 y Fs(\020)535 1697 y Fv(F)574 1676 y FC(\003)611
1697 y FE(\000)p 661 1658 V 11 w Fv(L)694 1668 y FC(\003)p
729 1657 V 729 1697 a Fv( )762 1709 y Ft(A)802 1697 y
FE(^)11 b Fv( )878 1704 y Ft(B)908 1697 y Fv(\017)928
1676 y Ft(AB)996 1697 y FE(\000)p 1045 1658 V 10 w Fv(L)1079
1668 y FC(\003)p 1113 1657 V 1113 1697 a Fv( )1147 1667
y Ft(A)1186 1697 y FE(^)h Fv( )1265 1676 y Ft(B)1295
1697 y Fv(\017)1315 1704 y Ft(AB)1371 1649 y Fs(\021)1412
1697 y Fv(k)1439 1676 y Ft(i)1451 1665 y Fm(?)1437 1709
y FC(\003)1485 1697 y FH(=)i(0)187 b(\(A.11\))217 1805
y FE(r)259 1787 y FC(2)279 1805 y Fv(\025)307 1787 y
Ft(iA)389 1805 y FH(+)481 1772 y(1)p 481 1794 25 2 v
481 1839 a(4)510 1805 y Fv(\015)535 1812 y Ft(ab)580
1805 y Fv(R)617 1785 y Ft(ab)653 1805 y Fv(\025)681 1785
y Ft(iA)733 1805 y FH(+)793 1772 y(i)p 787 1794 V 787
1839 a(2)821 1789 y Fs(c)817 1805 y Fv(K)t(\025)890 1785
y Ft(iA)942 1805 y FH(+)1002 1789 y Fs(b)991 1805 y Fv(R)1028
1785 y Ft(i)1040 1818 y(j)1058 1805 y Fv(\025)1086 1785
y Ft(j)r(A)1142 1805 y FE(\000)1202 1772 y FH(i)p 1197
1794 V 1197 1839 a(2)1238 1789 y Fs(b)1226 1805 y Fv(R)1263
1785 y Ft(A)1280 1818 y(B)1321 1805 y FE(^)11 b Fv(\025)1393
1785 y Ft(iB)1450 1805 y FH(=)j(0)222 b(\(A.12\))222
1923 y FE(r)264 1905 y FC(2)283 1923 y Fv(\025)311 1905
y Ft(i)323 1893 y Fm(?)311 1935 y Ft(A)389 1923 y FH(+)481
1889 y(1)p 481 1911 V 481 1957 a(4)510 1923 y Fv(\015)535
1930 y Ft(ab)580 1923 y Fv(R)617 1902 y Ft(ab)653 1923
y Fv(\025)681 1902 y Ft(i)693 1891 y Fm(?)681 1935 y
Ft(A)725 1923 y FE(\000)785 1889 y FH(i)p 780 1911 V
780 1957 a(2)813 1907 y Fs(c)809 1923 y Fv(K)t(\025)882
1902 y Ft(i)894 1891 y Fm(?)882 1935 y Ft(A)926 1923
y FH(+)986 1907 y Fs(b)975 1923 y Fv(R)1012 1902 y Ft(i)1024
1891 y Fm(?)1042 1935 y Ft(j)1058 1926 y Fm(?)1078 1923
y Fv(\025)1106 1899 y Ft(j)1122 1887 y Fm(?)1106 1935
y Ft(A)1154 1923 y FE(\000)1214 1889 y FH(i)p 1208 1911
V 1208 1957 a(2)1249 1907 y Fs(b)1238 1923 y Fv(R)1275
1902 y Ft(B)1291 1935 y(A)1331 1923 y FE(^)11 b Fv(\025)1403
1902 y Ft(i)1415 1891 y Fm(?)1403 1935 y Ft(B)1449 1923
y FH(=)j(0)223 b(\(A.13\))229 2026 y FE(r)p Fv(F)310
2008 y FC(\003)389 2026 y FE(\000)49 b(r)p 519 1987 34
2 v Fv(L)551 1997 y FC(\003)589 2026 y FE(^)p 633 1986
V 11 w Fv( )667 2038 y Ft(A)706 2026 y FE(^)12 b Fv( )783
2033 y Ft(B)813 2026 y Fv(\017)833 2005 y Ft(AB)900 2026
y FE(\000)f(r)p Fv(L)1025 2005 y FC(\003)1062 2026 y
FE(^)p 1107 1986 V 12 w Fv( )1140 1996 y Ft(A)1180 2026
y FE(^)g Fv( )1258 2005 y Ft(B)1288 2026 y Fv(\017)1308
2033 y Ft(AB)389 2107 y FH(+)49 b(2)p 500 2068 V Fv(L)533
2078 y FC(\003)p 560 2067 V 560 2107 a Fv( )593 2119
y Ft(A)633 2107 y FE(^)11 b Fv(\032)702 2114 y Ft(B)733
2107 y Fv(\017)753 2086 y Ft(AB)820 2107 y FH(+)g(2)p
Fv(L)926 2086 y FC(\003)p 953 2067 V 953 2107 a Fv( )987
2077 y Ft(A)1026 2107 y FE(^)h Fv( )1105 2086 y Ft(B)1135
2107 y Fv(\017)1155 2114 y Ft(AB)1225 2107 y FH(=)i(0)447
b(\(A.14\))218 2188 y FE(rU)296 2170 y Ft(A\013)389 2188
y FE(\000)49 b Fv(g)510 2140 y Fs(\020)535 2188 y Fv(F)574
2168 y FC(\003)611 2188 y FE(\000)p 661 2149 V 11 w Fv(L)694
2159 y FC(\003)p 729 2149 V 729 2188 a Fv( )762 2200
y Ft(A)802 2188 y FE(^)11 b Fv( )878 2195 y Ft(B)908
2188 y Fv(\017)928 2168 y Ft(AB)996 2188 y FE(\000)p
1045 2149 V 10 w Fv(L)1079 2159 y FC(\003)p 1113 2149
V 1113 2188 a Fv( )1147 2159 y Ft(A)1186 2188 y FE(^)h
Fv( )1265 2168 y Ft(B)1295 2188 y Fv(\017)1315 2195 y
Ft(AB)1371 2140 y Fs(\021)1412 2188 y Fv(k)1439 2168
y Ft(u)1437 2201 y FC(\003)1464 2188 y FH(\()p Fv(z)r
FH(\))p FE(U)1563 2168 y Ft(A\013)1558 2201 y(u)1628
2188 y FH(=)i(0)44 b(\(A.15\))229 2297 y FE(r)271 2279
y FC(2)290 2297 y Fv(\020)311 2304 y Ft(\013)389 2297
y FH(+)481 2263 y(1)p 481 2285 25 2 v 481 2331 a(4)510
2297 y Fv(R)547 2276 y Ft(ab)592 2297 y Fv(\015)617 2304
y Ft(ab)661 2297 y Fv(\020)682 2304 y Ft(\013)719 2297
y FH(+)778 2263 y(i)p 773 2285 V 773 2331 a(2)806 2280
y Fs(c)802 2297 y Fv(K)12 b(\020)876 2304 y Ft(\013)921
2297 y FH(+)981 2280 y Fs(b)970 2297 y Fv(R)1030 2276
y Ft(\014)1007 2309 y(\013)1053 2297 y Fv(\020)1074 2304
y Ft(\014)1112 2297 y FH(=)i(0)560 b(\(A.16\))227 2414
y FE(r)269 2396 y FC(2)288 2414 y Fv(\020)313 2396 y
Ft(\013)389 2414 y FH(+)481 2380 y(1)p 481 2403 V 481
2448 a(4)510 2414 y Fv(R)547 2394 y Ft(ab)592 2414 y
Fv(\015)617 2421 y Ft(ab)661 2414 y Fv(\020)686 2394
y Ft(\013)722 2414 y FE(\000)783 2380 y FH(i)p 777 2403
V 777 2448 a(2)811 2398 y Fs(c)806 2414 y Fv(K)13 b(\020)885
2394 y Ft(\013)929 2414 y FH(+)989 2398 y Fs(b)978 2414
y Fv(R)1015 2394 y Ft(\013)1038 2426 y(\014)1061 2414
y Fv(\020)1086 2394 y Ft(\014)1124 2414 y FH(=)h(0)548
b(\(A.17\))1748 2502 y(\(A.18\))68 2612 y(The)19 b(co)o(v)m(arian)o(t)g
(deriv)m(ativ)o(es)e FE(r)h FH(and)h FE(D)i FH(ha)o(v)o(e)d(b)q(een)h
(de\014ned)f(in)g(eq.s)37 b(A.1)p
 (#equation.A.1) [[414 140 432 152] [1 1 1 [3 3]] [0 0 1]] pdfm ({)19
b(A.5)p  (#equation.A.1) [[442 140 460 152] [1 1 1 [3 3]] [0 0 1]] pdfm 
18 w(and)g(include)-5 2672 y(the)e(gauged)g(connections)g(de\014ned)f
(in)g(eq.)g(7.57)p
 (#equation.7.57) [[267 126 288 138] [1 1 1 [3 3]] [0 0 1]] pdfm (.)23
b(F)l(urthermore)15 b(the)h(hat)h(on)g(the)f(scalar)h(manifolds)-5
2733 y(curv)m(atures)237 2716 y Fs(c)233 2733 y Fv(K)t(;)311
2716 y Fs(b)300 2733 y Fv(R)337 2715 y Ft(i)349 2745
y(j)375 2733 y Fv(;)417 2716 y Fs(b)405 2733 y Fv(R)442
2715 y Ft(\013)465 2745 y(\014)497 2733 y Fv(;)539 2716
y Fs(b)527 2733 y Fv(R)564 2715 y Ft(A)591 2745 y(B)637
2733 y FH(denotes)g(the)f(gauged)h(curv)m(atures)f(de\014ned)g(in)g
(7.58)p
 (#equation.7.58) [[438 111 459 123] [1 1 1 [3 3]] [0 0 1]] pdfm (.)916
2892 y(58)p eop
%%Page: 59 60
59 59 bop 68 15 a FH(The)16 b(solution)f(can)g(b)q(e)h(obtained)f(as)h
(follo)o(ws:)21 b(\014rst)15 b(of)h(all)e(one)i(requires)e(that)h(the)g
(expansion)h(of)-5 76 y(the)e(curv)m(atures)g(along)h(the)e(in)o
(trinsic)f Fv(p)p FH({forms)i(basis)h(in)e(sup)q(erspace)i(namely:)j
Fv(V)1530 58 y Ft(a)1551 76 y Fv(;)8 b(V)1612 58 y Ft(a)1639
76 y FE(^)e Fv(V)1718 58 y Ft(b)1735 76 y Fv(;)i( )r(;)g( )g
FE(^)-5 136 y Fv(V)35 118 y Ft(b)52 136 y Fv(;)g( )13
b FE(^)f Fv( )r FH(,)k(is)h(giv)o(en)g(in)g(terms)f(only)h(of)g(the)g
(ph)o(ysical)f(\014elds)h(\(rheonom)o(y\).)23 b(This)18
b(insures)f(that)h(no)-5 196 y(new)f(degree)e(of)i(freedom)d(is)i(in)o
(tro)q(duced)g(in)g(the)g(theory)l(.)-5 256 y(Secondly)22
b(one)h(writes)f(do)o(wn)h(suc)o(h)g(expansion)g(in)f(a)h(form)f(whic)o
(h)g(is)g(compatible)f(with)h(all)g(the)-5 316 y(symmetrie)o(s)15
b(of)j(the)g(theory)l(,)f(that)h(is:)24 b(co)o(v)m(ariance)17
b(under)h Fv(U)5 b FH(\(1\))18 b(K\177)-24 b(ahler)18
b(and)g Fv(S)s(U)5 b FH(\(2\))12 b FE(\012)g Fv(S)s(p)p
FH(\(2)p Fv(;)c(m)p FH(\),)-5 377 y(Loren)o(tz)15 b(transformations)h
(and)g(reparametrization)d(of)j(the)f(scalar)g(manifolds.)20
b(Besides)14 b(it)h(is)g(v)o(ery)-5 437 y(useful)g(to)g(tak)o(e)f(in)o
(to)h(accoun)o(t)g(the)f(in)o(v)m(ariance)g(under)h(the)g(follo)o(wing)
f(rigid)h(rescalings)g(of)g(the)f(\014elds)-5 497 y(\(and)j(their)f
(corresp)q(onding)h(curv)m(atures\):)503 598 y(\()p Fv(!)554
578 y Ft(ab)590 598 y Fv(;)8 b(A)649 578 y FC(\003)675
598 y Fv(;)g(q)721 578 y Ft(u)743 598 y Fv(;)g(z)790
578 y Ft(i)804 598 y Fv(;)g(z)851 578 y Ft(i)863 566
y Fm(?)882 598 y FH(\))14 b FE(!)g FH(\()p Fv(!)1030
578 y Ft(ab)1066 598 y Fv(;)8 b(A)1125 578 y FC(\003)1151
598 y Fv(;)g(q)1197 578 y Ft(u)1219 598 y Fv(;)g(z)1266
578 y Ft(i)1279 598 y Fv(;)g(z)1326 578 y Ft(i)1338 566
y Fm(?)1358 598 y FH(\))371 b(\(A.19\))831 700 y Fv(V)870
679 y Ft(a)905 700 y FE(!)14 b Fv(`V)1028 679 y Ft(a)1748
700 y FH(\(A.20\))696 790 y(\()p Fv( )749 769 y Ft(A)777
790 y Fv(;)8 b( )831 797 y Ft(A)859 790 y FH(\))13 b
FE(!)h Fv(`)980 756 y Fr(1)p 980 762 16 2 v 980 782 a(2)1003
790 y FH(\()p Fv( )1056 769 y Ft(A)1084 790 y Fv(;)8
b( )1138 797 y Ft(A)1166 790 y FH(\))563 b(\(A.21\))535
880 y(\()p Fv(\025)582 860 y Ft(iA)623 880 y Fv(;)8 b(\025)673
860 y Ft(i)685 848 y Fm(?)673 892 y Ft(A)705 880 y Fv(;)g(\020)752
860 y Ft(\013)777 880 y Fv(;)g(\020)820 887 y Ft(\013)845
880 y FH(\))14 b FE(!)f Fv(`)961 860 y FB(\000)993 846
y Fr(1)p 994 852 V 994 873 a(2)1016 880 y FH(\()p Fv(\025)1063
860 y Ft(iA)1104 880 y Fv(;)8 b(\025)1154 860 y Ft(i)1166
848 y Fm(?)1154 892 y Ft(A)1187 880 y Fv(;)g(\020)1234
860 y Ft(\013)1258 880 y Fv(;)g(\020)1301 887 y Ft(\013)1326
880 y FH(\))403 b(\(A.22\))-5 964 y(Indeed)16 b(these)f(rescalings)h
(and)g(the)g(corresp)q(onding)h(ones)g(for)f(the)g(curv)m(atures)g(lea)
o(v)o(e)e(in)o(v)m(arian)o(t)h(the)-5 1024 y(de\014nitions)h(of)h(the)f
(curv)m(atures)g(and)h(the)f(Bianc)o(hi)f(iden)o(tities.)-5
1084 y(Finally)23 b(w)o(e)h(note)g(that)h(w)o(e)e(are)h(lo)q(oking)h
(for)f(a)h(solution)f(of)h(the)f(coupled)f(system)g(of)h(Bianc)o(hi)-5
1144 y(iden)o(tities)19 b(of)i(the)f(gra)o(vitational)h(sector)f(with)h
(those)g(of)g(the)f(matter)g(sectors.)34 b(The)21 b(coupling)f(is)-5
1204 y(obtained)h(b)o(y)e(setting)h(the)g(auxiliary)f(\014elds)h(of)g
(the)g Fv(N)26 b FH(=)20 b(2)g(m)o(ultiplets)d(to)k(de\014nite)e
(expressions)-5 1265 y(in)h(the)g(ph)o(ysical)f(\014elds)h(compatible)e
(with)i(all)f(the)h(previously)f(men)o(tioned)f(requiremen)o(ts.)30
b(This)-5 1325 y(\014xes)23 b(completely)c(the)j(ansatz)i(for)e(the)h
(curv)m(atures)f(at)h(least)f(if)g(w)o(e)g(exclude)f(higher)i(deriv)m
(ativ)o(e)-5 1385 y(in)o(teractions.)68 1445 y(P)o(erforming)17
b(all)h(the)g(steps)h(requires)e(a)h(lot)h(of)f(w)o(ork.)28
b(F)l(or)18 b(a)h(more)e(detailed)g(explanation)h(the)-5
1505 y(in)o(terested)g(reader)h(is)g(referred)g(to)g(the)g(standard)i
(reference)d(of)h(the)g(geometrical)f(approac)o(h)i([31)p
 (#cite.CaDFb) [[506 406 518 418] [1 1 1 [3 3]] [0 0 1]] pdfm (].)-5
1566 y(The)d(\014nal)f(parametrizations)f(of)i(the)f(sup)q(erspace)g
(curv)m(atures,)g(are)h(giv)o(en)e(b)o(y:)217 1667 y
Fv(T)253 1646 y Ft(a)315 1667 y FH(=)41 b(0)1330 b(\(A.23\))220
1746 y Fv(\032)245 1753 y Ft(A)315 1746 y FH(=)399 1742
y Fs(e)394 1746 y Fv(\032)419 1754 y Ft(A)p FB(j)p Ft(ab)492
1746 y Fv(V)531 1726 y Ft(a)563 1746 y FE(^)11 b Fv(V)646
1726 y Ft(b)675 1746 y FH(+)724 1698 y Fs(\020)748 1746
y Fv(A)811 1721 y Ft(B)r FB(j)p Ft(b)785 1759 y(A)867
1746 y Fv(\021)891 1753 y Ft(ab)938 1746 y FH(+)g Fv(A)1024
1721 y FB(0)25 b Ft(B)r FB(j)p Ft(b)1024 1759 y(A)1114
1746 y Fv(\015)1139 1753 y Ft(ab)1176 1698 y Fs(\021)1209
1746 y Fv( )1241 1753 y Ft(B)1290 1746 y FE(^)20 b Fv(V)1382
1726 y Ft(a)394 1838 y FH(+)440 1790 y Fs(h)460 1838
y FH(i)8 b Fv(g)i(S)545 1845 y Ft(AB)602 1838 y Fv(\021)626
1845 y Ft(ab)673 1838 y FH(+)h Fv(\017)742 1845 y Ft(AB)799
1838 y FH(\()p Fv(T)854 1817 y FB(\000)847 1850 y Ft(ab)902
1838 y FH(+)19 b Fv(U)997 1817 y FC(+)992 1850 y Ft(ab)1028
1838 y FH(\))1047 1790 y Fs(i)1075 1838 y Fv(\015)1103
1817 y Ft(b)1120 1838 y Fv( )1154 1817 y Ft(B)1195 1838
y FE(^)12 b Fv(V)1279 1817 y Ft(a)1748 1838 y FH(\(A.24\))220
1942 y Fv(\032)245 1921 y Ft(A)315 1942 y FH(=)399 1938
y Fs(e)394 1942 y Fv(\032)419 1921 y Ft(A)419 1954 y
FB(j)p Ft(ab)465 1942 y Fv(V)504 1921 y Ft(a)536 1942
y FE(^)g Fv(V)620 1921 y Ft(b)648 1942 y FH(+)697 1881
y Fs(\022)p 728 1903 37 2 v 61 x Fv(A)764 1912 y Ft(A)p
FB(j)29 b Ft(b)801 1954 y(B)854 1942 y Fv(\021)878 1949
y Ft(ab)925 1942 y FH(+)p 974 1903 V 11 w Fv(A)1011 1912
y FB(0)p Ft(A)p FB(j)f Ft(b)1047 1954 y(B)1110 1942 y
Fv(\015)1135 1949 y Ft(ab)1172 1881 y Fs(\023)1210 1942
y Fv( )1244 1921 y Ft(B)1285 1942 y FE(^)12 b Fv(V)1369
1921 y Ft(a)394 2047 y FH(+)440 1999 y Fs(h)460 2047
y FH(i)c Fv(g)p 515 2008 33 2 v 10 w(S)548 2018 y Ft(AB)605
2047 y Fv(\021)629 2054 y Ft(ab)684 2047 y FH(+)20 b
Fv(\017)762 2027 y Ft(AB)827 1999 y Fs(\020)851 2047
y Fv(T)887 2027 y FC(+)880 2060 y Ft(ab)927 2047 y FH(+)11
b Fv(U)1014 2027 y FB(\000)1009 2060 y Ft(ab)1045 1999
y Fs(\021i)1106 2047 y Fv(\015)1134 2027 y Ft(b)1152
2047 y Fv( )1184 2054 y Ft(B)1225 2047 y FE(^)g Fv(V)1308
2027 y Ft(a)1748 2047 y FH(\(A.25\))200 2141 y Fv(R)237
2121 y Ft(ab)315 2141 y FH(=)406 2125 y Fs(e)394 2141
y Fv(R)431 2121 y Ft(ab)465 2154 y(cd)501 2141 y Fv(V)540
2121 y Ft(c)569 2141 y FE(^)g Fv(V)652 2121 y Ft(d)692
2141 y FE(\000)19 b FH(i)8 b(\()p 791 2102 34 2 v Fv( )824
2153 y Ft(A)853 2141 y Fv(\022)877 2121 y Ft(A)p FB(j)p
Ft(ab)876 2154 y(c)968 2141 y FH(+)p 1026 2102 V 20 w
Fv( )1059 2112 y Ft(A)1088 2141 y Fv(\022)1112 2121 y
Ft(ab)1111 2154 y(A)p FB(j)p Ft(c)1164 2141 y FH(\))j
FE(^)g Fv(V)1277 2121 y Ft(c)403 2231 y FH(+)d Fv(\017)469
2210 y Ft(abcf)p 549 2191 V 549 2231 a Fv( )582 2201
y Ft(A)622 2231 y FE(^)j Fv(\015)691 2238 y Ft(f)714
2231 y Fv( )746 2238 y Ft(B)776 2231 y FH(\()p Fv(A)832
2210 y FB(0)p Ft(B)860 2243 y(A)p FB(j)p Ft(c)925 2231
y FE(\000)p 974 2192 37 2 v 10 w Fv(A)1011 2202 y FB(0)26
b Ft(B)1011 2243 y(A)p FB(j)p Ft(c)1077 2231 y FH(\))394
2321 y(+)8 b(i)g Fv(\017)482 2300 y Ft(AB)p 547 2281
34 2 v 547 2321 a Fv( )581 2332 y Ft(A)620 2321 y FE(^)k
Fv( )697 2328 y Ft(B)727 2321 y FH(\()p Fv(T)782 2300
y FC(+)p Ft(ab)855 2321 y FH(+)f Fv(U)942 2300 y FB(\000)p
Ft(ab)1006 2321 y FH(\))19 b FE(\000)g FH(i)8 b Fv(\017)1144
2328 y Ft(AB)p 1201 2281 V 1201 2321 a Fv( )1234 2291
y Ft(A)1274 2321 y FE(^)j Fv( )1352 2300 y Ft(B)1382
2321 y FH(\()p Fv(T)1437 2300 y FB(\000)p Ft(ab)1511
2321 y FH(+)g Fv(U)1598 2300 y FC(+)p Ft(ab)1661 2321
y FH(\))394 2402 y FE(\000)d Fv(g)r(S)496 2409 y Ft(AB)p
562 2363 V 562 2402 a Fv( )595 2372 y Ft(A)635 2402 y
FE(^)j Fv(\015)707 2382 y Ft(ab)751 2402 y Fv( )785 2382
y Ft(B)834 2402 y FE(\000)19 b Fv(g)p 917 2363 33 2 v
2 w(S)951 2373 y Ft(AB)p 1016 2363 34 2 v 1016 2402 a
Fv( )1049 2414 y Ft(A)1089 2402 y FE(^)11 b Fv(\015)1161
2382 y Ft(ab)1205 2402 y Fv( )1237 2409 y Ft(B)1748 2402
y FH(\(A.26\))198 2554 y Fv(F)237 2534 y FC(\003)304
2554 y FH(=)395 2538 y Fs(e)383 2554 y Fv(F)422 2534
y FC(\003)415 2567 y Ft(ab)451 2554 y Fv(V)490 2534 y
Ft(a)522 2554 y FE(^)g Fv(V)606 2534 y Ft(b)634 2554
y FH(+)683 2506 y Fs(\020)708 2554 y FH(i)d Fv(f)759
2534 y FC(\003)754 2567 y Ft(i)p 794 2515 29 2 v 794
2554 a Fv(\025)822 2525 y Ft(iA)863 2554 y Fv(\015)888
2561 y Ft(a)909 2554 y Fv( )943 2534 y Ft(B)981 2554
y Fv(\017)1001 2561 y Ft(AB)1068 2554 y FH(+)j(i)p 1139
2515 30 2 v 8 w Fv(f)1169 2525 y FC(\003)1169 2567 y
Ft(i)1181 2557 y Fm(?)p 1209 2515 29 2 v 1209 2554 a
Fv(\025)1237 2525 y Ft(i)1249 2513 y Fm(?)1237 2567 y
Ft(A)1270 2554 y Fv(\015)1295 2561 y Ft(a)1316 2554 y
Fv( )1348 2561 y Ft(B)1386 2554 y Fv(\017)1406 2534 y
Ft(AB)1462 2506 y Fs(\021)1498 2554 y FE(^)h Fv(V)1582
2534 y Ft(a)1748 2554 y FH(\(A.27\))152 2653 y FE(r)p
Fv(\025)222 2633 y Ft(iA)304 2653 y FH(=)399 2637 y Fs(g)383
2653 y FE(r)425 2660 y Ft(a)446 2653 y Fv(\025)474 2619
y Ft(iA)515 2653 y Fv(V)554 2633 y Ft(a)586 2653 y FH(+)f(i)668
2637 y Fs(e)657 2653 y Fv(Z)694 2633 y Ft(i)690 2666
y(a)711 2653 y Fv(\015)739 2633 y Ft(a)760 2653 y Fv( )794
2633 y Ft(A)833 2653 y FH(+)g Fv(G)920 2633 y FB(\000)p
Ft(i)920 2666 y(ab)962 2653 y Fv(\015)990 2633 y Ft(ab)1026
2653 y Fv( )1058 2660 y Ft(B)1088 2653 y Fv(\017)1108
2633 y Ft(AB)1175 2653 y FH(+)1224 2605 y Fs(\020)1249
2653 y Fv(Y)1288 2633 y Ft(iAB)1376 2653 y FH(+)20 b
Fv(g)10 b(W)1520 2633 y Ft(iAB)1589 2605 y Fs(\021)1622
2653 y Fv( )1654 2660 y Ft(B)1748 2653 y FH(\(A.28\))160
2759 y FE(r)p Fv(\025)230 2739 y Ft(i)242 2727 y Fm(?)230
2772 y Ft(A)304 2759 y FH(=)399 2743 y Fs(g)383 2759
y FE(r)425 2766 y Ft(a)446 2759 y Fv(\025)474 2725 y
Ft(i)486 2713 y Fm(?)474 2772 y Ft(A)506 2759 y Fv(V)546
2739 y Ft(a)577 2759 y FH(+)h(i)655 2735 y Fs(e)p 648
2720 37 2 v 648 2759 a Fv(Z)685 2718 y Ft(i)697 2706
y Fm(?)685 2772 y Ft(a)717 2759 y Fv(\015)745 2739 y
Ft(a)766 2759 y Fv( )798 2766 y Ft(A)837 2759 y FH(+)g
Fv(G)924 2739 y FC(+)p Ft(i)963 2727 y Fm(?)924 2772
y Ft(ab)984 2759 y Fv(\015)1012 2739 y Ft(ab)1048 2759
y Fv( )1082 2739 y Ft(B)1112 2759 y Fv(\017)1132 2766
y Ft(AB)1200 2759 y FH(+)1249 2711 y Fs(\020)1273 2759
y Fv(Y)1313 2739 y Ft(i)1325 2727 y Fm(?)1332 2772 y
Ft(AB)1408 2759 y FH(+)19 b Fv(g)11 b(W)1552 2739 y Ft(i)1564
2727 y Fm(?)1575 2772 y Ft(AB)1631 2711 y Fs(\021)1665
2759 y Fv( )1699 2739 y Ft(B)1748 2759 y FH(\(A.29\))916
2892 y(59)p eop
%%Page: 60 61
60 60 bop 182 18 a FE(r)p Fv(z)249 -2 y Ft(i)304 18 y
FH(=)394 2 y Fs(e)383 18 y Fv(Z)420 -2 y Ft(i)416 30
y(a)438 18 y Fv(V)477 -2 y Ft(a)509 18 y FH(+)p 558 -21
29 2 v 11 w Fv(\025)586 -12 y Ft(iA)627 18 y Fv( )659
25 y Ft(A)1748 18 y FH(\(A.30\))164 100 y FE(r)p 206
74 25 2 v Fv(z)230 80 y Ft(i)242 68 y Fm(?)304 100 y
FH(=)394 84 y Fs(e)383 100 y Fv(Z)420 80 y Ft(i)432 68
y Fm(?)416 113 y Ft(a)452 100 y Fv(V)492 80 y Ft(a)524
100 y FH(+)p 573 61 29 2 v 11 w Fv(\025)601 70 y Ft(i)613
59 y Fm(?)601 113 y Ft(A)633 100 y Fv( )667 80 y Ft(A)1748
100 y FH(\(A.31\))389 269 y FE(U)425 248 y Ft(A\013)517
269 y FH(=)607 253 y Fs(e)597 269 y FE(U)633 248 y Ft(A\013)628
281 y(a)692 269 y Fv(V)732 248 y Ft(a)772 269 y FH(+)19
b Fv(\017)849 248 y Ft(AB)p 922 269 2 33 v 909 269 a
FH(C)944 248 y Ft(\013\014)p 999 229 34 2 v 999 269 a
Fv( )1032 281 y Ft(B)1063 269 y Fv(\020)1084 276 y Ft(\014)1127
269 y FH(+)p 1184 229 V 19 w Fv( )1218 239 y Ft(A)1246
269 y Fv(\020)1271 248 y Ft(\013)1748 269 y FH(\(A.32\))388
347 y FE(r)p Fv(\020)451 354 y Ft(\013)517 347 y FH(=)610
331 y Fs(g)597 347 y FE(r)639 354 y Ft(a)659 347 y Fv(\020)684
359 y Ft(\013)709 347 y Fv(V)748 327 y Ft(a)788 347 y
FH(+)h(i)886 331 y Fs(e)876 347 y FE(U)912 327 y Ft(B)r(\014)907
360 y(a)972 347 y Fv(\015)1000 327 y Ft(a)1021 347 y
Fv( )1055 327 y Ft(A)1083 347 y Fv(\017)1103 354 y Ft(AB)p
1176 347 2 33 v 1163 347 a FH(C)1198 354 y Ft(\013\014)1264
347 y FH(+)f Fv(g)11 b(N)1399 327 y Ft(A)1394 360 y(\013)1436
347 y Fv( )1468 354 y Ft(A)1748 347 y FH(\(A.33\))384
427 y FE(r)p Fv(\020)451 406 y Ft(\013)517 427 y FH(=)610
410 y Fs(g)597 427 y FE(r)639 434 y Ft(a)659 427 y Fv(\020)684
392 y Ft(\013)709 427 y Fv(V)748 406 y Ft(a)788 427 y
FH(+)20 b(i)886 411 y Fs(e)876 427 y FE(U)912 406 y Ft(A\013)907
439 y(a)971 427 y Fv(\015)999 406 y Ft(a)1020 427 y Fv( )1052
434 y Ft(A)1100 427 y FH(+)f Fv(g)11 b(N)1235 406 y Ft(\013)1230
439 y(A)1268 427 y Fv( )1302 406 y Ft(A)1748 427 y FH(\(A.34\))-5
537 y(where:)269 658 y Fv(A)332 632 y FB(j)p Ft(aB)306
670 y(A)433 658 y FH(=)41 b FE(\000)561 624 y FH(i)p
556 646 25 2 v 556 692 a(4)593 658 y Fv(g)616 665 y Ft(k)635
656 y Fm(?)654 665 y Ft(`)687 609 y Fs(\020)p 712 618
29 2 v 49 x Fv(\025)740 628 y Ft(k)759 616 y Fm(?)740
670 y Ft(A)780 658 y Fv(\015)808 637 y Ft(a)829 658 y
Fv(\025)857 637 y Ft(`B)921 658 y FE(\000)19 b Fv(\016)1003
637 y Ft(B)1001 670 y(A)p 1041 618 V 1041 658 a Fv(\025)1070
628 y Ft(k)1089 616 y Fm(?)1070 670 y Ft(C)1109 658 y
Fv(\015)1137 637 y Ft(a)1158 658 y Fv(\025)1186 637 y
Ft(`C)1230 609 y Fs(\021)1748 658 y FH(\(A.35\))260 775
y Fv(A)297 750 y FB(0)25 b(j)p Ft(aB)297 787 y(A)433
775 y FH(=)522 741 y(i)p 517 763 25 2 v 517 809 a(4)555
775 y Fv(g)578 782 y Ft(k)597 773 y Fm(?)615 782 y Ft(`)648
714 y Fs(\022)p 679 736 29 2 v 61 x Fv(\025)707 745 y
Ft(k)726 734 y Fm(?)707 787 y Ft(A)747 775 y Fv(\015)775
755 y Ft(a)796 775 y Fv(\025)824 755 y Ft(`B)880 775
y FE(\000)935 741 y FH(1)p 935 763 25 2 v 935 809 a(2)972
775 y Fv(\016)996 755 y Ft(B)994 787 y(A)p 1034 736 29
2 v 1034 775 a Fv(\025)1063 745 y Ft(k)1082 734 y Fm(?)1063
787 y Ft(C)1102 775 y Fv(\015)1130 755 y Ft(a)1151 775
y Fv(\025)1179 755 y Ft(C)r(`)1223 714 y Fs(\023)1273
775 y FH(+)1341 741 y(i)p 1336 763 25 2 v 1336 809 a(4)1373
775 y Fv(\025)8 b(\016)1433 755 y Ft(B)1431 787 y(A)p
1472 736 26 2 v 1472 775 a Fv(\020)1497 787 y Ft(\013)1522
775 y Fv(\015)1550 755 y Ft(a)1571 775 y Fv(\020)1596
755 y Ft(\013)1748 775 y FH(\(A.36\))396 917 y Fv(\022)420
891 y Ft(ab)p FB(j)p Ft(c)419 929 y(A)495 917 y FH(=)14
b(2)p Fv(\015)599 896 y FC([)p Ft(a)630 917 y Fv(\032)655
891 y Ft(b)p FC(])p Ft(c)655 929 y(A)709 917 y FH(+)d
Fv(\015)786 896 y Ft(c)803 917 y Fv(\032)828 896 y Ft(ab)828
929 y(A)864 917 y FH(;)57 b Fv(\022)959 896 y Ft(ab)16
b(A)958 929 y(c)1051 917 y FH(=)e(2)p Fv(\015)1155 896
y FC([)p Ft(a)1186 917 y Fv(\032)1211 896 y Ft(b)p FC(])p
Ft(c)p FB(j)p Ft(A)1301 917 y FH(+)d Fv(\015)1378 896
y Ft(c)1395 917 y Fv(\032)1420 896 y Ft(ab)p FB(j)p Ft(A)1748
917 y FH(\(A.37\))154 1063 y Fv(T)190 1042 y FB(\000)183
1075 y Ft(ab)233 1063 y FH(=)284 1014 y Fs(\020)309 1063
y FE(N)18 b(\000)p 418 1024 49 2 v 11 w(N)466 1014 y
Fs(\021)491 1090 y FC(\003\006)552 1063 y Fv(L)585 1045
y FC(\006)621 1014 y Fs(\020)657 1046 y(e)645 1063 y
Fv(F)684 1042 y FC(\003)p FB(\000)677 1075 y Ft(ab)749
1063 y FH(+)803 1043 y FC(1)p 803 1051 18 2 v 803 1080
a(8)825 1063 y FE(r)867 1070 y Ft(i)889 1063 y Fv(f)918
1045 y FC(\003)913 1075 y Ft(j)p 953 1023 29 2 v 953
1063 a Fv(\025)982 1033 y Ft(iA)1022 1063 y Fv(\015)1047
1070 y Ft(ab)1092 1063 y Fv(\025)1120 1045 y Ft(j)r(B)1175
1063 y Fv(\017)1195 1070 y Ft(AB)1263 1063 y FH(+)1317
1043 y FC(1)p 1317 1051 18 2 v 1317 1080 a(4)1348 1063
y Fv(\025)p 1393 1063 2 33 v 4 w FH(C)1415 1042 y Ft(\013\014)p
1469 1023 26 2 v 1469 1063 a Fv(\020)1495 1074 y Ft(\013)1519
1063 y Fv(\015)1544 1070 y Ft(ab)1589 1063 y Fv(\020)1610
1070 y Ft(\014)1642 1063 y Fv(L)1675 1045 y FC(\003)1702
1014 y Fs(\021)1748 1063 y FH(\(A.38\))152 1159 y Fv(T)188
1139 y FC(+)181 1172 y Ft(ab)230 1159 y FH(=)282 1111
y Fs(\020)307 1159 y FE(N)g(\000)p 416 1120 49 2 v 11
w(N)464 1111 y Fs(\021)489 1186 y FC(\003\006)p 549 1120
34 2 v 549 1159 a Fv(L)582 1130 y FC(\006)618 1111 y
Fs(\020)655 1143 y(e)643 1159 y Fv(F)682 1139 y FC(\003+)675
1172 y Ft(ab)747 1159 y FH(+)801 1140 y FC(1)p 801 1148
18 2 v 801 1176 a(8)823 1159 y FE(r)865 1166 y Ft(i)877
1157 y Fm(?)p 905 1120 30 2 v 905 1159 a Fv(f)934 1130
y FC(\003)934 1172 y Ft(j)950 1162 y Fm(?)p 979 1120
29 2 v 979 1159 a Fv(\025)1007 1130 y Ft(i)1019 1118
y Fm(?)1007 1172 y Ft(A)1039 1159 y Fv(\015)1064 1166
y Ft(ab)1109 1159 y Fv(\025)1137 1136 y Ft(j)1153 1124
y Fm(?)1137 1171 y Ft(B)1174 1159 y Fv(\017)1194 1141
y Ft(AB)1261 1159 y FH(+)1315 1140 y FC(1)p 1315 1148
18 2 v 1315 1176 a(4)1346 1159 y Fv(\025)p 1391 1159
2 33 v 4 w FH(C)1413 1166 y Ft(\013\014)p 1468 1120 26
2 v 1468 1159 a Fv(\020)1493 1130 y Ft(\013)1518 1159
y Fv(\015)1543 1166 y Ft(ab)1587 1159 y Fv(\020)1612
1141 y Ft(\014)p 1644 1120 34 2 v 1644 1159 a Fv(L)1677
1130 y FC(\003)1704 1111 y Fs(\021)1748 1159 y FH(\(A.39\))679
1357 y Fv(U)717 1336 y FB(\000)712 1369 y Ft(ab)789 1357
y FH(=)879 1323 y(i)p 874 1345 25 2 v 874 1391 a(4)912
1357 y Fv(\025)p 957 1357 2 33 v 4 w FH(C)979 1336 y
Ft(\013\014)p 1033 1317 26 2 v 1033 1357 a Fv(\020)1058
1369 y Ft(\013)1083 1357 y Fv(\015)1108 1364 y Ft(ab)1153
1357 y Fv(\020)1174 1364 y Ft(\014)1748 1357 y FH(\(A.40\))679
1474 y Fv(U)717 1454 y FC(+)712 1487 y Ft(ab)789 1474
y FH(=)879 1441 y(i)p 874 1463 25 2 v 874 1508 a(4)912
1474 y Fv(\025)p 957 1474 2 33 v 4 w FH(C)979 1481 y
Ft(\013\014)p 1033 1435 26 2 v 1033 1474 a Fv(\020)1058
1445 y Ft(\013)1083 1474 y Fv(\015)1108 1481 y Ft(ab)1153
1474 y Fv(\020)1178 1454 y Ft(\014)1748 1474 y FH(\(A.41\))309
1679 y Fv(G)347 1658 y Ft(i)p FB(\000)347 1692 y Ft(ab)430
1679 y FH(=)520 1645 y(i)p 515 1667 25 2 v 515 1713 a(2)553
1679 y Fv(g)578 1658 y Ft(ij)606 1647 y Fm(?)p 626 1639
30 2 v 626 1679 a Fv(f)655 1649 y FC(\000)655 1691 y
Ft(j)671 1682 y Fm(?)700 1631 y Fs(\020)725 1679 y FE(N)g(\000)p
834 1640 49 2 v 11 w(N)882 1631 y Fs(\021)907 1706 y
FC(\000\003)964 1631 y Fs(\020)1000 1663 y(e)988 1679
y Fv(F)1027 1658 y FC(\003)p FB(\000)1020 1692 y Ft(ab)1092
1679 y FH(+)1146 1645 y(1)p 1146 1667 25 2 v 1146 1713
a(8)1175 1679 y FE(r)1217 1686 y Ft(k)1238 1679 y Fv(f)1267
1658 y FC(\003)1262 1691 y Ft(`)p 1294 1639 29 2 v 1294
1679 a Fv(\025)1322 1649 y Ft(k)q(A)1370 1679 y Fv(\015)1395
1686 y Ft(ab)1440 1679 y Fv(\025)1468 1658 y Ft(`B)1513
1679 y Fv(\017)1533 1686 y Ft(AB)705 1796 y FH(+)748
1762 y(1)p 748 1784 25 2 v 748 1830 a(4)786 1796 y Fv(\025)p
831 1796 2 33 v 4 w FH(C)853 1775 y Ft(\013\014)p 907
1756 26 2 v 907 1796 a Fv(\020)933 1807 y Ft(\013)957
1796 y Fv(\015)982 1803 y Ft(ab)1027 1796 y Fv(\020)1048
1803 y Ft(\014)1080 1796 y Fv(L)1113 1775 y FC(\003)1140
1747 y Fs(\021)1748 1796 y FH(\(A.42\))291 1913 y Fv(G)329
1893 y Ft(i)341 1881 y Fm(?)359 1893 y FC(+)329 1926
y Ft(ab)430 1913 y FH(=)520 1879 y(i)p 515 1902 25 2
v 515 1947 a(2)553 1913 y Fv(g)578 1893 y Ft(i)590 1881
y Fm(?)608 1893 y Ft(j)626 1913 y Fv(f)655 1893 y FC(\000)650
1925 y Ft(j)688 1865 y Fs(\020)713 1913 y FE(N)g(\000)p
822 1874 49 2 v 11 w(N)870 1865 y Fs(\021)895 1940 y
FC(\000\003)952 1865 y Fs(\020)988 1897 y(e)976 1913
y Fv(F)1015 1893 y FC(\003+)1008 1926 y Ft(ab)1080 1913
y FH(+)1134 1879 y(1)p 1134 1902 25 2 v 1134 1947 a(8)1163
1913 y FE(r)1205 1920 y Ft(k)1224 1911 y Fm(?)p 1244
1874 30 2 v 1244 1913 a Fv(f)1273 1883 y FC(\003)1273
1925 y Ft(`)1287 1916 y Fm(?)p 1308 1874 29 2 v 1308
1913 a Fv(\025)1336 1883 y Ft(k)1355 1872 y Fm(?)1336
1925 y Ft(A)1376 1913 y Fv(\015)1401 1920 y Ft(ab)1445
1913 y Fv(\025)1473 1893 y Ft(`)1487 1881 y Fm(?)1473
1925 y Ft(B)1508 1913 y Fv(\017)1528 1893 y Ft(AB)705
2030 y FH(+)748 1996 y(1)p 748 2018 25 2 v 748 2064 a(4)786
2030 y Fv(\025)p 831 2030 2 33 v 4 w FH(C)853 2037 y
Ft(\013\014)p 907 1990 26 2 v 907 2030 a Fv(\020)933
2000 y Ft(\013)957 2030 y Fv(\015)982 2037 y Ft(ab)1027
2030 y Fv(\020)1052 2009 y Ft(\014)p 1084 1991 34 2 v
1084 2030 a Fv(L)1117 2001 y FC(\003)1143 1982 y Fs(\021)1748
2030 y FH(\(A.43\))1748 2118 y(\(A.44\))555 2301 y Fv(Y)594
2280 y Ft(iAB)705 2301 y FH(=)794 2267 y(i)p 789 2289
25 2 v 789 2335 a(2)818 2301 y Fv(g)843 2280 y Ft(ij)871
2269 y Fm(?)892 2301 y Fv(C)927 2308 y Ft(j)943 2299
y Fm(?)961 2308 y Ft(k)980 2299 y Fm(?)998 2308 y Ft(`)1012
2299 y Fm(?)p 1033 2261 29 2 v 1033 2301 a Fv(\025)1061
2271 y Ft(k)1080 2259 y Fm(?)1061 2313 y Ft(C)1100 2301
y Fv(\025)1128 2280 y Ft(`)1142 2269 y Fm(?)1128 2313
y Ft(D)1163 2301 y Fv(\017)1183 2280 y Ft(AC)1239 2301
y Fv(\017)1259 2280 y Ft(B)r(D)1748 2301 y FH(\(A.45\))578
2418 y Fv(Y)617 2398 y Ft(i)629 2386 y Fm(?)606 2431
y Ft(AB)705 2418 y FH(=)41 b FE(\000)833 2385 y FH(i)p
828 2407 25 2 v 828 2453 a(2)857 2418 y Fv(g)882 2398
y Ft(i)894 2386 y Fm(?)912 2398 y Ft(j)931 2418 y Fv(C)966
2425 y Ft(j)r(k)q(`)p 1017 2379 29 2 v 1017 2418 a Fv(\025)1046
2389 y Ft(k)q(C)1095 2418 y Fv(\025)1123 2398 y Ft(`D)1170
2418 y Fv(\017)1190 2425 y Ft(AC)1245 2418 y Fv(\017)1265
2425 y Ft(B)r(D)1748 2418 y FH(\(A.46\))650 2623 y Fv(S)680
2630 y Ft(AB)778 2623 y FH(=)868 2589 y(i)p 862 2611
25 2 v 862 2657 a(2)892 2623 y(\()p Fv(\033)939 2630
y Ft(x)960 2623 y FH(\))1006 2603 y Ft(C)979 2635 y(A)1035
2623 y Fv(\017)1055 2630 y Ft(B)r(C)1113 2623 y FE(P)1152
2603 y Ft(x)1148 2635 y FC(\003)1174 2623 y Fv(L)1207
2603 y FC(\003)p 647 2702 33 2 v 647 2741 a Fv(S)680
2711 y Ft(AB)778 2741 y FH(=)868 2707 y(i)p 862 2729
25 2 v 862 2775 a(2)892 2741 y(\()p Fv(\033)939 2748
y Ft(x)960 2741 y FH(\))1007 2720 y Ft(B)979 2753 y(C)1037
2741 y Fv(\017)1057 2720 y Ft(C)r(A)1113 2741 y FE(P)1152
2720 y Ft(x)1148 2753 y FC(\003)p 1174 2702 34 2 v 1174
2741 a Fv(L)1207 2711 y FC(\003)1748 2741 y FH(\(A.47\))916
2892 y(60)p eop
%%Page: 61 62
61 61 bop 694 18 a Fv(N)738 -3 y Ft(A)733 30 y(\013)809
18 y FH(=)41 b(2)8 b FE(U)956 -3 y Ft(A)951 30 y(\013)p
FB(j)p Ft(u)1015 18 y Fv(k)1042 -3 y Ft(u)1040 30 y FC(\003)p
1075 -21 34 2 v 1075 18 a Fv(L)1109 -12 y FC(\003)698
98 y Fv(N)742 77 y Ft(\013)737 110 y(A)809 98 y FH(=)41
b FE(\000)8 b FH(2)g FE(U)1003 77 y Ft(\013)998 110 y(A)p
FB(j)p Ft(u)1066 98 y Fv(k)1093 77 y Ft(u)1091 110 y
FC(\003)1126 98 y Fv(L)1159 77 y FC(\003)1748 98 y FH(\(A.48\))624
252 y Fv(W)677 231 y Ft(iAB)787 252 y FH(=)41 b Fv(W)919
231 y Ft(i)p FC([)p Ft(AB)r FC(])1018 252 y FH(+)11 b
Fv(W)1120 231 y Ft(i)p FC(\()p Ft(AB)r FC(\))642 324
y Fv(W)695 304 y Ft(i)707 292 y Fm(?)688 337 y Ft(AB)787
324 y FH(=)41 b Fv(W)919 304 y Ft(i)931 292 y Fm(?)912
337 y FC([)p Ft(AB)r FC(])1000 324 y FH(+)11 b Fv(W)1102
304 y Ft(i)1114 292 y Fm(?)1095 337 y FC(\()p Ft(AB)r
FC(\))579 397 y FH(where)j(:)1016 b(\(A.49\))604 478
y Fv(W)657 457 y Ft(i)p FC([)p Ft(AB)r FC(])787 478 y
FH(=)41 b Fv(\017)886 457 y Ft(AB)951 478 y Fv(k)978
457 y Ft(i)976 490 y FC(\003)p 1003 439 V 1003 478 a
Fv(L)1036 449 y FC(\003)623 551 y Fv(W)676 530 y Ft(i)688
518 y Fm(?)669 563 y FC([)p Ft(AB)r FC(])787 551 y FH(=)g
Fv(\017)886 558 y Ft(AB)951 551 y Fv(k)978 530 y Ft(i)990
518 y Fm(?)976 563 y FC(\003)1010 551 y Fv(L)1043 530
y FC(\003)596 640 y Fv(W)649 620 y Ft(i)p FC(\()p Ft(AB)r
FC(\))787 640 y FH(=)g(i\()p Fv(\033)927 647 y Ft(x)948
640 y FH(\))995 620 y Ft(B)967 653 y(C)1025 640 y Fv(\017)1045
620 y Ft(C)r(A)1101 640 y FE(P)1140 620 y Ft(x)1136 653
y FC(\003)1162 640 y Fv(g)1187 620 y Ft(ij)1215 608 y
Fm(?)p 1235 601 30 2 v 1235 640 a Fv(f)1265 610 y FC(\003)1265
653 y Ft(j)1281 643 y Fm(?)615 719 y Fv(W)668 699 y Ft(i)680
687 y Fm(?)661 732 y FC(\()p Ft(AB)r FC(\))787 719 y
FH(=)g(i\()p Fv(\033)927 726 y Ft(x)948 719 y FH(\))994
699 y Ft(C)967 732 y(A)1023 719 y Fv(\017)1043 726 y
Ft(B)r(C)1101 719 y FE(P)1140 699 y Ft(x)1136 732 y FC(\003)1162
719 y Fv(g)1187 699 y Ft(i)1199 687 y Fm(?)1217 699 y
Ft(j)1235 719 y Fv(f)1264 699 y FC(\003)1259 732 y Ft(j)1748
719 y FH(\(A.50\))68 821 y(As)15 b(promised)e(the)i(solution)g(for)g
(the)f(curv)m(atures)h(is)g(giv)o(en)f(as)h(an)g(expansion)g(along)h
(the)e(2{form)-5 882 y(basis)j(\()p Fv(V)22 b FE(^)12
b Fv(V)19 b(;)d(V)23 b FE(^)11 b Fv( )f(;)16 b( )d FE(^)e
Fv( )r FH(\))16 b(or)g(the)g(1{form)g(basis)h(\()p Fv(V)i(;)e( )r
FH(\))e(with)h(co)q(e\016cien)o(ts)f(giv)o(en)h(in)g(terms)-5
942 y(of)h(the)f(ph)o(ysical)f(\014elds.)-5 1009 y(The)g("on{shell")h
(auxiliary)f(\014elds)f(are)i(giv)o(en)e(in)h(our)g(case)g(b)o(y)g(the)
g(comp)q(osite)f(connections)1760 993 y Fs(b)1745 1009
y FE(Q)8 b Fv(;)1825 987 y Fs(d)1824 1009 y Fv(!)1856
992 y Ft(A)1854 1021 y(B)-5 1069 y FH(and)17 b(b)o(y)f
Fv(T)194 1048 y FB(\007)187 1081 y Ft(ab)231 1069 y Fv(;)g(W)314
1051 y Ft(iAB)399 1069 y FH(and)h Fv(S)524 1076 y Ft(AB)581
1069 y FH(.)68 1134 y(It)h(is)f(imp)q(ortan)o(t)g(to)h(stress)g(that)h
(the)e(\014eld)g(strengths)1126 1118 y Fs(e)1115 1134
y Fv(R)1152 1116 y Ft(ab)1186 1146 y(cd)1221 1134 y FH(,)1258
1130 y Fs(e)1253 1134 y Fv(\032)1278 1142 y Ft(A)p FB(j)p
Ft(ab)1350 1134 y FH(,)1394 1118 y Fs(e)1382 1134 y Fv(F)1421
1116 y FC(\003)1414 1146 y Ft(ab)1467 1134 y FH(,)1510
1118 y Fs(e)1499 1134 y FE(U)1535 1116 y Ft(A\013)1530
1146 y(a)1603 1134 y FE(\021)f(U)1694 1116 y Ft(A\013)1689
1146 y(u)1758 1118 y Fs(g)1745 1134 y FE(r)1787 1141
y Ft(a)1807 1134 y Fv(q)1831 1100 y Ft(u)1853 1134 y
FH(,)11 1195 y Fs(g)-5 1212 y FE(r)37 1219 y Ft(a)58
1212 y Fv(\025)86 1177 y Ft(iA)127 1212 y FH(,)169 1195
y Fs(g)155 1212 y FE(r)197 1219 y Ft(a)217 1212 y Fv(\020)242
1223 y Ft(\013)281 1212 y FH(and)g(their)d(hermitian)g(conjugates)i
(are)f(not)h(space{time)e(\014eld)h(strengths)h(since)f(they)-5
1272 y(are)19 b(comp)q(onen)o(ts)f(along)h(the)f(b)q(osonic)i(vielb)q
(eins)d Fv(V)988 1254 y Ft(a)1026 1272 y FH(=)h Fv(V)1121
1254 y Ft(a)1110 1284 y(\026)1142 1272 y Fv(dx)1195 1254
y Ft(\026)1239 1272 y FH(+)j Fv(V)1338 1254 y Ft(a)1326
1284 y(\013)1358 1272 y Fv(d\022)1407 1254 y Ft(\013)1451
1272 y FH(where)d(\()p Fv(V)1652 1254 y Ft(a)1641 1284
y(\026)1682 1272 y Fv(;)e(V)1751 1254 y Ft(a)1740 1284
y(\013)1772 1272 y FH(\))i(is)h(a)-5 1332 y(submatrix)f(of)h(the)f(sup)
q(er{vielb)q(ein)g(matrix)f Fv(E)898 1314 y Ft(I)936
1332 y FE(\021)h FH(\()p Fv(V)1051 1314 y Ft(a)1080 1332
y Fv(;)e( )r FH(\).)28 b(The)19 b(ph)o(ysical)f(\014eld)g(strengths)h
(are)-5 1392 y(giv)o(en)j(b)o(y)f(the)h(expansion)h(of)f(the)g(forms)f
(along)i(the)f Fv(dx)1095 1374 y Ft(\026)1118 1392 y
FH(-di\013eren)o(tials)g(and)g(b)o(y)g(restricting)f(the)-5
1452 y(sup)q(er\014elds)h(to)f(space{time)f(\()p Fv(\022)j
FH(=)g(0)e(comp)q(onen)o(t\).)36 b(F)l(or)21 b(example,)f(from)g(the)h
(parametrization)-5 1513 y(\(27\),)c(expanding)f(along)h(the)f
Fv(dx)613 1495 y Ft(\026)637 1513 y FH({basis)h(one)f(\014nds:)292
1624 y Fv(F)331 1603 y FC(\003)324 1636 y Ft(\026\027)380
1624 y FH(=)444 1608 y Fs(e)432 1624 y Fv(F)471 1603
y FC(\003)464 1636 y Ft(ab)500 1624 y Fv(V)539 1603 y
Ft(a)528 1636 y FC([)p Ft(\026)561 1624 y Fv(V)600 1603
y Ft(b)589 1636 y(\027)r FC(])632 1624 y FH(+)11 b(i)d
Fv(f)732 1603 y FC(\003)727 1636 y Ft(i)p 767 1584 29
2 v 767 1624 a Fv(\025)796 1594 y Ft(iA)836 1624 y Fv(\015)861
1631 y Ft(a)882 1624 y Fv( )916 1603 y Ft(B)914 1636
y FC([)p Ft(\026)947 1624 y Fv(V)986 1603 y Ft(a)975
1636 y(\027)r FC(])1015 1624 y Fv(\017)1035 1631 y Ft(AB)1103
1624 y FH(+)j(i)p 1174 1584 30 2 v 8 w Fv(f)1203 1594
y FC(\003)1203 1636 y Ft(i)1215 1627 y Fm(?)p 1244 1584
29 2 v 1244 1624 a Fv(\025)1272 1594 y Ft(i)1284 1583
y Fm(?)1272 1636 y Ft(A)1304 1624 y Fv(\015)1329 1631
y Ft(a)1350 1624 y Fv( )1382 1632 y Ft(B)r FC([)p Ft(\026)1443
1624 y Fv(V)1483 1603 y Ft(a)1471 1636 y(\027)r FC(])1512
1624 y Fv(\017)1532 1603 y Ft(AB)1748 1624 y FH(\(A.51\))-5
1726 y(where:)440 1786 y Fv(F)479 1765 y FC(\003)519
1786 y FH(=)i FE(F)611 1765 y FC(\003)657 1786 y FH(+)19
b Fv(L)747 1765 y FC(\003)p 774 1746 34 2 v 774 1786
a Fv( )808 1756 y Ft(A)847 1786 y FE(^)11 b Fv( )925
1765 y Ft(B)963 1786 y Fv(\017)983 1793 y Ft(AB)1059
1786 y FH(+)p 1117 1747 V 20 w Fv(L)1150 1757 y FC(\003)p
1176 1746 V 1176 1786 a Fv( )1210 1798 y Ft(A)1249 1786
y FE(^)h Fv( )1326 1793 y Ft(B)1364 1786 y Fv(\017)1384
1765 y Ft(AB)1748 1786 y FH(\(A.52\))-5 1870 y(according)k(to)f
(equations)30 b(8.11)p
 (#equation.8.9) [[193 318 214 330] [1 1 1 [3 3]] [0 0 1]] pdfm (,)h
(A.27)p
 (#equation.A.27) [[224 318 248 330] [1 1 1 [3 3]] [0 0 1]] pdfm (.)20
b(When)15 b(all)g(the)f(sup)q(er\014elds)i(are)f(restricted)e(to)j
(space{time)-5 1930 y(w)o(e)22 b(ma)o(y)e(treat)i(the)g
Fv(V)438 1912 y Ft(a)427 1942 y(\026)480 1930 y FH(vielb)q(ein)f(as)h
(the)g(usual)g(4{dimensional)f(in)o(v)o(ertible)e(matrix)h(con)o(v)o
(erting)-5 1990 y(in)o(trinsic)15 b(indices)g(in)h(co)q(ordinate)h
(indices)e(and)i(w)o(e)f(obtain:)241 2076 y Fs(e)230
2092 y Fv(F)269 2071 y FC(\003)262 2104 y Ft(\026\027)346
2092 y FH(=)41 b FE(F)466 2071 y FC(\003)461 2104 y Ft(\026\027)523
2092 y FH(+)19 b Fv(L)613 2071 y FC(\003)p 640 2052 V
640 2092 a Fv( )674 2062 y Ft(A)674 2104 y(\026)702 2092
y Fv( )736 2071 y Ft(B)734 2104 y(\027)774 2092 y Fv(\017)794
2099 y Ft(AB)870 2092 y FH(+)p 919 2053 V 11 w Fv(L)952
2063 y FC(\003)p 979 2052 V 979 2092 a Fv( )1012 2104
y Ft(A\026)1062 2092 y Fv( )1094 2099 y Ft(B)r(\027)1144
2092 y Fv(\017)1164 2071 y Ft(AB)1239 2092 y FE(\000)11
b FH(i)d Fv(f)1340 2071 y FC(\003)1335 2104 y Ft(i)p
1375 2052 29 2 v 1375 2092 a Fv(\025)1404 2062 y Ft(iA)1444
2092 y Fv(\015)1469 2100 y FC([)p Ft(\027)1501 2092 y
Fv( )1535 2071 y Ft(B)1533 2104 y(\026)p FC(])1574 2092
y Fv(\017)1594 2099 y Ft(AB)425 2182 y FE(\000)p FH(i)p
486 2143 30 2 v 8 w Fv(f)515 2153 y FC(\003)515 2195
y Ft(i)527 2185 y Fm(?)p 555 2143 29 2 v 555 2182 a Fv(\025)584
2153 y Ft(i)596 2141 y Fm(?)584 2195 y Ft(A)616 2182
y Fv(\015)641 2190 y FC([)p Ft(\027)673 2182 y Fv( )705
2190 y Ft(B)r(\026)p FC(])774 2182 y Fv(\017)794 2162
y Ft(AB)1748 2182 y FH(\(A.53\))-5 2284 y(By)16 b(the)g(same)f(tok)o
(en)h(w)o(e)g(also)g(get:)49 2380 y Fs(g)33 2397 y FE(r)75
2404 y Ft(\026)98 2397 y Fv(\025)126 2362 y Ft(iA)208
2397 y FH(=)42 b FE(r)330 2404 y Ft(\026)352 2397 y Fv(\025)380
2377 y Ft(iA)441 2397 y FE(\000)11 b FH(i)513 2349 y
Fs(\020)537 2397 y FE(r)579 2404 y Ft(\026)602 2397 y
Fv(z)627 2377 y Ft(i)660 2397 y FE(\000)p 710 2358 V
11 w Fv(\025)739 2367 y Ft(iB)781 2397 y Fv( )813 2405
y Ft(B)r FB(j)p Ft(\027)872 2349 y Fs(\021)905 2397 y
Fv(\015)933 2377 y Ft(\027)955 2397 y Fv( )989 2377 y
Ft(A)987 2409 y(\026)1036 2397 y FE(\000)g Fv(G)1124
2377 y FB(\000)p Ft(i)1124 2409 y(\027)r(\032)1166 2397
y Fv(\015)1194 2377 y Ft(\027)r(\032)1234 2397 y Fv( )1266
2405 y Ft(B)r FB(j)p Ft(\026)1327 2397 y Fv(\017)1347
2377 y Ft(AB)288 2488 y FE(\000)335 2440 y Fs(\020)359
2488 y Fv(Y)399 2468 y Ft(iAB)487 2488 y FH(+)19 b Fv(g)10
b(W)630 2468 y Ft(iAB)699 2440 y Fs(\021)732 2488 y Fv( )764
2496 y Ft(B)r FB(j)p Ft(\026)67 2566 y Fs(g)52 2582 y
FE(r)94 2589 y Ft(\026)117 2582 y Fv(\020)142 2598 y
Ft(\013)208 2582 y FH(=)42 b FE(r)330 2589 y Ft(\026)352
2582 y Fv(\020)373 2589 y Ft(\013)418 2582 y FE(\000)11
b FH(i)490 2534 y Fs(\020)514 2582 y FE(U)550 2562 y
Ft(B)r(\014)545 2595 y(u)602 2582 y FE(r)644 2589 y Ft(\027)665
2582 y Fv(q)689 2562 y Ft(u)731 2582 y FE(\000)f Fv(\017)800
2562 y Ft(B)r(C)p 875 2582 2 33 v 862 2582 a FH(C)897
2562 y Ft(\014)r(\015)p 949 2543 34 2 v 949 2582 a Fv( )982
2594 y Ft(C)r FB(j)p Ft(\027)1041 2582 y Fv(\020)1062
2589 y Ft(\015)1104 2582 y FE(\000)p 1154 2543 V 11 w
Fv( )1187 2553 y Ft(B)1187 2595 y(\027)1218 2582 y Fv(\020)1243
2562 y Ft(\014)1266 2534 y Fs(\021)1299 2582 y Fv(\015)1327
2562 y Ft(\027)1349 2582 y Fv( )1383 2562 y Ft(A)1381
2595 y(\026)1411 2582 y Fv(\017)1431 2589 y Ft(AB)p 1504
2582 2 33 v 1491 2582 a FH(C)1526 2589 y Ft(\013\014)1592
2582 y FE(\000)h Fv(g)f(N)1719 2562 y Ft(A)1714 2595
y(\013)1756 2582 y Fv( )1788 2590 y Ft(A)p FB(j)p Ft(\026)121
2660 y Fs(e)110 2676 y Fv(Z)147 2656 y Ft(i)143 2689
y(\026)208 2676 y FH(=)42 b FE(r)330 2683 y Ft(\026)352
2676 y Fv(z)377 2656 y Ft(i)411 2676 y FE(\000)p 461
2637 29 2 v 11 w Fv(\025)489 2647 y Ft(iA)529 2676 y
Fv( )561 2684 y Ft(A)p FB(j)p Ft(\026)90 2748 y Fs(e)79
2764 y FE(U)115 2744 y Ft(A\013)110 2777 y(\026)208 2764
y FH(=)g FE(U)324 2744 y Ft(A\013)319 2777 y(u)375 2764
y FE(r)417 2771 y Ft(\026)440 2764 y Fv(q)464 2744 y
Ft(u)505 2764 y FE(\000)11 b Fv(\017)575 2744 y Ft(AB)p
648 2764 2 33 v 635 2764 a FH(C)670 2743 y Ft(\013\014)p
725 2725 34 2 v 725 2764 a Fv( )758 2776 y Ft(B)r FB(j)p
Ft(\026)819 2764 y Fv(\020)840 2771 y Ft(\014)884 2764
y FE(\000)p 934 2725 V 11 w Fv( )967 2734 y Ft(A)967
2777 y(\026)996 2764 y Fv(\020)1021 2744 y Ft(\013)1748
2764 y FH(\(A.54\))916 2892 y(61)p eop
%%Page: 62 63
62 62 bop -5 15 a FH(W)l(e)17 b(note)g(that)g(in)g(the)g(comp)q(onen)o
(t)f(approac)o(h)i(the)e("tilded")h(\014eld)f(strengths)i(de\014ned)f
(in)f(the)h(pre-)-5 76 y(vious)g(equations)f(are)g(usually)g(referred)f
(to)i(as)g(the)f Fu(sup)n(er)n(c)n(ovariant)f FH(\014eld)h(strengths.)
68 136 y(The)g(ph)o(ysical)f(\014elds)h(app)q(earing)h(in)f(the)g
(parametrizations)f(are)h(actually)f(further)h(required)f(to)-5
196 y(satisfy)i(extra{constrain)o(ts)f(whic)o(h)g(are)g(essen)o(tially)
f(of)h(t)o(w)o(o)g(t)o(yp)q(es:)55 298 y(1.)24 b(The)17
b(sup)q(erco)o(v)m(arian)o(t)f(\014eld)g(strengths)i(satisfy)e(a)h(set)
f(of)h(di\013eren)o(tial)e(constrain)o(ts)i(whic)o(h)f(are)117
358 y(to)d(b)q(e)h(iden)o(ti\014ed,)d(when)i(the)g(\014elds)f(are)h
(restricted)f(to)h(space{time)f(only)l(,)g(with)h(the)g(equations)117
418 y(of)h(motion)f(of)h(the)g(theory)l(.)20 b(Indeed)13
b(the)g(analysis)h(of)h(the)e(Bianc)o(hi)f(iden)o(tities)g(for)i(the)g
(fermion)117 478 y(\014elds)h(giv)o(e)g(suc)o(h)g(equations)h(\(in)f
(the)g(sector)g(con)o(taining)h(the)f(2{form)g(basis)p
1568 439 34 2 v 16 w Fv( )1602 490 y Ft(A)1630 478 y
Fv(\015)1658 460 y Ft(a)1679 478 y Fv( )1713 460 y Ft(A)1741
478 y FH(\).)21 b(F)l(ur-)117 545 y(ther)e(the)h(sup)q(erspace)g(deriv)
m(ativ)o(e)d(along)k(the)e Fv( )1039 552 y Ft(A)1084
497 y Fs(\020)1109 545 y Fv( )1143 527 y Ft(A)1171 497
y Fs(\021)1215 545 y FH(directions,)g(whic)o(h)g(amoun)o(ts)g(to)h(a)
117 605 y(sup)q(ersymmetry)12 b(transformation,)i(yields)f(the)h
(equations)h(of)f(motion)g(of)h(the)f(b)q(osonic)h(\014elds.)117
665 y(This)h(is)f(not)h(a)g(surprise)f(since)g(the)g(closure)g(of)g
(the)h(Bianc)o(hi)e(iden)o(tities)f(is)i(in)g(fact)h(equiv)m(alen)o(t)
117 725 y(to)j(the)g(closure)g(of)g(the)f Fv(N)24 b FH(=)18
b(2)h(sup)q(ersymmetry)d(algebra)k(on)f(the)g(ph)o(ysical)e(\014elds)i
(and)g(w)o(e)117 786 y(kno)o(w)g(that)g(in)f(general)g(suc)o(h)g
(closure)g(implies)e(the)i(equations)h(of)f(motion)g(for)h(the)f
(fermion)117 846 y(\014elds.)39 b(Indeed)21 b(in)h(our)h(case)f(the)g
(usual)g(auxiliary)f(\014elds)h(of)g Fv(N)29 b FH(=)24
b(2)f(theory)f(ha)o(v)o(e)f(b)q(een)117 906 y(determined)14
b(as)j(suitable)f(expressions)g(in)g(the)g(ph)o(ysical)f(\014elds.)117
987 y(Finally)c(w)o(e)g(also)h(note)g(that)g(since)f(the)h(expressions)
g(for)g(the)f(curv)m(atures)h(imply)d(the)j(equations)117
1047 y(of)17 b(motion)e(it)h(follo)o(ws)h(that)g(in)f(the)g(ungauged)i
(case)e(\()p Fv(g)g FH(=)e(0\))j(the)f(form)o(ulae)31
b(8.24)p
 (#equation.8.24) [[453 516 474 528] [1 1 1 [3 3]] [0 0 1]] pdfm ({)18
b(8.26)p
 (#equation.8.24) [[484 516 505 528] [1 1 1 [3 3]] [0 0 1]] pdfm 
17 w(are)117 1107 y(symplectic)13 b(co)o(v)m(arian)o(t)j(since)g(the)g
(ungauged)h(theory)f(is)g(on-shell)h(symplectic)c(co)o(v)m(arian)o(t.)
55 1209 y(2.)24 b(The)17 b(second)h(t)o(yp)q(e)e(of)i(constrain)o(ts)f
(follo)o(wing)g(from)f(the)h(closure)g(of)h(Bianc)o(hi)d(iden)o(tities)
h(is)h(a)117 1275 y(set)j(of)g(di\013eren)o(tial)f(constrain)o(ts)h(on)
g(the)g(upp)q(er)g(part)g Fv(L)1200 1257 y FC(\003)1227
1275 y Fv(;)p 1257 1236 V 16 w(L)1290 1246 y FC(\003)1317
1275 y Fv(;)c(f)1376 1257 y FC(\003)1371 1288 y Ft(i)1403
1275 y Fv(;)p 1433 1236 30 2 v 16 w(f)1462 1245 y FC(\003)1462
1288 y Ft(i)1474 1278 y Fm(?)1514 1275 y FH(of)21 b(the)e(symplectic)
117 1335 y(sections)f Fv(V)29 b FH(and)18 b Fv(U)487
1342 y Ft(i)519 1335 y FH(and)g(of)g(the)g FE(T)13 b(M)857
1315 y FC(3)889 1335 y FE(\012)f(L)974 1317 y FC(2)1012
1335 y FH(sections)17 b Fv(C)1230 1342 y Ft(ij)r(k)1298
1335 y FH(\()g(together)h(with)g(its)f(complex)117 1396
y(conjugate)g Fv(C)373 1403 y Ft(i)385 1394 y Fm(?)403
1403 y Ft(j)419 1394 y Fm(?)437 1403 y Ft(k)456 1394
y Fm(?)476 1396 y FH(\).)117 1456 y(One)f(\014nds:)799
1516 y FE(r)841 1523 y Ft(i)853 1514 y Fm(?)873 1516
y Fv(L)906 1495 y FC(\003)946 1516 y FH(=)e FE(r)1040
1523 y Ft(i)p 1054 1477 34 2 v 1054 1516 a Fv(L)1087
1487 y FC(\003)1127 1516 y FH(=)g(0)545 b(\(A.55\))717
1612 y Fv(f)746 1591 y FC(\003)741 1624 y Ft(i)787 1612
y FH(=)14 b FE(r)881 1619 y Ft(i)894 1612 y Fv(L)927
1591 y FC(\003)954 1612 y FH(;)p 1025 1572 30 2 v 57
w Fv(f)1054 1582 y FC(\003)1054 1624 y Ft(i)1066 1615
y Fm(?)1100 1612 y FH(=)g FE(r)1194 1619 y Ft(i)1206
1610 y Fm(?)p 1225 1573 34 2 v 1225 1612 a Fv(L)1258
1583 y FC(\003)1748 1612 y FH(\(A.56\))708 1749 y FE(r)750
1756 y Ft(`)764 1747 y Fm(?)784 1749 y Fv(C)819 1756
y Ft(ij)r(k)910 1749 y FH(=)42 b FE(r)1032 1756 y Ft(`)1048
1749 y Fv(C)1083 1756 y Ft(i)1095 1747 y Fm(?)1113 1756
y Ft(j)1129 1747 y Fm(?)1147 1756 y Ft(k)1166 1747 y
Fm(?)1200 1749 y FH(=)14 b(0)472 b(\(A.57\))707 1822
y FE(r)749 1829 y FC([)p Ft(`)774 1822 y Fv(C)809 1829
y Ft(i)p FC(])p Ft(j)r(k)910 1822 y FH(=)42 b FE(r)1032
1836 y FC([)p 1042 1808 15 2 v Ft(`)1057 1822 y Fv(C)1092
1829 y Ft(i)1104 1820 y Fm(?)1122 1829 y FC(])p Ft(j)1148
1820 y Fm(?)1166 1829 y Ft(k)1185 1820 y Fm(?)1219 1822
y FH(=)14 b(0)453 b(\(A.58\))753 1913 y FE(r)795 1920
y Ft(j)813 1913 y Fv(f)842 1893 y FC(\003)837 1925 y
Ft(k)910 1913 y FH(=)42 b(i)p Fv(g)1029 1893 y Ft(i)p
1041 1865 V(`)p 1057 1874 30 2 v 1057 1913 a Fv(f)1086
1883 y FC(\003)1086 1925 y Ft(`)1100 1916 y Fm(?)1121
1913 y Fv(C)1156 1920 y Ft(ij)r(k)1748 1913 y FH(\(A.59\))117
2023 y(Using)13 b(the)g(iden)o(tities)e(of)i(Sp)q(ecial)g(Geometry)e
(\(4.18)p
 (#equation.4.18) [[311 281 332 293] [1 1 1 [3 3]] [0 0 1]] pdfm (,)i
(4.26)p
 (#equation.4.26) [[338 281 359 293] [1 1 1 [3 3]] [0 0 1]] pdfm (,)h
(4.30)p
 (#equation.4.30) [[366 281 386 293] [1 1 1 [3 3]] [0 0 1]] pdfm (,)27
b(4.37)p
 (#equation.4.37) [[396 281 417 293] [1 1 1 [3 3]] [0 0 1]] pdfm (\),)
14 b Fv(C)1519 2030 y Ft(ij)r(k)1581 2023 y FH(can)f(b)q(e)h(written)
117 2083 y(as:)698 2144 y Fv(C)733 2151 y Ft(ij)r(k)796
2144 y FH(=)848 2095 y Fs(\020)873 2144 y FE(N)26 b(\000)p
998 2105 49 2 v 19 w(N)1047 2095 y Fs(\021)1071 2171
y FC(\003\006)1132 2144 y Fv(f)1161 2123 y FC(\003)1156
2156 y Ft(i)1188 2144 y FE(r)1230 2151 y Ft(j)1247 2144
y Fv(f)1276 2123 y FC(\006)1271 2156 y Ft(k)1748 2144
y FH(\(A.60\))117 2236 y(In)21 b(particular)f(equation)g(A.59)p
 (#equation.A.57) [[220 230 243 242] [1 1 1 [3 3]] [0 0 1]] pdfm 
21 w(implies)e(the)i(constrain)o(t)h(giv)o(en)f(in)g(4.18)p
 (#equation.4.18) [[413 230 433 242] [1 1 1 [3 3]] [0 0 1]] pdfm 
21 w(for)h(the)g(Riemann)117 2296 y(tensor)14 b(of)g(the)f(K\177)-24
b(ahler-Ho)q(dge)14 b(manifold)f(while)f(equations)28
b(A.57)p
 (#equation.A.57) [[374 216 398 228] [1 1 1 [3 3]] [0 0 1]] pdfm 
({A.58)p
 (#equation.A.57) [[403 216 427 228] [1 1 1 [3 3]] [0 0 1]] pdfm 
13 w(are)14 b(actually)f(equiv-)117 2357 y(alen)o(t)h(to)i(the)e(other)
h(equations)30 b(4.18)p
 (#equation.4.18) [[248 201 269 213] [1 1 1 [3 3]] [0 0 1]] pdfm (,)16
b(using)30 b(4.19)p
 (#equation.4.19) [[310 201 331 213] [1 1 1 [3 3]] [0 0 1]] pdfm (.)22
b(Therefore)14 b(the)h(constrain)o(ts)g(A.55)p
 (#equation.A.55) [[471 201 495 213] [1 1 1 [3 3]] [0 0 1]] pdfm 
({A.59)p
 (#equation.A.57) [[501 201 524 213] [1 1 1 [3 3]] [0 0 1]] pdfm 
117 2417 a(imply)f(that)i(the)g(K\177)-24 b(ahler-Ho)q(dge)17
b(manifold)d(w)o(e)i(started)g(from)f(is)h(actually)f(a)i(sp)q(ecial)e
(K\177)-24 b(ahler)117 2477 y(manifold.)117 2537 y(W)l(e)20
b(ma)o(y)f(also)h(v)o(erify)f(that)h(the)g(same)f(equations)h(A.55)p
 (#equation.A.55) [[336 158 360 170] [1 1 1 [3 3]] [0 0 1]] pdfm 
({A.59)p
 (#equation.A.57) [[366 158 390 170] [1 1 1 [3 3]] [0 0 1]] pdfm 
21 w(hold)g(pro)o(vided)f(w)o(e)h(replace)117 2597 y
Fv(L)150 2579 y FC(\003)191 2597 y FE(!)13 b Fv(M)301
2604 y FC(\003)340 2597 y FH(and)f Fv(f)459 2579 y FC(\003)454
2610 y Ft(i)499 2597 y FE(!)i Fv(h)591 2604 y FC(\003)p
Ft(i)641 2597 y FH(\(together)e(with)f(their)g(c.c.\).)18
b(Hence)10 b(w)o(e)h(ha)o(v)o(e)f(a)i(set)f(of)h(symplectic)117
2658 y(co)o(v)m(arian)o(t)k(constrain)o(ts,)g(namely:)786
2768 y FE(r)828 2775 y Ft(i)842 2768 y Fv(V)52 b FH(=)42
b Fv(U)1035 2775 y Ft(i)916 2892 y FH(62)p eop
%%Page: 63 64
63 63 bop 770 15 a FE(r)812 22 y Ft(j)830 15 y Fv(U)863
22 y Ft(j)922 15 y FH(=)42 b(i)p Fv(C)1051 22 y Ft(ij)r(k)1100
15 y Fv(g)1125 -5 y Ft(k)q(`)1158 -17 y Fm(?)1179 15
y Fv(U)1212 22 y Ft(`)1226 14 y Fm(?)756 88 y FE(r)798
95 y Ft(i)812 88 y Fv(U)845 95 y Ft(j)861 86 y Fm(?)922
88 y FH(=)g Fv(g)1025 95 y Ft(ij)1053 86 y Fm(?)1073
88 y Fv(V)768 161 y FE(r)810 168 y Ft(i)822 159 y Fm(?)842
161 y Fv(V)52 b FH(=)42 b(0)722 b(\(A.61\))117 254 y(whic)o(h)23
b(giv)o(e)f(an)h(alternativ)o(e)f(de\014nition)h(of)g(Sp)q(ecial)f
(Geometry)g(in)g(terms)g(of)h(di\013eren)o(tial)117 315
y(constrain)o(ts)c(on)g(a)g(symplectic)c(bundle)j(of)h(the)f(K\177)-24
b(ahler-Ho)q(dge)19 b(manifold.)27 b(This)19 b(de\014nition)117
375 y(of)d(Sp)q(ecial)g(Geometry)e(w)o(as)j(in)e(fact)h(\014rst)g
(deduced)g(in)g([27)p
 (#cite.CaDF) [[353 677 365 689] [1 1 1 [3 3]] [0 0 1]] pdfm (])f(from)
g Fv(N)k FH(=)14 b(2)i(Bianc)o(hi)f(iden)o(tities)117
435 y(\(i.e.)k(for)14 b(the)f(closure)g(of)h Fv(N)19
b FH(=)14 b(2)f(susy)h(algebra\).)21 b(F)l(urthermore)11
b(there)i(is)g(a)h(close)f(connection,)117 495 y(exploited)d(in)h(ref.)
19 b([70)p
 (#cite.pincopallo) [[186 648 198 660] [1 1 1 [3 3]] [0 0 1]] pdfm 
1 w(],)11 b(b)q(et)o(w)o(een)f(the)h(di\013eren)o(tial)f(constrain)o
(ts)23 b(A.61)p
 (#equation.A.61) [[389 648 413 660] [1 1 1 [3 3]] [0 0 1]] pdfm 
11 w(and)12 b(the)f(Picard{F)l(uc)o(hs)117 555 y(equations)17
b(for)f(the)g(p)q(erio)q(ds)h(of)g(a)f(3{dimensional)g(Calabi{Y)l(au)g
(manifold)f([71)p
 (#cite.anche) [[446 634 457 646] [1 1 1 [3 3]] [0 0 1]] pdfm 
1 w(,)g(70)p
 (#cite.pincopallo) [[464 634 476 646] [1 1 1 [3 3]] [0 0 1]] pdfm 
1 w(])h(.)68 643 y(The)i(determination)d(of)i(the)g(sup)q(erspace)h
(curv)m(atures)f(enables)g(us)h(to)f(write)g(do)o(wn)h(the)f
Fv(N)j FH(=)c(2)-5 703 y(SUSY)k(transformation)g(la)o(ws.)32
b(Indeed)20 b(w)o(e)f(recall)g(that)i(from)e(the)g(sup)q(erspace)i(p)q
(oin)o(t)f(of)g(view)g(a)-5 764 y(sup)q(ersymmetry)14
b(transformation)i(is)g(a)g(Lie)g(deriv)m(ativ)o(e)f(along)i(the)f
(tangen)o(t)h(v)o(ector:)733 857 y Fv(\017)d FH(=)p 818
831 20 2 v 13 w Fv(\017)838 837 y Ft(A)882 845 y Fv(~)875
857 y(D)915 864 y Ft(A)963 857 y FH(+)p 1020 831 V 19
w Fv(\017)1040 864 y Ft(A)1085 845 y Fv(~)1077 857 y(D)1118
837 y Ft(A)1748 857 y FH(\(A.62\))-5 955 y(where)i(the)g(basis)h
(tangen)o(t)f(v)o(ectors)691 943 y Fv(~)683 955 y(D)723
962 y Ft(A)760 955 y Fv(;)798 943 y(~)790 955 y(D)831
937 y Ft(A)877 955 y FH(are)g(dual)h(to)f(the)g(gra)o(vitino)g
(1{forms:)683 1037 y Fv(~)676 1049 y(D)716 1056 y Ft(A)753
1001 y Fs(\020)778 1049 y Fv( )812 1029 y Ft(B)842 1001
y Fs(\021)880 1049 y FH(=)940 1037 y Fv(~)932 1049 y(D)973
1029 y Ft(A)1011 1049 y FH(\()p Fv( )1062 1056 y Ft(B)1092
1049 y FH(\))e(=)f FD(1)544 b FH(\(A.63\))-5 1143 y(where)16
b FD(1)g FH(is)h(the)f(unit)f(in)h(spinor)h(space.)68
1203 y(Denoting)24 b(b)o(y)f Fv(\026)390 1185 y Ft(I)434
1203 y FH(and)h Fv(R)573 1185 y Ft(I)617 1203 y FH(the)f(set)g(of)h
(one{forms)1093 1155 y Fs(\020)1118 1203 y Fv(V)1157
1185 y Ft(a)1178 1203 y Fv(;)16 b( )1240 1210 y Ft(A)1268
1203 y Fv(;)g( )1332 1185 y Ft(A)1360 1203 y Fv(;)h(A)1428
1185 y FC(\003)1454 1155 y Fs(\021)1502 1203 y FH(and)24
b(of)g(t)o(w)o(o{forms)-5 1234 y Fs(\020)20 1282 y Fv(R)57
1264 y Ft(a)78 1282 y Fv(;)17 b(\032)134 1289 y Ft(a)155
1282 y Fv(;)f(\032)210 1264 y Ft(A)238 1282 y Fv(;)h(F)308
1264 y Ft(\025)330 1234 y Fs(\021)371 1282 y FH(resp)q(ectiv)o(ely)l(,)
c(one)j(has:)552 1391 y Fv(`\026)601 1371 y Ft(I)635
1391 y FH(=)e(\()p Fv(i)723 1398 y Ft(\017)739 1391 y
Fv(d)20 b FH(+)f Fv(di)883 1398 y Ft(\017)899 1391 y
FH(\))8 b Fv(\026)955 1371 y Ft(I)990 1391 y FE(\021)13
b FH(\()p Fv(D)q(\017)p FH(\))1142 1367 y Ft(I)1181 1391
y FH(+)19 b Fv(i)1255 1398 y Ft(\017)1271 1391 y Fv(R)1308
1371 y Ft(I)1748 1391 y FH(\(A.64\))-5 1485 y(where)d(D)f(is)h(the)f
(deriv)m(ativ)o(e)f(co)o(v)m(arian)o(t)i(with)f(resp)q(ect)g(to)h(the)g
Fv(N)j FH(=)14 b(2)i(P)o(oincar)o(\023)-23 b(e)15 b(sup)q(eralgebra)h
(and)-5 1545 y Fv(i)12 1552 y Ft(\017)45 1545 y FH(is)g(the)g(con)o
(traction)g(op)q(erator)h(along)g(the)f(tangen)o(t)h(v)o(ector)e
Fv(\017)p FH(.)68 1606 y(In)h(our)h(case:)586 1699 y(\()p
Fv(D)q(\017)p FH(\))686 1675 y Ft(a)748 1699 y FH(=)42
b(i)850 1651 y Fs(\020)p 874 1660 34 2 v 874 1699 a Fv( )908
1711 y Ft(A)936 1699 y Fv(\015)964 1679 y Ft(a)985 1699
y Fv(\017)1005 1679 y Ft(A)1053 1699 y FH(+)p 1110 1660
V 19 w Fv( )1144 1670 y Ft(A)1172 1699 y Fv(\015)1200
1679 y Ft(a)1221 1699 y Fv(\017)1241 1706 y Ft(A)1269
1651 y Fs(\021)1748 1699 y FH(\(A.65\))583 1779 y(\()o
Fv(D)q(\017)p FH(\))682 1755 y Ft(\013)748 1779 y FH(=)g
FE(r)p Fv(\017)890 1759 y Ft(\013)1748 1779 y FH(\(A.66\))581
1852 y(\()p Fv(D)q(\017)p FH(\))680 1828 y FC(\003)748
1852 y FH(=)g(0)896 b(\(A.67\))-5 1946 y(\(here)16 b
Fv(\013)h FH(is)f(a)g(spinor)h(index\))-5 2012 y(F)l(or)j(the)g
(0{forms)f(whic)o(h)g(w)o(e)h(denote)f(shortly)h(as)h
Fv(\027)998 1994 y Ft(I)1038 2012 y FE(\021)1096 1964
y Fs(\020)1121 2012 y Fv(q)1145 1994 y Ft(u)1167 2012
y Fv(;)16 b(z)1222 1994 y Ft(i)1236 2012 y Fv(;)g(z)1291
1994 y Ft(i)1303 1982 y Fm(?)1323 2012 y Fv(;)g(\025)1381
1994 y Ft(iA)1422 2012 y Fv(;)g(\025)1480 1994 y Ft(i)1492
1982 y Fm(?)1480 2024 y Ft(A)1513 2012 y Fv(;)g(\020)1564
2019 y Ft(\013)1589 2012 y Fv(;)g(\020)1644 1994 y Ft(\013)1669
1964 y Fs(\021)1714 2012 y FH(w)o(e)j(ha)o(v)o(e)-5 2072
y(the)d(simpler)e(result:)490 2132 y Fv(`)510 2139 y
Ft(\017)540 2132 y FH(=)g Fv(i)609 2139 y Ft(\017)625
2132 y Fv(d\027)677 2112 y Ft(I)711 2132 y FH(=)g Fv(i)780
2139 y Ft(\017)804 2084 y Fs(\020)829 2132 y FE(r)p Fv(\027)898
2112 y Ft(I)937 2132 y FE(\000)19 b Fv(connection)8 b(ter)q(ms)1366
2084 y Fs(\021)1748 2132 y FH(\(A.68\))-5 2222 y(Using)18
b(the)f(parametrizations)f(giv)o(en)h(for)g Fv(R)835
2204 y Ft(I)873 2222 y FH(and)h FE(r)p Fv(\027)1038 2204
y Ft(I)1075 2222 y FH(and)g(iden)o(tifying)e Fv(\016)1437
2229 y Ft(\017)1471 2222 y FH(with)h(the)g(restriction)-5
2282 y(of)j Fv(`)74 2289 y Ft(\017)111 2282 y FH(to)g(space{time)d(it)j
(is)f(imme)o(diate)e(to)j(\014nd)g(the)f Fv(N)25 b FH(=)19
b(2)h(susy)g(la)o(ws)g(for)g(all)f(the)g(\014elds.)31
b(The)-5 2343 y(explicit)14 b(form)o(ulae)h(are)h(giv)o(en)g(in)f
(section)h(8)p
 (#section.8) [[263 205 269 217] [1 1 1 [3 3]] [0 0 1]] pdfm (.)-5
2507 y Fw(App)r(endix)24 b(B:)j(Deriv)l(ation)c(of)j(the)g(space)f
(time)g(Lagrangian)-5 2598 y(from)i(the)g(geometric)g(approac)n(h)-5
2707 y FH(In)18 b(App)q(endix)f(A)g(w)o(e)g(ha)o(v)o(e)g(seen)g(ho)o(w)
i(to)f(reconstruct)f(the)g Fv(N)22 b FH(=)16 b(2)i(susy)g
(transformation)g(la)o(ws)g(of)-5 2768 y(the)e(ph)o(ysical)g(\014elds)f
(from)h(the)g(solution)g(of)h(the)f(Bianc)o(hi)e(iden)o(tities)h(in)h
(sup)q(erspace.)916 2892 y(63)p eop
%%Page: 64 65
64 64 bop -5 15 a FH(In)18 b(principle,)f(since)h(the)g(Bianc)o(hi)f
(iden)o(tities)g(imply)f(the)i(equations)g(of)h(motion,)f(the)g
(Lagrangian)-5 76 y(could)e(also)h(b)q(e)g(completely)c(determined.)18
b(Ho)o(w)o(ev)o(er)d(this)h(w)o(ould)g(b)q(e)h(a)f(cum)o(b)q(ersome)e
(pro)q(cedure.)68 136 y(In)20 b(this)g(App)q(endix)g(w)o(e)f(giv)o(e)g
(a)i(short)g(accoun)o(t)f(of)g(the)g(construction)g(of)g(the)g
(Lagrangian)j(on)-5 196 y(space{time)15 b(from)g(a)i(geometrical)d
(Lagrangian)k(in)e(sup)q(erspace.)-5 256 y(In)i(the)g(geometric)e
(\(rheonomic\))h(approac)o(h)i(the)f(sup)q(erspace)g(action)g(is)g(a)h
(4{form)f(in)g(sup)q(erspace)-5 316 y(in)o(tegrated)e(on)h(a)f
(4{dimensional)g(\(b)q(osonic\))h(h)o(yp)q(ersurface)e
FE(M)1210 298 y FC(4)1246 316 y FH(lo)q(cally)h(em)o(b)q(edded)e(in)i
FE(M)1748 298 y FC(4)p FB(j)p FC(8)1795 316 y FH(:)764
430 y FE(A)e FH(=)869 372 y Fs(Z)893 466 y FB(M)935 457
y Fr(4)952 466 y FB(\032M)1021 456 y Fr(4)p Fn(j)p Fr(8)1082
430 y FE(L)659 b FH(\(B.1\))-5 545 y(Pro)o(vided)19 b(w)o(e)h(do)g(not)
g(in)o(tro)q(duce)f(the)h(Ho)q(dge)g(dualit)o(y)f(op)q(erator)i(in)e
(the)g(construction)h(of)g FE(L)g FH(the)-5 606 y(equations)14
b(of)f(motions)g(deriv)o(ed)f(from)g(the)h(generalized)f(v)m
(ariational)i(principle)d Fv(\016)r FE(A)i FH(=)h(0)g(are)f(3{form)-5
666 y(or)j(4{form)f(equations)h(indep)q(enden)o(t)f(from)f(the)i
(particular)f(h)o(yp)q(ersurface)g FE(M)1477 648 y FC(4)1512
666 y FH(on)h(whic)o(h)f(w)o(e)g(in)o(te-)-5 726 y(grate.)-5
786 y(These)g(sup)q(erspace)h(equations)f(of)h(motion)e(can)h(b)q(e)g
(analyzed)g(along)h(the)f Fv(p)p FH({form)g(basis.)21
b(The)15 b(com-)-5 846 y(p)q(onen)o(ts)j(of)g(the)f(equations)h
(obtained)g(along)g(b)q(osonic)g(vielb)q(eins)e(giv)o(e)h(the)g
(di\013eren)o(tial)f(equations)-5 907 y(for)j(the)e(\014elds)h(whic)o
(h,)f(iden)o(tifying)g FE(M)744 889 y FC(4)781 907 y
FH(with)h(space{time,)e(are)i(the)g(ordinary)g(equations)g(of)h(mo-)-5
967 y(tion)g(of)g(the)g(theory)l(.)29 b(The)19 b(comp)q(onen)o(ts)f(of)
h(the)g(same)e(equations)i(along)h Fv(p)p FH({forms)f(con)o(taining)g
(at)-5 1027 y(least)g(one)g(gra)o(vitino)f(\("outer)h(comp)q(onen)o
(ts"\))g(giv)o(e)e(instead)i(algebraic)f(relations)h(whic)o(h)f(iden)o
(tify)-5 1087 y(the)e(comp)q(onen)o(ts)g(of)g(the)g(v)m(arious)h("sup)q
(ercurv)m(atures")h(in)e(sup)q(erspace.)68 1147 y(The)22
b(Lagrangian)h(m)o(ust)d(b)q(e)i(constructed)f(according)g(to)h(the)f
(principles)f(of)h(rheonom)o(y:)30 b(the)-5 1208 y("outer)21
b(comp)q(onen)o(ts")f(computed)f(from)h(the)g(v)m(ariational)h
(equations)f(m)o(ust)f(b)q(e)i(all)f(expressed)f(in)-5
1268 y(terms)13 b(of)h(the)g(sup)q(erco)o(v)m(arian)o(t)g(comp)q(onen)o
(ts)f(\(comp)q(onen)o(ts)g(along)i(the)f(vielb)q(eins)f(basis\).)21
b(Actually)-5 1328 y(if)16 b(w)o(e)g(ha)o(v)o(e)g(already)g(solv)o(ed)g
(the)g(Bianc)o(hi)g(iden)o(tities)e(this)i(requiremen)o(t)e(is)i(equiv)
m(alen)o(t)f(to)i(iden)o(tify)-5 1388 y(the)d(outer)f(comp)q(onen)o(ts)
g(of)h(the)f(curv)m(atures)h(obtained)g(from)e(the)i(v)m(ariational)f
(principle)f(with)i(those)-5 1448 y(obtained)j(from)e(the)h(Bianc)o(hi)
f(iden)o(tities.)68 1509 y(There)21 b(are)f(simple)f(rules)h(whic)o(h)g
(can)h(b)q(e)g(used)g(in)f(order)h(to)g(write)f(do)o(wn)h(the)f(most)g
(general)-5 1569 y(Lagrangian)f(compatible)14 b(with)i(this)g
(requiremen)o(t.)-5 1629 y(The)22 b(implem)o(en)o(tation)d(of)j(these)f
(rules)h(is)f(describ)q(ed)g(in)h(detail)f(in)g(the)h(literature)e(to)i
(whic)o(h)f(w)o(e)-5 1689 y(refer)c(the)g(in)o(terested)f(reader.)25
b(Actually)16 b(one)h(writes)g(do)o(wn)h(the)f(most)g(general)g(4{form)
g(as)h(a)g(sum)-5 1749 y(of)j(terms)d(with)i(indeterminate)e(co)q
(e\016cien)o(ts)h(in)h(suc)o(h)g(a)g(w)o(a)o(y)g(that)h
FE(L)f FH(b)q(e)g(a)h(scalar)f(with)g(resp)q(ect)-5 1809
y(to)c(all)f(the)h(symmetry)c(transformations)k(of)g(the)f(theory)h
(\(Loren)o(tz)g(in)o(v)m(ariance,)e Fv(S)s(U)g FH(\()o(2\))d
FE(\012)e Fv(S)s(p)f FH(\()q(2)p Fv(m)p FH(\))-5 1870
y(and)14 b Fv(U)g FH(\(1\))g(K\177)-24 b(ahler)13 b(in)o(v)m(ariance,)f
(in)o(v)m(ariance)g(under)i(the)f(rescaling)g(A.22)p
 (#equation.A.22) [[372 318 396 330] [1 1 1 [3 3]] [0 0 1]] pdfm (\).)
20 b(V)l(arying)13 b(the)g(action)g(and)-5 1930 y(comparing)g(the)g
(outer)h(equations)g(of)f(motion)g(with)g(the)h(actual)f(solution)h(of)
g(the)f(Bianc)o(hi)f(iden)o(tities)-5 1990 y(one)17 b(then)f(\014xes)g
(all)g(the)g(undetermined)d(co)q(e\016cien)o(ts.)68 2050
y(Let)18 b(us)f(p)q(erform)g(the)g(steps)g(previously)g(indicated.)23
b(The)17 b(most)g(general)g(Lagrangian)i(has)f(the)-5
2110 y(follo)o(wing)e(form:)302 2209 y FE(L)23 b FH(=)f
FE(L)453 2216 y Ft(g)q(r)q(av)547 2209 y FH(+)d FE(L)638
2216 y Ft(k)q(in)713 2209 y FH(+)g FE(L)804 2216 y Ft(P)5
b(auli)915 2209 y FH(+)19 b FE(L)1006 2216 y Ft(tor)q(sion)1142
2209 y FH(+)g FE(L)1233 2216 y FC(4)p Ft(f)t(er)q(m)1358
2209 y FH(+)g FE(L)1449 2216 y Ft(g)q(aug)q(ing)1775
2209 y FH(\(B.2\))73 2357 y FE(L)107 2364 y Ft(g)q(r)q(av)231
2357 y FH(=)50 b Fv(\017)339 2364 y Ft(abcd)408 2357
y Fv(R)445 2336 y Ft(ab)493 2357 y FE(^)11 b Fv(V)576
2336 y Ft(c)605 2357 y FE(^)g Fv(V)688 2336 y Ft(d)728
2357 y FE(\000)19 b FH(4)827 2309 y Fs(\020)p 852 2317
34 2 v 48 x Fv( )885 2327 y Ft(A)914 2357 y Fv(\015)939
2364 y Ft(a)960 2357 y Fv(\032)985 2364 y Ft(A)1033 2357
y FE(\000)p 1091 2317 V 19 w Fv( )1124 2369 y Ft(A)1153
2357 y Fv(\015)1178 2364 y Ft(a)1199 2357 y Fv(\032)1224
2336 y Ft(A)1253 2309 y Fs(\021)1294 2357 y Fv(V)1333
2336 y Ft(a)92 2451 y FE(L)126 2458 y Ft(k)q(in)231 2451
y FH(=)50 b Fv(\014)347 2458 y FC(1)366 2451 y Fv(g)389
2458 y Ft(ij)417 2449 y Fm(?)454 2403 y Fs(h)474 2451
y Fv(Z)511 2431 y Ft(i)507 2463 y(a)545 2403 y Fs(\020)570
2451 y FE(r)p 612 2425 25 2 v Fv(z)636 2431 y Ft(j)652
2419 y Fm(?)692 2451 y FE(\000)p 750 2411 34 2 v 19 w
Fv( )783 2421 y Ft(A)812 2451 y Fv(\025)840 2427 y Ft(j)856
2416 y Fm(?)840 2463 y Ft(A)876 2403 y Fs(\021)921 2451
y FH(+)p 978 2412 37 2 v 19 w Fv(Z)1015 2422 y Ft(j)1031
2410 y Fm(?)1015 2463 y Ft(a)1068 2403 y Fs(\020)1093
2451 y FE(r)p Fv(z)1160 2431 y Ft(i)1192 2451 y FE(\000)p
1251 2411 34 2 v 20 w Fv( )1284 2463 y Ft(A)1313 2451
y Fv(\025)1341 2431 y Ft(iA)1381 2403 y Fs(\021i)1445
2451 y FE(^)12 b Fv(V)1529 2431 y Ft(b)1557 2451 y FE(^)f
Fv(V)1641 2431 y Ft(c)1669 2451 y FE(^)g Fv(V)1753 2431
y Ft(d)1773 2451 y Fv(\017)1793 2431 y Ft(a)1811 2463
y(bcd)311 2545 y FH(+)d Fv(b)378 2552 y FC(1)397 2545
y Fv(\017)417 2552 y Ft(AB)p 482 2545 2 33 v 469 2545
a FH(C)504 2552 y Ft(\013\014)559 2545 y FE(U)595 2524
y Ft(A\013)590 2557 y(a)655 2497 y Fs(\020)679 2545 y
FE(U)715 2524 y Ft(B)r(\014)787 2545 y FE(\000)p 845
2505 34 2 v 19 w Fv( )878 2515 y Ft(B)909 2545 y Fv(\020)934
2524 y Ft(\014)977 2545 y FE(\000)19 b Fv(\017)1055 2524
y Ft(B)r(C)p 1121 2545 2 33 v 1108 2545 a FH(C)1143 2524
y Ft(\014)r(\015)p 1195 2505 34 2 v 1195 2545 a Fv( )1228
2557 y Ft(C)1258 2545 y Fv(\020)1279 2552 y Ft(\015)1301
2497 y Fs(\021)1346 2545 y FE(^)11 b Fv(V)1429 2524 y
Ft(b)1457 2545 y FE(^)h Fv(V)1541 2524 y Ft(c)1569 2545
y FE(^)g Fv(V)1653 2524 y Ft(d)1673 2545 y Fv(\017)1693
2524 y Ft(a)1712 2557 y(bcd)311 2652 y FE(\000)363 2619
y FH(1)p 363 2641 25 2 v 363 2687 a(4)409 2592 y Fs(\022)439
2652 y Fv(\014)467 2659 y FC(1)486 2652 y Fv(g)509 2659
y Ft(ij)537 2650 y Fm(?)558 2652 y Fv(Z)595 2632 y Ft(i)591
2665 y(l)p 609 2613 37 2 v 609 2652 a Fv(Z)646 2623 y
Ft(j)662 2611 y Fm(?)646 2665 y Ft(m)702 2652 y FH(+)764
2619 y(1)p 764 2641 25 2 v 764 2687 a(2)793 2652 y Fv(b)814
2659 y FC(1)834 2652 y Fv(\017)854 2659 y Ft(AB)p 927
2652 2 33 v 914 2652 a FH(C)949 2659 y Ft(\013\014)995
2652 y FE(U)1031 2632 y Ft(A\013)1026 2665 y(l)1083 2652
y FE(U)1119 2632 y Ft(B)r(\014)1114 2665 y(m)1171 2592
y Fs(\023)1210 2652 y Fv(\021)1236 2632 y Ft(lm)1280
2652 y Fv(\017)1300 2659 y Ft(abcd)1377 2652 y Fv(V)1416
2632 y Ft(a)1448 2652 y FE(^)f Fv(V)1532 2632 y Ft(b)1560
2652 y FE(^)g Fv(V)1643 2632 y Ft(c)1672 2652 y FE(^)g
Fv(V)1755 2632 y Ft(d)311 2759 y FH(+)d(i)g Fv(\014)407
2766 y FC(2)426 2759 y Fv(g)449 2766 y Ft(ij)477 2757
y Fm(?)514 2711 y Fs(\020)p 539 2720 29 2 v 48 x Fv(\025)567
2730 y Ft(iA)608 2759 y Fv(\015)636 2739 y Ft(a)657 2759
y FE(r)p Fv(\025)727 2736 y Ft(j)743 2724 y Fm(?)727
2772 y Ft(A)782 2759 y FH(+)p 840 2720 V 20 w Fv(\025)868
2730 y Ft(j)884 2718 y Fm(?)868 2772 y Ft(A)904 2759
y Fv(\015)932 2739 y Ft(a)953 2759 y FE(r)p Fv(\025)1023
2739 y Ft(iA)1064 2711 y Fs(\021)1100 2759 y FE(^)j Fv(V)1183
2739 y Ft(b)1211 2759 y FE(^)h Fv(V)1295 2739 y Ft(c)1323
2759 y FE(^)g Fv(V)1407 2739 y Ft(d)1427 2759 y Fv(\017)1447
2766 y Ft(abcd)916 2892 y FH(64)p eop
%%Page: 65 66
65 65 bop 311 15 a FH(+i)8 b Fv(b)392 22 y FC(2)428 -33
y Fs(\020)p 452 -24 26 2 v 452 15 a Fv(\020)477 -14 y
Ft(\013)502 15 y Fv(\015)530 -5 y Ft(a)551 15 y FE(r)p
Fv(\020)614 22 y Ft(\013)658 15 y FH(+)p 715 -24 V 19
w Fv(\020)740 27 y Ft(\013)765 15 y Fv(\015)793 -5 y
Ft(a)814 15 y FE(r)p Fv(\020)881 -5 y Ft(\013)905 -33
y Fs(\021)941 15 y FE(^)j Fv(V)1025 -5 y Ft(b)1053 15
y FE(^)g Fv(V)1136 -5 y Ft(c)1165 15 y FE(^)g Fv(V)1248
-5 y Ft(d)1269 15 y Fv(\017)1289 22 y Ft(abcd)311 109
y FH(+)d(i)g Fv(\014)407 116 y FC(3)443 61 y Fs(\020)467
109 y FE(N)508 116 y FC(\003\006)560 109 y Fv(F)599 89
y FC(+\003)592 122 y Ft(ab)672 109 y FH(+)p 729 70 49
2 v 19 w FE(N)778 116 y FC(\003\006)830 109 y Fv(F)869
89 y FB(\000)p FC(\003)862 122 y Ft(ab)922 61 y Fs(\021)g(h)975
109 y Fv(F)1014 89 y FC(\006)1060 109 y FE(\000)19 b
FH(i)1140 61 y Fs(\020)1165 109 y Fv(f)1194 89 y FC(\006)1189
122 y Ft(i)p 1230 70 29 2 v 1230 109 a Fv(\025)1258 80
y Ft(iA)1299 109 y Fv(\015)1324 116 y Ft(c)1341 109 y
Fv( )1375 89 y Ft(B)1405 109 y Fv(\017)1425 116 y Ft(AB)994
204 y FH(+)8 b Fv(f)1069 183 y FC(\006)1064 216 y Ft(i)1076
207 y Fm(?)p 1105 164 V 1105 204 a Fv(\025)1133 174 y
Ft(i)1145 163 y Fm(?)1133 216 y Ft(A)1166 204 y Fv(\015)1191
211 y Ft(c)1208 204 y Fv( )1240 211 y Ft(B)1270 204 y
Fv(\017)1290 183 y Ft(AB)1347 156 y Fs(\021)1383 204
y FE(^)j Fv(V)1466 183 y Ft(c)1483 156 y Fs(i)1514 204
y FE(^)g Fv(V)1598 183 y Ft(a)1630 204 y FE(^)g Fv(V)1713
183 y Ft(b)311 311 y FE(\000)375 278 y FH(1)p 363 300
49 2 v 363 345 a(24)425 311 y Fv(\014)453 318 y FC(3)480
263 y Fs(\020)p 505 272 V 48 x FE(N)553 318 y FC(\003\006)605
311 y Fv(F)644 291 y FB(\000)p FC(\003)637 324 y Ft(lm)698
311 y Fv(F)737 291 y FB(\000)p FC(\006)p FB(j)p Ft(lm)862
311 y FE(\000)19 b(N)961 318 y FC(\003\006)1013 311 y
Fv(F)1052 291 y FC(+\003)1045 324 y Ft(lm)1106 311 y
Fv(F)1145 291 y FC(+\006)p FB(j)p Ft(lm)1251 263 y Fs(\021)1284
311 y Fv(\017)1304 318 y Ft(abcd)1373 311 y Fv(V)1412
291 y Ft(a)1444 311 y FE(^)12 b Fv(V)1528 291 y Ft(b)1556
311 y FE(^)f Fv(V)1640 291 y Ft(c)1668 311 y FE(^)g Fv(V)1752
291 y Ft(d)56 415 y FE(L)90 422 y Ft(P)5 b(auli)231 415
y FH(=)50 b Fv(\014)347 422 y FC(5)366 415 y Fv(F)405
394 y FC(\003)439 366 y Fs(\020)464 415 y FE(N)505 422
y FC(\003\006)557 415 y Fv(L)590 394 y FC(\006)p 618
375 34 2 v 618 415 a Fv( )651 385 y Ft(A)680 415 y Fv( )714
394 y Ft(B)744 415 y Fv(\017)764 422 y Ft(AB)840 415
y FH(+)p 897 376 49 2 v 19 w FE(N)945 422 y FC(\003\006)p
997 376 34 2 v 997 415 a Fv(L)1030 385 y FC(\006)p 1058
375 V 1058 415 a Fv( )1091 426 y Ft(A)1120 415 y Fv( )1152
422 y Ft(B)1182 415 y Fv(\017)1202 394 y Ft(AB)1258 366
y Fs(\021)319 509 y FH(+)8 b(i)g Fv(\014)415 516 y FC(6)434
509 y Fv(F)473 489 y FC(\003)508 461 y Fs(\020)p 532
470 49 2 v 532 509 a FE(N)581 516 y FC(\003\006)633 509
y Fv(f)662 489 y FC(\006)657 521 y Ft(i)p 698 470 29
2 v 698 509 a Fv(\025)726 479 y Ft(iA)767 509 y Fv(\015)792
516 y Ft(a)813 509 y Fv( )847 489 y Ft(B)877 509 y Fv(\017)897
516 y Ft(AB)973 509 y FH(+)19 b FE(N)1071 516 y FC(\003\006)p
1123 470 30 2 v 1123 509 a Fv(f)1152 479 y FC(\006)1152
521 y Ft(i)1164 512 y Fm(?)p 1184 470 29 2 v 1184 509
a Fv(\025)1213 479 y Ft(i)1225 468 y Fm(?)1213 521 y
Ft(A)1245 509 y Fv(\015)1270 516 y Ft(a)1291 509 y Fv( )1323
516 y Ft(B)1353 509 y Fv(\017)1373 489 y Ft(AB)1429 461
y Fs(\021)1465 509 y FE(^)11 b Fv(V)1549 489 y Ft(a)319
603 y FH(+)d Fv(\014)393 610 y FC(7)412 603 y Fv(F)451
582 y FC(\003)486 555 y Fs(\020)510 603 y FE(N)27 b(\000)p
636 564 49 2 v 19 w(N)684 555 y Fs(\021)709 630 y FC(\003\006)770
555 y Fs(\020)794 603 y FE(r)836 610 y Ft(i)850 603 y
Fv(f)879 582 y FC(\006)874 615 y Ft(j)p 907 563 29 2
v 907 603 a Fv(\025)935 573 y Ft(iA)976 603 y Fv(\015)1001
610 y Ft(ab)1037 603 y Fv(\025)1065 582 y Ft(j)r(B)1112
603 y Fv(\017)1132 610 y Ft(AB)603 700 y FE(\000)8 b(r)692
707 y Ft(i)704 698 y Fm(?)724 700 y Fv(f)753 679 y FC(\006)748
712 y Ft(j)764 703 y Fm(?)p 784 660 V 784 700 a Fv(\025)813
670 y Ft(i)825 658 y Fm(?)813 712 y Ft(A)845 700 y Fv(\015)870
707 y Ft(ab)906 700 y Fv(\025)934 676 y Ft(j)950 664
y Fm(?)934 712 y Ft(B)971 700 y Fv(\017)991 679 y Ft(AB)1047
652 y Fs(\021)1083 700 y FE(^)j Fv(V)1167 679 y Ft(a)1198
700 y FE(^)h Fv(V)1282 679 y Ft(b)319 793 y FH(+)c Fv(b)386
800 y FC(5)406 793 y Fv(F)445 773 y FC(\003)479 745 y
Fs(\020)504 793 y FE(N)26 b(\000)p 629 754 49 2 v 19
w(N)678 745 y Fs(\021)702 820 y FC(\003\006)763 745 y
Fs(\020)787 793 y Fv(L)820 773 y FC(\006)p 848 754 26
2 v 848 793 a Fv(\020)873 805 y Ft(\013)898 793 y Fv(\015)923
800 y Ft(ab)959 793 y Fv(\020)980 800 y Ft(\014)1004
793 y Fv(C)1043 773 y Ft(\013\014)1108 793 y FE(\000)p
1166 754 34 2 v 19 w Fv(L)1200 764 y FC(\006)p 1227 754
26 2 v 1227 793 a Fv(\020)1252 763 y Ft(\013)1277 793
y Fv(\015)1302 800 y Ft(ab)1338 793 y Fv(\020)1363 773
y Ft(\014)1387 793 y Fv(C)1422 800 y Ft(\013\014)1468
745 y Fs(\021)1504 793 y FE(^)11 b Fv(V)1587 773 y Ft(a)1619
793 y FE(^)g Fv(V)1703 773 y Ft(b)319 890 y FH(+)d Fv(\014)393
897 y FC(8)412 890 y Fv(g)435 897 y Ft(ij)463 888 y Fm(?)492
842 y Fs(\020)p 517 850 29 2 v 48 x Fv(\025)546 860 y
Ft(iA)586 890 y Fv(\015)614 869 y Ft(ab)650 890 y Fv( )682
897 y Ft(A)719 890 y FE(r)p 761 863 25 2 v Fv(z)785 869
y Ft(j)801 857 y Fm(?)841 890 y FH(+)p 898 850 29 2 v
19 w Fv(\025)926 860 y Ft(j)942 848 y Fm(?)926 902 y
Ft(A)963 890 y Fv(\015)988 897 y Ft(ab)1024 890 y Fv( )1058
869 y Ft(A)1086 890 y FE(r)p Fv(z)1153 869 y Ft(i)1166
842 y Fs(\021)1202 890 y FE(^)j Fv(V)1286 869 y Ft(c)1314
890 y FE(^)g Fv(V)1398 869 y Ft(d)1418 890 y Fv(\017)1438
897 y Ft(abcd)319 981 y FH(+)d Fv(b)386 988 y FC(3)422
933 y Fs(\020)p 447 941 26 2 v 48 x Fv(\020)472 993 y
Ft(\013)497 981 y Fv(\015)525 961 y Ft(ab)561 981 y Fv( )593
988 y Ft(A)629 981 y FE(U)665 961 y Ft(\013A)736 981
y FH(+)p 793 941 V 19 w Fv(\020)818 951 y Ft(\013)843
981 y Fv(\015)871 961 y Ft(ab)907 981 y Fv( )941 961
y Ft(A)977 981 y FE(U)1008 988 y Ft(\013A)1060 933 y
Fs(\021)1096 981 y FE(^)j Fv(V)1179 961 y Ft(c)1207 981
y FE(^)h Fv(V)1291 961 y Ft(d)1311 981 y Fv(\017)1331
988 y Ft(abcd)32 1075 y FE(L)66 1082 y Ft(tor)q(sion)231
1075 y FH(=)319 1027 y Fs(\020)344 1075 y Fv(\014)372
1082 y FC(4)391 1075 y Fv(g)414 1082 y Ft(ij)442 1073
y Fm(?)p 471 1035 29 2 v 471 1075 a Fv(\025)499 1045
y Ft(iA)540 1075 y Fv(\015)565 1082 y Ft(b)582 1075 y
Fv(\025)610 1051 y Ft(j)626 1040 y Fm(?)610 1087 y Ft(A)666
1075 y FH(+)20 b Fv(b)745 1082 y FC(4)p 773 1035 26 2
v 773 1075 a Fv(\020)798 1045 y Ft(\013)822 1075 y Fv(\015)847
1082 y Ft(b)865 1075 y Fv(\020)886 1082 y Ft(\013)911
1027 y Fs(\021)944 1075 y Fv(T)973 1082 y Ft(a)1004 1075
y FE(^)12 b Fv(V)1088 1054 y Ft(a)1120 1075 y FE(^)f
Fv(V)1203 1054 y Ft(b)42 1169 y FE(L)76 1176 y FC(4)p
Ft(f)t(er)q(m)231 1169 y FH(=)50 b Fv(\013)350 1176 y
FC(1)386 1121 y Fs(\020)411 1169 y Fv(L)444 1148 y FC(\003)p
471 1129 34 2 v 471 1169 a Fv( )504 1139 y Ft(A)533 1169
y Fv( )567 1148 y Ft(B)597 1169 y Fv(\017)617 1176 y
Ft(AB)693 1169 y FH(+)p 750 1130 V 19 w Fv(L)783 1140
y FC(\003)p 810 1129 V 810 1169 a Fv( )843 1181 y Ft(A)872
1169 y Fv( )904 1176 y Ft(B)934 1169 y Fv(\017)954 1148
y Ft(AB)1010 1121 y Fs(\021)1046 1169 y FE(^)1090 1121
y Fs(\020)1115 1169 y FE(N)1156 1176 y FC(\003\006)1208
1169 y Fv(L)1241 1148 y FC(\006)p 1269 1129 V 1269 1169
a Fv( )1302 1139 y Ft(C)1332 1169 y Fv( )1366 1148 y
Ft(D)1397 1169 y Fv(\017)1417 1176 y Ft(C)r(D)701 1262
y FH(+)p 747 1223 49 2 v 8 w FE(N)795 1269 y FC(\003\006)p
847 1223 34 2 v 847 1262 a Fv(L)881 1233 y FC(\006)p
908 1223 V 908 1262 a Fv( )942 1274 y Ft(C)971 1262 y
Fv( )1003 1269 y Ft(D)1035 1262 y Fv(\017)1055 1242 y
Ft(C)r(D)1114 1214 y Fs(\021)311 1357 y FH(+)8 b Fv(\013)388
1364 y FC(2)424 1309 y Fs(\020)449 1357 y Fv(f)478 1336
y FC(\003)473 1369 y Ft(i)p 513 1317 29 2 v 513 1357
a Fv(\025)542 1327 y Ft(iA)582 1357 y Fv(\015)607 1364
y Ft(a)628 1357 y Fv( )662 1336 y Ft(B)692 1357 y Fv(\017)712
1364 y Ft(AB)788 1357 y FH(+)19 b Fv(f)874 1336 y FC(\003)869
1369 y Ft(i)881 1360 y Fm(?)p 901 1317 V 901 1357 a Fv(\025)930
1327 y Ft(i)942 1315 y Fm(?)930 1369 y Ft(A)962 1357
y Fv(\015)987 1364 y Ft(a)1008 1357 y Fv( )1040 1364
y Ft(B)1070 1357 y Fv(\017)1090 1336 y Ft(AB)1147 1309
y Fs(\021)1182 1357 y FE(^)1227 1309 y Fs(\020)p 1251
1318 49 2 v 1251 1357 a FE(N)1300 1364 y FC(\003\006)1352
1357 y Fv(f)1381 1336 y FC(\006)1376 1369 y Ft(j)p 1417
1317 29 2 v 1417 1357 a Fv(\025)1445 1327 y Ft(j)r(C)1491
1357 y Fv(\015)1516 1364 y Ft(b)1534 1357 y Fv( )1568
1336 y Ft(D)1599 1357 y Fv(\017)1619 1364 y Ft(C)r(D)896
1452 y FH(+)8 b FE(N)983 1459 y FC(\003\006)1035 1452
y Fv(f)1064 1431 y FC(\006)1059 1464 y Ft(j)1075 1454
y Fm(?)p 1095 1412 V 1095 1452 a Fv(\025)1124 1422 y
Ft(j)1140 1410 y Fm(?)1124 1464 y Ft(C)1160 1452 y Fv(\015)1185
1459 y Ft(b)1203 1452 y Fv( )1235 1459 y Ft(D)1266 1452
y Fv(\017)1286 1431 y Ft(C)r(D)1345 1403 y Fs(\021)1390
1452 y FE(^)j Fv(V)1473 1431 y Ft(a)1505 1452 y FE(^)g
Fv(V)1589 1431 y Ft(b)311 1546 y FH(+)d Fv(\013)388 1553
y FC(3)424 1498 y Fs(\020)449 1546 y FE(N)27 b(\000)p
575 1507 49 2 v 19 w(N)623 1498 y Fs(\021)648 1573 y
FC(\003\006)716 1498 y Fs(\020)741 1546 y Fv(f)770 1526
y FC(\003)765 1558 y Ft(i)797 1546 y FE(r)839 1553 y
Ft(k)858 1544 y Fm(?)878 1546 y Fv(f)907 1526 y FC(\006)902
1558 y Ft(j)918 1549 y Fm(?)p 947 1507 29 2 v 947 1546
a Fv(\025)975 1516 y Ft(iA)1015 1546 y Fv(\015)1040 1553
y Ft(c)1058 1546 y Fv( )1092 1526 y Ft(B)p 1130 1507
V 1130 1546 a Fv(\025)1159 1516 y Ft(k)1178 1505 y Fm(?)1159
1558 y Ft(C)1198 1546 y Fv(\015)1223 1553 y Ft(ab)1259
1546 y Fv(\025)1287 1522 y Ft(j)1303 1511 y Fm(?)1287
1558 y Ft(D)1332 1546 y Fv(\017)1352 1553 y Ft(AB)1409
1546 y Fv(\017)1429 1526 y Ft(C)r(D)603 1643 y FE(\000)p
650 1603 30 2 v 8 w Fv(f)680 1613 y FC(\003)680 1655
y Ft(i)692 1646 y Fm(?)712 1643 y FE(r)754 1650 y Ft(k)775
1643 y Fv(f)804 1622 y FC(\006)799 1655 y Ft(j)p 840
1603 29 2 v 840 1643 a Fv(\025)868 1613 y Ft(i)880 1601
y Fm(?)868 1655 y Ft(A)900 1643 y Fv(\015)925 1650 y
Ft(c)943 1643 y Fv( )975 1650 y Ft(B)p 1013 1603 V 1013
1643 a Fv(\025)1042 1613 y Ft(k)q(C)1091 1643 y Fv(\015)1116
1650 y Ft(ab)1152 1643 y Fv(\025)1180 1622 y Ft(j)r(D)1237
1643 y Fv(\017)1257 1622 y Ft(AB)1313 1643 y Fv(\017)1333
1650 y Ft(C)r(D)1392 1595 y Fs(\021)1437 1643 y FE(^)11
b Fv(V)1520 1622 y Ft(a)1552 1643 y FE(^)g Fv(V)1636
1622 y Ft(b)1664 1643 y FE(^)g Fv(V)1747 1622 y Ft(c)311
1737 y FH(+)d Fv(a)383 1744 y FC(1)419 1689 y Fs(\020)444
1737 y FE(N)26 b(\000)p 569 1698 49 2 v 19 w(N)618 1689
y Fs(\021)642 1764 y FC(\003\006)711 1689 y Fs(\020)p
736 1698 30 2 v 48 x Fv(f)765 1708 y FC(\003)765 1750
y Ft(i)777 1740 y Fm(?)797 1737 y Fv(L)830 1717 y FC(\006)p
858 1698 29 2 v 858 1737 a Fv(\025)886 1708 y Ft(i)898
1696 y Fm(?)886 1750 y Ft(A)918 1737 y Fv(\015)943 1744
y Ft(c)961 1737 y Fv( )993 1744 y Ft(B)p 1031 1698 26
2 v 1031 1737 a Fv(\020)1057 1749 y Ft(\013)1081 1737
y Fv(\015)1106 1744 y Ft(ab)1142 1737 y Fv(\020)1163
1744 y Ft(\014)1196 1737 y Fv(\017)1216 1717 y Ft(AB)p
1280 1737 2 33 v 1267 1737 a FH(C)1303 1716 y Ft(\013\014)798
1833 y FE(\000)8 b Fv(f)874 1813 y FC(\003)869 1846 y
Ft(i)p 901 1794 34 2 v 901 1833 a Fv(L)935 1804 y FC(\006)p
962 1794 29 2 v 962 1833 a Fv(\025)991 1804 y Ft(iA)1031
1833 y Fv(\015)1056 1840 y Ft(c)1074 1833 y Fv( )1108
1813 y Ft(B)p 1146 1794 26 2 v 1146 1833 a Fv(\020)1171
1804 y Ft(\013)1196 1833 y Fv(\015)1221 1840 y Ft(ab)1257
1833 y Fv(\020)1282 1813 y Ft(\014)1314 1833 y Fv(\017)1334
1840 y Ft(AB)p 1399 1833 2 33 v 1386 1833 a FH(C)1421
1840 y Ft(\013\014)1467 1785 y Fs(\021)1511 1833 y FE(^)k
Fv(V)1595 1813 y Ft(a)1627 1833 y FE(^)f Fv(V)1710 1813
y Ft(b)1738 1833 y FE(^)h Fv(V)1822 1813 y Ft(c)311 1927
y FH(+)c Fv(a)383 1934 y FC(2)419 1879 y Fs(\020)p 444
1888 34 2 v 48 x Fv( )477 1898 y Ft(A)506 1927 y Fv( )540
1907 y Ft(B)p 578 1888 26 2 v 578 1927 a Fv(\020)603
1898 y Ft(\013)628 1927 y Fv(\015)653 1934 y Ft(ab)689
1927 y Fv(\020)714 1907 y Ft(\014)737 1927 y Fv(\017)757
1934 y Ft(AB)p 822 1927 2 33 v 809 1927 a FH(C)844 1934
y Ft(\013\014)910 1927 y FH(+)p 967 1888 34 2 v 19 w
Fv( )1001 1939 y Ft(A)1029 1927 y Fv( )1061 1934 y Ft(B)p
1100 1888 26 2 v 1100 1927 a Fv(\020)1125 1939 y Ft(\013)1150
1927 y Fv(\015)1175 1934 y Ft(ab)1211 1927 y Fv(\020)1232
1934 y Ft(\014)1264 1927 y Fv(\017)1284 1907 y Ft(AB)p
1349 1927 2 33 v 1336 1927 a FH(C)1371 1906 y Ft(\013\014)1417
1879 y Fs(\021)1461 1927 y FE(^)k Fv(V)1545 1907 y Ft(a)1577
1927 y FE(^)f Fv(V)1660 1907 y Ft(b)311 2021 y FH(+)365
1973 y Fs(\020)390 2021 y Fv(\013)421 2028 y FC(4)441
2021 y Fv(g)464 2028 y Ft(ij)492 2019 y Fm(?)p 521 1982
29 2 v 521 2021 a Fv(\025)549 1991 y Ft(iA)590 2021 y
Fv(\015)615 2028 y Ft(b)632 2021 y Fv(\025)660 1998 y
Ft(j)676 1986 y Fm(?)660 2033 y Ft(B)716 2021 y FH(+)19
b Fv(a)799 2028 y FC(3)827 2021 y Fv(\016)851 2001 y
Ft(A)849 2034 y(B)p 879 1982 26 2 v 879 2021 a Fv(\020)904
1991 y Ft(\013)929 2021 y Fv(\015)954 2028 y Ft(b)971
2021 y Fv(\020)992 2028 y Ft(\013)1017 1973 y Fs(\021)p
1059 1982 34 2 v 1059 2021 a Fv( )1092 2033 y Ft(A)1121
2021 y Fv(\015)1146 2028 y Ft(a)1167 2021 y Fv( )1201
2001 y Ft(B)1242 2021 y FE(^)11 b Fv(V)1325 2001 y Ft(a)1357
2021 y FE(^)h Fv(V)1441 2001 y Ft(b)311 2115 y FH(+)c
Fv(\013)388 2122 y FC(5)416 2067 y Fs(\020)441 2115 y
Fv(C)476 2122 y Ft(ij)r(k)p 525 2076 29 2 v 525 2115
a Fv(\025)554 2085 y Ft(iA)594 2115 y Fv(\015)622 2095
y Ft(a)643 2115 y Fv( )677 2095 y Ft(B)p 715 2076 V 715
2115 a Fv(\025)744 2085 y Ft(j)r(C)789 2115 y Fv(\025)817
2095 y Ft(k)q(D)877 2115 y Fv(\017)897 2122 y Ft(AC)953
2115 y Fv(\017)973 2122 y Ft(B)r(D)506 2210 y FE(\000)g
Fv(C)588 2217 y Ft(i)600 2208 y Fm(?)618 2217 y Ft(j)634
2208 y Fm(?)652 2217 y Ft(k)671 2208 y Fm(?)p 691 2170
V 691 2210 a Fv(\025)720 2180 y Ft(i)732 2168 y Fm(?)720
2222 y Ft(A)752 2210 y Fv(\015)780 2189 y Ft(a)801 2210
y Fv( )833 2217 y Ft(B)p 871 2170 V 871 2210 a Fv(\025)899
2180 y Ft(i)911 2168 y Fm(?)899 2222 y Ft(C)931 2210
y Fv(\025)959 2189 y Ft(k)978 2177 y Fm(?)959 2222 y
Ft(D)999 2210 y Fv(\017)1019 2189 y Ft(AC)1075 2210 y
Fv(\017)1095 2189 y Ft(B)r(D)1155 2162 y Fs(\021)1199
2210 y FE(^)j Fv(V)1283 2189 y Ft(b)1311 2210 y FE(^)g
Fv(V)1394 2189 y Ft(c)1423 2210 y FE(^)g Fv(V)1506 2189
y Ft(d)1535 2210 y Fv(\017)1555 2217 y Ft(abcd)311 2326
y FH(+)366 2292 y(1)p 354 2314 49 2 v 354 2360 a(72)407
2253 y Fs(")440 2326 y Fv(\015)465 2333 y FC(1)502 2326
y FH(\()o Fv(R)557 2333 y Ft(ij)585 2324 y Fm(?)604 2333
y Ft(lk)634 2324 y Fm(?)673 2326 y FH(+)g Fv(p)d(g)777
2333 y Ft(ik)808 2324 y Fm(?)838 2326 y Fv(g)861 2333
y Ft(lj)888 2324 y Fm(?)928 2326 y FH(+)j Fv(q)f(g)1032
2333 y Ft(ij)1060 2324 y Fm(?)1089 2326 y Fv(g)1112 2333
y Ft(lk)1142 2324 y Fm(?)1162 2326 y FH(\))p 1190 2286
29 2 v 9 w Fv(\025)1218 2296 y Ft(iA)1259 2326 y Fv(\025)1287
2305 y Ft(lB)p 1328 2286 V 1328 2326 a Fv(\025)1357 2296
y Ft(j)1373 2285 y Fm(?)1357 2338 y Ft(A)1393 2326 y
Fv(\025)1421 2305 y Ft(k)1440 2294 y Fm(?)1421 2338 y
Ft(B)311 2445 y FH(+)e Fv(\015)382 2452 y FC(2)410 2397
y Fs(\020)435 2445 y FE(r)477 2452 y Ft(m)518 2445 y
Fv(C)553 2452 y Ft(j)r(k)q(l)p 601 2406 V 601 2445 a
Fv(\025)630 2415 y Ft(j)r(A)675 2445 y Fv(\025)703 2425
y Ft(mB)p 765 2406 V 765 2445 a Fv(\025)793 2415 y Ft(k)q(C)842
2445 y Fv(\025)870 2425 y Ft(lD)913 2445 y Fv(\017)933
2452 y Ft(AC)989 2445 y Fv(\017)1009 2452 y Ft(B)r(D)1080
2445 y FE(\000)j Fv(h:c:)1207 2397 y Fs(\021)311 2540
y FH(+)d Fv(\015)382 2547 y FC(3)419 2491 y Fs(\020)443
2540 y FE(N)27 b(\000)p 569 2501 49 2 v 19 w(N)617 2491
y Fs(\021)642 2567 y FC(\003\006)702 2491 y Fs(\020)727
2540 y Fv(C)762 2547 y Ft(ij)r(k)820 2540 y Fv(C)855
2547 y Ft(lmn)920 2540 y Fv(g)945 2519 y Ft(k)p 964 2500
17 2 v 1 w(r)992 2540 y Fv(g)1017 2519 y Ft(n)p 1038
2500 V(s)1057 2540 y Fv(f)1086 2519 y FC(\003)p 1081
2533 19 2 v 1081 2552 a Ft(r)1121 2540 y Fv(f)1150 2519
y FC(\006)p 1145 2533 V 1145 2552 a Ft(s)p 1186 2500
29 2 v 1186 2540 a Fv(\025)1215 2510 y Ft(iA)1255 2540
y Fv(\015)1280 2547 y Ft(lm)1325 2540 y Fv(\025)1353
2519 y Ft(j)r(B)p 1400 2500 V 1400 2540 a Fv(\025)1428
2510 y Ft(k)q(C)1477 2540 y Fv(\015)1505 2519 y Ft(lm)1549
2540 y Fv(\025)1577 2519 y Ft(lD)1629 2540 y Fv(\017)1649
2547 y Ft(AB)1706 2540 y Fv(\017)1726 2547 y Ft(C)r(D)1091
2633 y FH(+)p Fv(h:c:)1206 2585 y Fs(\021)311 2727 y
FH(+)p Fv(\015)374 2734 y FC(4)410 2727 y Fv(g)433 2734
y Ft(ij)461 2725 y Fm(?)p 490 2687 26 2 v 490 2727 a
Fv(\020)515 2697 y Ft(\013)540 2727 y Fv(\015)565 2734
y Ft(a)586 2727 y Fv(\020)607 2734 y Ft(\013)p 640 2687
29 2 v 640 2727 a Fv(\025)669 2697 y Ft(iA)709 2727 y
Fv(\015)737 2706 y Ft(a)758 2727 y Fv(\025)786 2703 y
Ft(j)802 2692 y Fm(?)786 2739 y Ft(A)916 2892 y FH(65)p
eop
%%Page: 66 67
66 66 bop 311 18 a FH(+)8 b Fv(\015)382 25 y FC(5)410
18 y FE(R)452 -2 y Ft(\013)475 31 y(\014)r(ts)536 18
y FE(U)572 -2 y Ft(t)567 31 y(A\015)624 18 y FE(U)660
-2 y Ft(s)655 31 y(B)r(\016)703 18 y Fv(\017)723 -2 y
Ft(AB)787 18 y Fv(C)826 -2 y Ft(\016)q(\021)p 864 -21
26 2 v 864 18 a Fv(\020)889 30 y Ft(\013)922 18 y Fv(\020)943
25 y Ft(\021)p 972 -21 V 972 18 a Fv(\020)997 -11 y Ft(\014)1029
18 y Fv(\020)1054 -2 y Ft(\015)311 106 y FH(+)p Fv(\015)374
113 y FC(6)402 58 y Fs(\020)427 106 y FE(N)26 b(\000)p
552 67 49 2 v 19 w(N)601 58 y Fs(\021)625 133 y FC(\003\006)686
58 y Fs(\020)711 106 y Fv(L)744 86 y FC(\003)770 106
y FE(r)812 113 y Ft(i)826 106 y Fv(f)855 86 y FC(\006)850
119 y Ft(j)p 883 67 26 2 v 883 106 a Fv(\020)908 118
y Ft(\013)933 106 y Fv(\015)958 113 y Ft(ab)994 106 y
Fv(\020)1015 113 y Ft(\014)p 1047 67 29 2 v 1047 106
a Fv(\025)1075 77 y Ft(iA)1116 106 y Fv(\015)1144 86
y Ft(ab)1180 106 y Fv(\025)1208 86 y Ft(j)r(B)1271 106
y Fv(\017)1291 113 y Ft(AB)p 1365 106 2 33 v 1352 106
a FH(C)1387 85 y Ft(\013\014)1444 106 y FH(+)11 b Fv(h:c:)1570
58 y Fs(\021)311 200 y FH(+)p Fv(\015)374 207 y FC(7)402
152 y Fs(\020)427 200 y FE(N)26 b(\000)p 552 161 49 2
v 19 w(N)601 152 y Fs(\021)625 227 y FC(\003\006)686
152 y Fs(\020)711 200 y Fv(L)744 179 y FC(\003)779 200
y Fv(L)812 179 y FC(\006)p 839 160 26 2 v 839 200 a Fv(\020)864
211 y Ft(\013)889 200 y Fv(\015)914 207 y Ft(ab)950 200
y Fv(\020)971 207 y Ft(\014)p 1004 160 V 1004 200 a Fv(\020)1029
211 y Ft(\015)1051 200 y Fv(\015)1079 179 y Ft(ab)1115
200 y Fv(\020)1136 207 y Ft(\016)p 1172 200 2 33 v 1159
200 a FH(C)1194 179 y Ft(\013\014)p 1257 200 V 1244 200
a FH(C)1279 179 y Ft(\015)r(\016)896 318 y FH(+)p Fv(h:c:)1011
270 y Fs(\021)1043 245 y(#)1067 318 y Fv(V)1107 297 y
Ft(a)1139 318 y FE(^)11 b Fv(V)1222 297 y Ft(b)1250 318
y FE(^)h Fv(V)1334 297 y Ft(c)1362 318 y FE(^)g Fv(V)1446
297 y Ft(d)1474 318 y Fv(\017)1494 325 y Ft(abcd)18 437
y FE(L)52 444 y Ft(g)q(aug)q(ing)231 437 y FH(=)50 b
FE(\000)8 b FH(i)g Fv(g)i(\016)443 444 y FC(1)471 389
y Fs(\020)496 437 y Fv(S)526 444 y Ft(AB)p 582 397 34
2 v 582 437 a Fv( )616 407 y Ft(A)645 437 y Fv(\015)670
444 y Ft(ab)706 437 y Fv( )740 416 y Ft(B)781 437 y FH(+)h
Fv(h:c:)907 389 y Fs(\021)939 437 y Fv(V)978 416 y Ft(a)1010
437 y FE(^)g Fv(V)1094 416 y Ft(b)311 531 y FH(+i)d Fv(g)i(\016)426
538 y FC(2)454 531 y Fv(g)477 538 y Ft(ij)505 529 y Fm(?)533
483 y Fs(\020)558 531 y Fv(W)611 511 y Ft(iAB)p 680 492
29 2 v 680 531 a Fv(\025)708 502 y Ft(j)724 490 y Fm(?)708
544 y Ft(A)745 531 y Fv(\015)773 511 y Ft(a)793 531 y
Fv( )825 538 y Ft(B)866 531 y FH(+)h Fv(h:c:)992 483
y Fs(\021)1028 531 y FE(^)g Fv(V)1111 511 y Ft(b)1139
531 y FE(^)h Fv(V)1223 511 y Ft(c)1251 531 y FE(^)g Fv(V)1335
511 y Ft(d)1363 531 y Fv(\017)1383 538 y Ft(abcd)311
623 y FH(+i)c Fv(g)i(\016)426 630 y FC(3)454 575 y Fs(\020)478
623 y Fv(N)522 602 y Ft(A)517 635 y(\013)p 559 583 26
2 v 559 623 a Fv(\020)584 593 y Ft(\013)609 623 y Fv(\015)637
602 y Ft(a)658 623 y Fv( )690 630 y Ft(A)729 623 y FH(+)h
Fv(h:c:)855 575 y Fs(\021)890 623 y FE(^)h Fv(V)974 602
y Ft(b)1002 623 y FE(^)f Fv(V)1086 602 y Ft(c)1114 623
y FE(^)g Fv(V)1198 602 y Ft(d)1226 623 y Fv(\017)1246
630 y Ft(abcd)311 714 y FH(+)p Fv(g)374 666 y Fs(h)393
714 y Fv(\016)415 721 y FC(4)435 714 y FE(r)477 721 y
Ft(u)499 714 y Fv(N)543 694 y Ft(\013)538 726 y(A)576
714 y FE(U)612 694 y Ft(u)607 726 y(B)r(\014)659 714
y Fv(\017)679 694 y Ft(AB)p 744 714 2 33 v 731 714 a
FH(C)766 693 y Ft(\014)r(\015)p 810 675 26 2 v 810 714
a Fv(\020)835 726 y Ft(\013)860 714 y Fv(\020)881 721
y Ft(\015)914 714 y FH(+)g Fv(\016)985 721 y FC(5)1004
714 y FE(r)1046 721 y Ft(i)1060 714 y Fv(N)1104 694 y
Ft(\013)1099 726 y(A)p 1129 675 V 1129 714 a Fv(\020)1154
726 y Ft(\013)1179 714 y Fv(\025)1207 694 y Ft(iA)311
808 y FH(+)p Fv(\016)371 815 y FC(6)398 808 y Fv(g)421
815 y Ft(i)p 433 796 14 2 v 1 x(|)449 808 y FE(r)491
815 y Ft(k)512 808 y Fv(W)p 565 765 16 2 v 565 784 a
Ft(|)558 820 y(AB)p 615 768 29 2 v 615 808 a Fv(\025)643
778 y Ft(iA)684 808 y Fv(\025)712 787 y Ft(k)q(B)773
808 y FH(+)19 b Fv(h:c:)907 760 y Fs(i)926 808 y Fv(V)965
787 y Ft(a)997 808 y FE(^)11 b Fv(V)1080 787 y Ft(b)1109
808 y FE(^)g Fv(V)1192 787 y Ft(c)1221 808 y FE(^)g Fv(V)1304
787 y Ft(d)1324 808 y Fv(\017)1344 815 y Ft(abcd)311
893 y FH(+)p Fv(\016)371 900 y FC(7)398 893 y Fv(g)423
873 y FC(2)451 893 y FH(V)488 900 y Ft(potential)638
893 y Fv(V)677 873 y Ft(a)709 893 y FE(^)h Fv(V)793 873
y Ft(b)821 893 y FE(^)f Fv(V)905 873 y Ft(c)933 893 y
FE(^)g Fv(V)1017 873 y Ft(d)1045 893 y Fv(\017)1065 900
y Ft(abcd)1775 893 y FH(\(B.3\))-5 996 y(where:)401 1099
y(V)438 1106 y Ft(potential)629 1099 y FH(=)708 1051
y Fs(\020)733 1099 y Fv(g)756 1106 y Ft(ij)784 1097 y
Fm(?)813 1099 y Fv(k)840 1078 y Ft(i)838 1111 y FC(\003)873
1099 y Fv(k)900 1075 y Ft(j)916 1063 y Fm(?)898 1111
y FC(\006)956 1099 y FH(+)19 b(4)8 b Fv(h)1073 1106 y
Ft(uv)1115 1099 y Fv(k)1142 1078 y Ft(u)1140 1111 y FC(\003)1175
1099 y Fv(k)1202 1078 y Ft(v)1200 1111 y FC(\006)1228
1051 y Fs(\021)p 1261 1060 34 2 v 1261 1099 a Fv(L)1294
1070 y FC(\003)1329 1099 y Fv(L)1362 1078 y FC(\006)708
1192 y FH(+)g Fv(g)779 1172 y Ft(ij)807 1160 y Fm(?)836
1192 y Fv(f)865 1172 y FC(\003)860 1204 y Ft(i)900 1192
y Fv(f)929 1172 y FC(\006)924 1204 y Ft(j)940 1195 y
Fm(?)969 1192 y FE(P)1008 1172 y Ft(x)1004 1204 y FC(\003)1039
1192 y FE(P)1078 1172 y Ft(x)1074 1204 y FC(\006)1120
1192 y FE(\000)19 b FH(3)p 1210 1153 V 8 w Fv(L)1244
1163 y FC(\003)1279 1192 y Fv(L)1312 1172 y FC(\006)1348
1192 y FE(P)1387 1172 y Ft(x)1383 1204 y FC(\003)1417
1192 y FE(P)1456 1172 y Ft(x)1452 1204 y FC(\006)1775
1192 y FH(\(B.4\))-5 1295 y(W)l(e)f(note)h(that)f(the)g(kinetic)f
(terms)g(of)h(the)g(Lagrangian)j(ha)o(v)o(e)c(b)q(een)h(written)g(in)g
(\014rst{order)h(form)-5 1355 y(to)j(a)o(v)o(oid)f(the)g(Ho)q(dge{op)q
(erator)i(whic)o(h)e(w)o(ould)g(destro)o(y)h(the)f(indep)q(endence)f
(of)i(the)f(v)m(ariational)-5 1415 y(equations)j(from)e(the)h
(particular)f(h)o(yp)q(ersurface)h(of)h(in)o(tegration.)41
b(Sp)q(eci\014cally)22 b(one)h(in)o(tro)q(duces)-5 1482
y(auxiliary)18 b(0{forms)h(namely)e Fv(F)598 1461 y FB(\006)p
FC(\003)591 1494 y Ft(ab)651 1482 y FH(,)i Fv(Z)721 1464
y Ft(i)717 1494 y(a)746 1482 y Fv(;)p 776 1443 37 2 v
16 w(Z)813 1452 y Ft(i)825 1441 y Fm(?)813 1494 y Ft(a)845
1482 y FH(,)g FE(U)914 1464 y Ft(A\013)909 1494 y(a)984
1482 y FH(whose)h(v)m(ariational)f(equations)g(iden)o(tify)e(them)-5
1563 y(with)120 1547 y Fs(e)109 1563 y Fv(F)148 1542
y FB(\006)p FC(\003)141 1575 y Ft(ab)201 1563 y FH(,)244
1547 y Fs(e)233 1563 y Fv(Z)270 1545 y Ft(i)266 1575
y(a)296 1563 y Fv(;)333 1538 y Fs(e)p 326 1524 V 326
1563 a Fv(Z)363 1522 y Ft(i)375 1510 y Fm(?)363 1575
y Ft(a)395 1563 y FH(,)438 1547 y Fs(e)428 1563 y FE(U)464
1545 y Ft(A\013)459 1575 y(a)533 1563 y FH(de\014ned)h(in)g(App)q
(endix)g(A.)g(Of)g(course)g(also)h(the)g(spin)f(connection)g
Fv(!)1849 1545 y Ft(ab)-5 1623 y FH(has)k(to)g(b)q(e)f(treated)g(as)h
(an)g(indep)q(enden)o(t)e(\014eld:)31 b(indeed)20 b(the)h(term)f
FE(L)1354 1639 y FH(torsion)1524 1623 y(app)q(earing)i(in)f(the)-5
1683 y(Lagrangian)26 b(has)f(b)q(een)f(c)o(hosen)g(in)g(suc)o(h)g(a)g
(w)o(a)o(y)g(that)g(the)g(equation)g(of)g(motion)f(of)i
Fv(!)1722 1665 y Ft(ab)1782 1683 y FH(giv)o(es)-5 1744
y Fv(T)31 1725 y Ft(a)65 1744 y FH(=)14 b(0.)68 1804
y(The)19 b(analysis)f(of)h(the)f(v)m(ariational)h(equations)g(for)f
(the)g(other)h Fv(p)p FH({forms)f(con)o(taining)h(at)f(least)h(a)-5
1864 y(fermionic)11 b(vielb)q(ein)g Fv( )417 1846 y Ft(A)453
1864 y FH(\()p Fv( )504 1871 y Ft(A)532 1864 y FH(\))i(then)g(\014xes)g
(completely)d(all)i(the)h(co)q(e\016cien)o(ts,)f(except)g(the)g(co)q
(e\016cien)o(ts)-5 1924 y(of)19 b(terms)d(that)j(are)f(prop)q(ortional)
h(to)g Fv(V)764 1906 y Ft(a)785 1924 y Fv(V)824 1906
y Ft(b)841 1924 y Fv(V)880 1906 y Ft(c)898 1924 y Fv(V)937
1906 y Ft(d)957 1924 y Fv(\017)977 1931 y Ft(abcd)1046
1924 y FH(,)f(whic)o(h,)g(after)g(v)m(ariation,)g(do)h(not)f(con)o
(tain)-5 1984 y(an)o(y)e Fv( )121 1966 y Ft(A)158 1984
y FH(\()p Fv( )209 1991 y Ft(A)237 1984 y FH(\))g(and)h(therefore)f
(app)q(ear)h(in)f(the)g(space{time)e(equations)j(of)f(motion.)-5
2044 y(These)g(undetermined)e(co)q(e\016cien)o(ts,)g(ho)o(w)o(ev)o(er,)
g(can)i(b)q(e)g(retriev)o(ed)e(b)o(y)h(comparing)g(the)h(space{time)-5
2105 y(equations)h(of)f(motion)f(for)i(the)f(0{form)f(fermion)g
(\014elds)h Fv(\025)1087 2087 y Ft(iA)1136 2105 y Fv(;)g(\025)1194
2087 y Ft(i)1206 2075 y Fm(?)1225 2087 y Ft(A)1261 2105
y Fv(;)h(\020)1317 2087 y Ft(\013)1350 2105 y Fv(;)f(\020)1401
2112 y Ft(\013)1442 2105 y FH(as)h(obtained)f(from)f(the)-5
2165 y(Bianc)o(hi)c(iden)o(tities)g(with)h(those)h(obtained)f(from)g
(the)g(Lagrangian.)22 b(In)12 b(this)g(w)o(a)o(y)g(all)g(the)g(co)q
(e\016cien)o(ts)-5 2225 y(ha)o(v)o(e)k(b)q(een)g(\014xed.)21
b(The)16 b(result)g(is:)97 2338 y Fv(\014)125 2345 y
FC(1)166 2338 y FH(=)231 2304 y(2)p 231 2326 25 2 v 231
2372 a(3)269 2338 y(;)g Fv(\014)327 2345 y FC(2)368 2338
y FH(=)22 b FE(\000)480 2304 y FH(1)p 480 2326 V 480
2372 a(3)518 2338 y(;)16 b Fv(\014)576 2345 y FC(3)618
2338 y FH(=)22 b(4)8 b(i)g(;)16 b Fv(\014)790 2345 y
FC(4)832 2338 y FH(=)22 b FE(\000)8 b FH(1)g(;)17 b Fv(\014)1030
2345 y FC(5)1071 2338 y FH(=)22 b(4)8 b(;)17 b Fv(\014)1222
2345 y FC(6)1263 2338 y FH(=)23 b FE(\000)8 b FH(4)g(;)16
b Fv(\014)1461 2345 y FC(7)1503 2338 y FH(=)1568 2304
y(1)p 1568 2326 V 1568 2372 a(2)1606 2338 y(;)g Fv(\014)1664
2345 y FC(8)1705 2338 y FH(=)22 b FE(\000)8 b FH(1)g(;)97
2454 y Fv(b)118 2461 y FC(1)159 2454 y FH(=)22 b FE(\000)271
2420 y FH(4)p 271 2443 V 271 2488 a(3)301 2454 y Fv(\025)8
b FH(;)17 b Fv(b)389 2461 y FC(2)430 2454 y FH(=)495
2420 y(2)p 495 2443 V 495 2488 a(3)525 2454 y Fv(\025)8
b FH(;)17 b Fv(b)613 2461 y FC(3)654 2454 y FH(=)22 b(2)p
Fv(\025)8 b FH(;)17 b Fv(b)826 2461 y FC(4)868 2454 y
FH(=)22 b FE(\000)8 b FH(2)p Fv(\025)g FH(;)17 b Fv(b)1087
2461 y FC(5)1129 2454 y FH(=)22 b Fv(\025)8 b FH(;)97
2572 y Fv(\013)128 2579 y FC(1)170 2572 y FH(=)22 b FE(\000)8
b FH(2)g(;)16 b Fv(\013)370 2579 y FC(2)412 2572 y FH(=)22
b(2)8 b(;)17 b Fv(\013)566 2579 y FC(3)608 2572 y FH(=)679
2538 y(i)p 673 2560 V 673 2606 a(2)711 2572 y(;)f Fv(\013)772
2579 y FC(4)814 2572 y FH(=)22 b FE(\000)8 b FH(2)g(i)g(;)17
b Fv(\013)1037 2579 y FC(5)1079 2572 y FH(=)22 b FE(\000)1191
2538 y FH(1)p 1191 2560 V 1191 2606 a(9)1228 2572 y(;)97
2657 y Fv(a)123 2664 y FC(1)164 2657 y FH(=)g FE(\000)8
b FH(i)p Fv(\025)g FH(;)17 b Fv(a)378 2664 y FC(2)419
2657 y FH(=)22 b FE(\000)8 b FH(i)p Fv(\025)g FH(;)g
Fv(a)624 2664 y FC(3)666 2657 y FH(=)22 b FE(\000)8 b
FH(4)g(i)p Fv(\025)g FH(;)97 2750 y Fv(\015)122 2757
y FC(1)164 2750 y FH(=)22 b(3)8 b(;)17 b Fv(\015)312
2757 y FC(2)354 2750 y FH(=)22 b FE(\000)8 b FH(i)g(;)16
b Fv(\015)538 2757 y FC(3)580 2750 y FH(=)651 2716 y(3i)p
645 2738 49 2 v 645 2784 a(16)707 2750 y(;)g Fv(\015)762
2757 y FC(4)805 2750 y FH(=)22 b FE(\000)8 b FH(3)g Fv(\025)g
FH(;)17 b Fv(\015)1036 2757 y FC(5)1078 2750 y FH(=)23
b FE(\000)8 b FH(6)p Fv(\025)g(p)23 b FH(=)f(1)8 b(;)17
b Fv(q)24 b FH(=)e FE(\000)1574 2716 y FH(2)p 1574 2738
25 2 v 1574 2784 a(3)1612 2750 y(;)916 2892 y(66)p eop
%%Page: 67 68
67 67 bop 97 31 a Fv(\015)122 38 y FC(6)164 31 y FH(=)22
b FE(\000)276 -2 y FH(3)p 276 20 25 2 v 276 66 a(4)305
31 y(i)8 b Fv(\025)g FH(;)17 b Fv(\015)419 38 y FC(7)461
31 y FH(=)22 b FE(\000)573 -2 y FH(3)p 573 20 V 573 66
a(4)603 31 y(i)8 b Fv(\025)653 11 y FC(2)681 31 y FH(;)97
148 y Fv(\016)119 155 y FC(1)160 148 y FH(=)22 b(4)8
b(;)17 b Fv(\016)305 155 y FC(2)346 148 y FH(=)412 114
y(2)p 412 136 V 412 182 a(3)449 148 y(;)f Fv(\016)501
155 y FC(3)543 148 y FH(=)22 b FE(\000)655 114 y FH(4)p
655 136 V 655 182 a(3)693 148 y Fv(\025)8 b FH(;)16 b
Fv(\016)781 155 y FC(4)823 148 y FH(=)22 b FE(\000)947
114 y FH(1)p 935 136 49 2 v 935 182 a(12)997 148 y Fv(\025)8
b FH(;)17 b Fv(\016)1086 155 y FC(5)1127 148 y FH(=)23
b FE(\000)1240 114 y FH(1)p 1240 136 25 2 v 1240 182
a(3)1277 148 y Fv(\025)8 b FH(;)17 b Fv(\016)1366 155
y FC(6)1408 148 y FH(=)1485 114 y(1)p 1473 136 49 2 v
1473 182 a(18)1535 148 y(;)f Fv(\016)1587 155 y FC(7)1628
148 y FH(=)22 b FE(\000)1740 114 y FH(1)p 1740 136 25
2 v 1740 182 a(6)1775 148 y(\(B.5\))12 271 y(In)17 b(order)g(to)g
(obtain)h(the)f(space{time)e(Lagrangian)k(the)e(last)g(step)g(to)g(p)q
(erform)f(is)h(the)g(restriction)-5 331 y(of)23 b(the)f(4{form)g
(Lagrangian)j(from)d(sup)q(erspace)h(to)f(space{time.)39
b(Namely)20 b(w)o(e)i(restrict)f(all)h(the)-5 391 y(terms)c(to)j(the)e
Fv(\022)i FH(=)e(0)8 b Fv(;)17 b(d\022)k FH(=)f(0)g(h)o(yp)q(ersurface)
f FE(M)968 373 y FC(4)988 391 y FH(.)32 b(In)19 b(practice)g(one)h
(\014rst)g(go)q(es)g(to)g(the)g(second)-5 451 y(order)d(formalism)d(b)o
(y)i(iden)o(tifying)f(the)h(auxiliary)g(0{form)g(\014elds)h(as)g
(explained)f(b)q(efore.)22 b(Then)17 b(one)-5 512 y(expands)23
b(all)f(the)g(forms)f(along)i(the)f Fv(dx)773 493 y Ft(\026)819
512 y FH(di\013eren)o(tials)f(and)i(restricts)f(the)g(sup)q(er\014elds)
g(to)h(their)-5 572 y(lo)o(w)o(est)16 b(\()p Fv(\022)f
FH(=)f(0\))i(comp)q(onen)o(t.)k(Finally)15 b(the)h(co)q(e\016cien)o(ts)
f(of:)511 704 y Fv(dx)564 684 y Ft(\026)598 704 y FE(^)d
Fv(dx)696 684 y Ft(\027)728 704 y FE(^)g Fv(dx)826 684
y Ft(\032)857 704 y FE(^)f Fv(dx)954 684 y Ft(\033)1000
704 y FH(=)1065 671 y Fv(\017)1085 652 y Ft(\026\027)r(\032\033)p
1065 693 102 2 v 1083 708 a FE(p)p 1124 708 26 2 v 1124
738 a Fv(g)1180 656 y Fs(\020)1205 671 y FE(p)p 1247
671 V 33 x Fv(g)r(d)1297 684 y FC(4)1317 704 y Fv(x)1345
656 y Fs(\021)1775 704 y FH(\(B.6\))-5 844 y(giv)o(e)j(the)g
(Lagrangian)j(densit)o(y)c(written)i(in)f(c)o(hapter)g(8.)21
b(The)14 b(o)o(v)o(erall)g(normalisation)f(of)i(the)g(space{)-5
904 y(time)f(action)j(has)g(b)q(een)f(c)o(hosen)g(suc)o(h)g(as)h(to)f
(b)q(e)h(the)f(standard)h(one)g(for)f(the)g(Einstein)g(term.)-5
1071 y Fw(App)r(endix)26 b(C:)h(Sup)r(ergra)n(vit)n(y)f(theory)g(on)h
Fd(S)t(T)10 b Fc([2)p Fd(;)i(n)p Fc(])k Fb(\012)g Fd(H)6
b(Q)p Fc([)p Fd(m)p Fc(])-5 1180 y FH(In)23 b(this)f(app)q(endix,)i(as)
f(an)g(illustration)f(of)g(the)h(general)f(metho)q(d)g(and)h(also)g
(for)g(its)f(in)o(terest)f(in)-5 1240 y(applications)d(to)g(tree)e(lev)
o(el)g(e\013ectiv)o(e)f(lagrangians)k(of)f(heterotic)e(string)i(theory)
l(,)f(w)o(e)g(consider)g(the)-5 1300 y(sp)q(ecialization)e(of)i(our)f
(form)o(ulae)f(to)h(the)g(case)g(where)g(the)f(scalar)i(manifold)d(of)j
(N=2)f(sup)q(ergra)o(vit)o(y)-5 1361 y(is)d(c)o(hosen)f(as)h(in)f(eq.)g
(1.1)p  (#equation.1.1) [[162 440 177 452] [1 1 1 [3 3]] [0 0 1]] pdfm 
(.)20 b(This)13 b(c)o(hoice)e(is)i(b)o(y)f(no)h(means)e(new)i(in)f(the)
g(literature,)g(but)h(the)f(in)o(teresting)-5 1421 y(p)q(oin)o(t)h(is)f
(to)h(utilize)d(the)i(symplectic)e(gauge)j(where)f(the)g(holomorphic)f
(prep)q(oten)o(tial)h Fv(F)7 b FH(\()p Fv(X)t FH(\))12
b(do)q(es)i(not)-5 1481 y(exist.)19 b(This)11 b(is)h(the)f(gauge)h(c)o
(hosen)f(b)o(y)g(string)g(theory)g(and)h(also)g(that)g(where)f(partial)
g(sup)q(ersymmetry)-5 1541 y(breaking)16 b(can)h(b)q(e)f(obtained.)-5
1686 y Fk(The)29 b Fj(S)t(T)15 b Fi([2)p Fh(;)10 b(n)p
Fi(])29 b Fk(sp)r(ecial)g(manifolds)g(and)g(the)g(Calabi)g(Visen)n
(tini)h(co)r(ordi-)-5 1760 y(nates)-5 1853 y FH(When)c(w)o(e)g(studied)
g(the)g(symplectic)c(em)o(b)q(eddings)j(of)h(the)g FE(S)t(T)13
b FH([)p Fv(m;)8 b(n)p FH(])25 b(manifolds,)i(de\014ned)f(b)o(y)-5
1913 y(eq.)e(3.19)p
 (#equation.3.19) [[91 308 112 320] [1 1 1 [3 3]] [0 0 1]] pdfm (,)i(a)
f(study)f(that)h(lead)f(us)h(to)g(the)f(general)g(form)o(ula)f(in)h
(eq.)f(3.34)p
 (#equation.3.34) [[400 308 421 320] [1 1 1 [3 3]] [0 0 1]] pdfm (,)k
(w)o(e)c(remark)o(ed)g(that)-5 1973 y(the)c(sub)q(class)i
FE(S)t(T)12 b FH([2)p Fv(;)c(n)p FH(])19 b(constitutes)g(a)h(family)d
(of)j(sp)q(ecial)e(K\177)-24 b(ahler)19 b(manifolds:)27
b(actually)18 b(a)i(quite)-5 2033 y(relev)m(an)o(t)c(one.)21
b(Here)15 b(w)o(e)h(surv)o(ey)f(the)h(sp)q(ecial)g(geometry)f(of)h
(this)g(class.)68 2093 y(Besides)k(their)f(applications)i(in)f(the)g
(large)g(radius)h(limit)c(of)k(sup)q(erstring)g(compacti\014cations,)-5
2154 y(the)d FE(S)t(T)13 b FH([2)p Fv(;)8 b(n)p FH(])18
b(manifolds)f(are)h(in)o(teresting)f(under)h(another)h(resp)q(ect.)27
b(They)18 b(pro)o(vide)g(an)g(example)-5 2214 y(where)h(the)f
(holomorphic)g(prep)q(oten)o(tial)g(can)h(b)q(e)g(non{existing.)29
b(F)l(urthermore)17 b(it)i(is)f(precisely)f(in)-5 2274
y(the)g(symplectic)e(gauge)j(where)f Fv(F)7 b FH(\()p
Fv(x)p FH(\))17 b(do)q(es)h(not)g(exist)f(that)g(the)h(mo)q(del)e
Fv(n)g FH(=)g(1,)h Fv(m)f FH(=)g(1)i(of)f(eq.)g(1.1)p
 (#equation.1.1) [[510 221 524 233] [1 1 1 [3 3]] [0 0 1]] pdfm 
-5 2334 a(exhibits)e(partial)i(sup)q(ersymmetry)c(breaking)j
Fv(N)j FH(=)14 b(2)22 b FE(\000)-8 b(!)22 b Fv(N)d FH(=)14
b(1)i([29)p
 (#cite.FGP1) [[384 207 396 219] [1 1 1 [3 3]] [0 0 1]] pdfm 
1 w(].)68 2394 y(Consider)k(a)f(standard)i(parametrization)c(of)j(the)f
Fv(S)s(O)q FH(\(2)p Fv(;)8 b(n)p FH(\))p Fv(=S)s(O)q
FH(\(2\))15 b FE(\002)d Fv(S)s(O)q FH(\()p Fv(n)p FH(\))20
b(manifold,)e(lik)o(e)-5 2455 y(for)i(instance)f(that)g(in)g(eq.)f
(3.31)p
 (#equation.3.31) [[195 178 216 190] [1 1 1 [3 3]] [0 0 1]] pdfm (.)31
b(In)18 b(the)h Fv(m)g FH(=)f(2)i(case)f(w)o(e)g(can)g(in)o(tro)q(duce)
g(a)g(canonical)g(complex)-5 2515 y(structure)d(on)h(the)f(manifold)f
(b)o(y)h(setting:)144 2644 y(\010)179 2624 y FC(\003)205
2644 y FH(\()p Fv(X)t FH(\))23 b FE(\021)396 2611 y FH(1)p
376 2633 66 2 v 376 2642 a FE(p)p 417 2642 25 2 v 417
2683 a FH(2)463 2596 y Fs(\020)488 2644 y Fv(L)521 2624
y FC(\003)546 2657 y(0)576 2644 y FH(+)11 b(i)d Fv(L)680
2624 y FC(\003)705 2657 y(1)725 2596 y Fs(\021)855 2644
y FH(;)106 b(\(\003)13 b(=)h(0)p Fv(;)8 b FH(1)p Fv(;)g(a)49
b(a)13 b FH(=)h(2)p Fv(;)8 b(:)g(:)g(:)g(;)g(n)j FH(+)g(1\))157
b(\(C.1\))916 2892 y(67)p eop
%%Page: 68 69
68 68 bop -5 15 a FH(The)16 b(relations)g(satis\014ed)h(b)o(y)f(the)g
(upp)q(er)g(t)o(w)o(o)g(ro)o(ws)h(of)f(the)g(coset)g(represen)o(tativ)o
(e)f(\(consequence)g(of)-5 76 y Fv(L)p FH(\()p Fv(X)t
FH(\))i(b)q(eing)f(pseudo{orthogona)q(l)i(with)e(resp)q(ect)g(to)h
(metric)d Fv(\021)1187 83 y FC(\003\006)1253 76 y FH(=)f(diag)r(\(+)p
Fv(;)8 b FH(+)p Fv(;)g FE(\000)p Fv(;)g(:)g(:)g(:)e(;)i
FE(\000)p FH(\)\):)290 186 y Fv(L)323 165 y FC(\003)347
198 y(0)375 186 y Fv(L)408 165 y FC(\006)433 198 y(0)461
186 y Fv(\021)485 193 y FC(\003\006)559 186 y FH(=)22
b(1)50 b(;)56 b Fv(L)796 165 y FC(\003)821 198 y(0)849
186 y Fv(L)882 165 y FC(\006)906 198 y(1)934 186 y Fv(\021)958
193 y FC(\003\006)1033 186 y FH(=)22 b(0)49 b(;)57 b
Fv(L)1270 165 y FC(\003)1294 198 y(1)1322 186 y Fv(L)1355
165 y FC(\006)1380 198 y(1)1408 186 y Fv(\021)1432 193
y FC(\003\006)1506 186 y FH(=)22 b(1)184 b(\(C.2\))-5
296 y(can)17 b(b)q(e)f(summarized)d(in)o(to)j(the)g(complex)e
(equations:)p 600 372 36 2 v 600 411 a(\010)635 382 y
FC(\003)670 411 y FH(\010)705 391 y FC(\006)733 411 y
Fv(\021)757 418 y FC(\003\006)831 411 y FH(=)22 b(1)49
b(;)57 b(\010)1070 391 y FC(\006)1098 411 y Fv(\021)1122
418 y FC(\003\006)1196 411 y FH(=)22 b(0)494 b(\(C.3\))-5
521 y(Eq.s)33 b(C.3)p
 (#equation.C.3) [[101 642 118 654] [1 1 1 [3 3]] [0 0 1]] pdfm 
16 w(are)16 b(solv)o(ed)g(b)o(y)g(p)q(osing:)725 659
y(\010)760 639 y FC(\003)809 659 y FH(=)977 626 y Fv(X)1021
608 y FC(\003)p 874 648 278 2 v 874 656 a Fs(q)p 915
656 236 2 v 915 676 45 2 v 915 715 a Fv(X)960 685 y FC(\003)994
715 y Fv(X)1038 700 y FC(\006)1075 715 y Fv(\021)1099
722 y FC(\003\006)1774 659 y FH(\(C.4\))-5 824 y(where)e
Fv(X)178 806 y FC(\003)218 824 y FH(denotes)g(an)o(y)g(set)f(of)h
(complex)e(parameters,)h(determined)e(up)j(to)g(an)g(o)o(v)o(erall)e(m)
o(ultiplic)o(a-)-5 884 y(tiv)o(e)j(constan)o(t)i(and)g(satisfying)f
(the)g(constrain)o(t:)773 994 y Fv(X)817 973 y FC(\003)852
994 y Fv(X)896 973 y FC(\006)924 994 y Fv(\021)948 1001
y FC(\003\006)1023 994 y FH(=)22 b(0)667 b(\(C.5\))-5
1104 y(In)21 b(this)g(w)o(a)o(y)g(w)o(e)g(ha)o(v)o(e)g(pro)o(v)o(ed)f
(the)h(iden)o(ti\014cation,)g(as)h(di\013eren)o(tiable)e(manifolds,)g
(of)i(the)f(coset)-5 1164 y(space)14 b Fv(S)s(O)q FH(\(2)p
Fv(;)8 b(n)p FH(\))p Fv(=S)s(O)q FH(\(2\))e FE(\002)g
Fv(S)s(O)q FH(\()p Fv(n)p FH(\))17 b(with)d(the)f(v)m(anishing)h(lo)q
(cus)h(of)f(the)f(quadric)h(in)f(eq.)g(C.5)p
 (#equation.C.5) [[463 488 481 500] [1 1 1 [3 3]] [0 0 1]] pdfm (.)21
b(T)l(aking)-5 1224 y(an)o(y)16 b(holomorphic)g(solution)g(of)h(eq.)e
(C.5)p  (#equation.C.5) [[236 473 254 485] [1 1 1 [3 3]] [0 0 1]] pdfm 
(,)h(for)g(instance:)646 1391 y Fv(X)690 1370 y FC(\003)717
1391 y FH(\()p Fv(y)r FH(\))21 b FE(\021)863 1293 y Fs(0)863
1366 y(B)863 1392 y(@)920 1330 y FH(1)p Fv(=)p FH(2)10
b(\(1)h(+)g Fv(y)1131 1312 y FC(2)1150 1330 y FH(\))925
1390 y(i)p Fv(=)p FH(2)e(\(1)i FE(\000)g Fv(y)1126 1372
y FC(2)1145 1390 y FH(\))1022 1451 y Fv(y)1048 1432 y
Ft(a)1190 1293 y Fs(1)1190 1366 y(C)1190 1392 y(A)1774
1391 y FH(\(C.6\))-5 1557 y(where)22 b Fv(y)168 1539
y Ft(a)210 1557 y FH(is)g(a)g(set)g(of)g Fv(n)g FH(indep)q(enden)o(t)f
(complex)f(co)q(ordinates,)j(inserting)f(it)f(in)o(to)h(eq.)e(C.4)p
 (#equation.C.4) [[483 393 500 405] [1 1 1 [3 3]] [0 0 1]] pdfm 
22 w(and)-5 1617 y(comparing)i(with)h(eq.)f(C.1)p
 (#equation.C.1) [[178 379 196 391] [1 1 1 [3 3]] [0 0 1]] pdfm 
23 w(w)o(e)h(obtain)g(the)g(relation)g(b)q(et)o(w)o(een)f(whatev)o(er)g
(co)q(ordinates)i(w)o(e)e(had)-5 1678 y(previously)17
b(used)h(to)h(write)e(the)h(coset)g(represen)o(tativ)o(e)e
Fv(L)p FH(\()p Fv(X)t FH(\))i(and)h(the)f(complex)d(co)q(ordinates)k
Fv(y)1851 1659 y Ft(a)1871 1678 y FH(.)-5 1738 y(In)g(other)g(w)o(ords)
h(w)o(e)f(can)g(regard)g(the)g(matrix)f Fv(L)h FH(as)h(a)f(function)g
(of)g(the)g Fv(y)1425 1720 y Ft(a)1465 1738 y FH(that)g(are)g(named)f
(the)-5 1798 y(Calabi)f(Visen)o(tini)d(co)q(ordinates)j([68)p
 (#cite.calvis) [[223 335 234 347] [1 1 1 [3 3]] [0 0 1]] pdfm (].)68
1858 y(Consider)k(in)f(addition)h(the)f Fu(axion{dilaton)h
FH(\014eld)f Fv(S)k FH(that)c(parametrizes)f(the)h Fv(S)s(U)5
b FH(\(1)p Fv(;)j FH(1\))p Fv(=U)d FH(\(1\))-5 1918 y(coset)13
b(according)g(with)f(eq.)f(3.30)p
 (#equation.3.30) [[194 307 215 319] [1 1 1 [3 3]] [0 0 1]] pdfm (.)21
b(The)13 b(sp)q(ecial)f(geometry)f(of)i(the)f(manifold)f
FE(S)t(T)i FH([2)p Fv(;)8 b(n)p FH(])k(is)g(completely)-5
1979 y(sp)q(eci\014ed)k(b)o(y)g(writing)g(the)g(holomorphic)f
(symplectic)e(section)j(\012)g(as)h(follo)o(ws)f(\([4)p
 (#cite.CDFVP) [[432 292 437 304] [1 1 1 [3 3]] [0 0 1]] pdfm (]\):)541
2110 y(\012\()p Fv(y)r(;)8 b(S)s FH(\))22 b(=)777 2050
y Fs(\022)816 2080 y Fv(X)860 2062 y FC(\003)822 2140
y Fv(F)854 2147 y FC(\003)895 2050 y Fs(\023)948 2110
y FH(=)1008 2050 y Fs(\022)1106 2080 y Fv(X)1150 2062
y FC(\003)1177 2080 y FH(\()p Fv(y)r FH(\))1047 2140
y FE(S)12 b Fv(\021)1113 2147 y FC(\003\006)1165 2140
y Fv(X)1209 2122 y FC(\006)1237 2140 y FH(\()p Fv(y)r
FH(\))1309 2050 y Fs(\023)1774 2110 y FH(\(C.7\))-5 2219
y(Notice)k(that)i(with)f(the)g(ab)q(o)o(v)o(e)g(c)o(hoice,)e(it)i(is)g
(not)h(p)q(ossible)f(to)h(describ)q(e)e Fv(F)1405 2226
y FC(\003)1448 2219 y FH(as)i(deriv)m(ativ)o(es)e(of)h(an)o(y)-5
2279 y(prep)q(oten)o(tial.)j(Y)l(et)14 b(ev)o(erything)g(else)g(can)h
(b)q(e)g(calculated)f(utilizing)f(the)i(form)o(ulae)e(w)o(e)h(presen)o
(ted)g(in)-5 2339 y(the)i(text.)21 b(The)16 b(K\177)-24
b(ahler)16 b(p)q(oten)o(tial)g(is:)407 2449 y FE(K)23
b FH(=)f FE(K)566 2456 y FC(1)585 2449 y FH(\()p Fv(S)s
FH(\))11 b(+)g FE(K)754 2456 y FC(2)774 2449 y FH(\()p
Fv(y)r FH(\))22 b(=)g FE(\000)p FH(logi\()p 1054 2410
33 2 v Fv(S)13 b FE(\000)e Fv(S)s FH(\))g FE(\000)g FH(log)e
Fv(X)1375 2428 y Ft(T)1403 2449 y Fv(\021)r(X)305 b FH(\(C.8\))-5
2559 y(The)17 b(K\177)-24 b(ahler)15 b(metric)f(is)i(blo)q(c)o(k)g
(diagonal:)360 2701 y Fv(g)383 2708 y Ft(ij)411 2699
y Fm(?)454 2701 y FH(=)514 2628 y Fs( )567 2670 y Fv(g)590
2684 y Ft(S)p 613 2657 24 2 v 2 w(S)697 2670 y FD(0)589
2731 y(0)64 b Fv(g)704 2745 y Ft(a)p 723 2717 16 2 v(b)761
2628 y Fs(!)154 b(\()1003 2665 y Fv(g)1026 2679 y Ft(S)p
1049 2651 24 2 v 2 w(S)1089 2665 y FH(=)13 b Fv(@)1166
2672 y Ft(S)1191 2665 y Fv(@)p 1217 2651 26 2 v 14 x
Ft(S)1243 2665 y FE(K)1281 2672 y FC(1)1314 2665 y FH(=)1408
2645 y FB(\000)p FC(1)p 1371 2653 119 2 v 1371 2686 a(\()p
1385 2658 24 2 v Ft(S)r FB(\000)p Ft(S)r FC(\))1472 2676
y Fr(2)1003 2736 y Fv(g)1026 2750 y Ft(a)p 1045 2722
16 2 v(b)1062 2736 y FH(\()p Fv(y)r FH(\))g(=)h Fv(@)1217
2743 y Ft(a)1238 2736 y Fv(@)p 1264 2722 18 2 v 14 x
Ft(b)1281 2736 y FE(K)1319 2743 y FC(2)1774 2701 y FH(\(C.9\))916
2892 y(68)p eop
%%Page: 69 70
69 69 bop -5 15 a FH(as)17 b(exp)q(ected.)k(The)c(anomalous)f(magnetic)
f(momen)o(ts-Y)l(uk)m(a)o(w)o(a)f(couplings)j Fv(C)1467
22 y Ft(ij)r(k)1533 15 y FH(\()p Fv(i)d FH(=)g Fv(S;)8
b(a)p FH(\))16 b(ha)o(v)o(e)g(a)-5 76 y(v)o(ery)f(simple)f(expression)i
(in)g(the)g(c)o(hosen)g(co)q(ordinates:)731 165 y Fv(C)766
172 y Ft(S)r(ab)839 165 y FH(=)e FE(\000)p FH(exp)o([)p
FE(K)q FH(])8 b Fv(\016)1101 172 y Ft(ab)1136 165 y Fv(;)600
b FH(\(C.10\))-5 254 y(all)16 b(the)g(other)g(comp)q(onen)o(ts)g(b)q
(eing)g(zero.)68 314 y(Using)h(the)f(de\014nition)f(of)i(the)f
Fu(p)n(erio)n(d)g(matrix)g FH(giv)o(en)f(in)h(eq.)g(4.37)p
 (#equation.4.37) [[362 692 383 704] [1 1 1 [3 3]] [0 0 1]] pdfm 
17 w(w)o(e)f(obtain)513 433 y FE(N)554 440 y FC(\003\006)620
433 y FH(=)f(\()p Fv(S)g FE(\000)p 785 394 33 2 v 11
w Fv(S)r FH(\))841 400 y Fv(X)881 407 y FC(\003)p 908
361 45 2 v 908 400 a Fv(X)953 407 y FC(\006)991 400 y
FH(+)p 1040 361 V 11 w Fv(X)1085 407 y FC(\003)1111 400
y Fv(X)1151 407 y FC(\006)p 841 422 339 2 v 939 439 45
2 v 939 478 a Fv(X)984 449 y Ft(T)1011 478 y Fv(\021)r(X)1195
433 y FH(+)p 1244 394 33 2 v 11 w Fv(S)s(\021)1301 440
y FC(\003\006)1353 433 y Fv(:)383 b FH(\(C.11\))-5 556
y(In)16 b(order)g(to)g(see)g(that)g(eq.)f(C.11)p
 (#equation.C.11) [[193 634 216 646] [1 1 1 [3 3]] [0 0 1]] pdfm 
17 w(just)h(coincides)f(with)g(eq.)g(3.34)p
 (#equation.3.34) [[337 634 358 646] [1 1 1 [3 3]] [0 0 1]] pdfm 
17 w(it)g(su\016ces)h(to)g(note)g(that)h(as)f(a)h(con-)-5
616 y(sequence)e(of)h(its)f(de\014nition)g(C.1)p
 (#equation.C.1) [[200 619 218 631] [1 1 1 [3 3]] [0 0 1]] pdfm 
16 w(and)i(of)e(the)h(pseudo{orthogonalit)o(y)h(of)f(the)f(coset)h
(represen)o(tativ)o(e)-5 676 y Fv(L)p FH(\()p Fv(X)t
FH(\),)h(the)f(v)o(ector)f(\010)406 658 y FC(\003)449
676 y FH(satis\014es)i(the)f(follo)o(wing)g(iden)o(tit)o(y:)479
788 y(\010)514 767 y FC(\003)p 549 749 36 2 v 549 788
a FH(\010)585 759 y FC(\006)623 788 y FH(+)11 b(\010)707
767 y FC(\006)p 743 749 V 743 788 a FH(\010)779 759 y
FC(\003)827 788 y FH(=)892 754 y(1)p 892 776 25 2 v 892
822 a(2)930 788 y Fv(L)963 767 y FC(\003)988 800 y(\000)1020
788 y Fv(L)1053 767 y FC(\006)1079 800 y(\001)1118 740
y Fs(\020)1143 788 y Fv(\016)1167 767 y FC(\000\001)1231
788 y FH(+)g Fv(\021)1306 767 y FC(\000\001)1368 740
y Fs(\021)1750 788 y FH(\(C.12\))-5 890 y(Inserting)16
b(eq.)f(C.12)p
 (#equation.C.12) [[138 553 162 565] [1 1 1 [3 3]] [0 0 1]] pdfm 
17 w(in)o(to)h(eq.)f(C.11)p
 (#equation.C.11) [[208 553 231 565] [1 1 1 [3 3]] [0 0 1]] pdfm (,)i
(form)o(ula)31 b(3.34)p
 (#equation.3.34) [[286 553 306 565] [1 1 1 [3 3]] [0 0 1]] pdfm 
17 w(is)16 b(retriev)o(ed.)68 950 y(This)23 b(completes)d(the)i(pro)q
(of)h(that)f(the)g(c)o(hoice)f(C.7)p
 (#equation.C.7) [[310 539 328 551] [1 1 1 [3 3]] [0 0 1]] pdfm 
23 w(of)h(the)g(sp)q(ecial)g(geometry)e(holomorphic)-5
1010 y(section)h(corresp)q(onds)i(to)e(the)g(symplectic)d(em)o(b)q
(edding)i(3.26)p
 (#equation.3.26) [[333 525 353 537] [1 1 1 [3 3]] [0 0 1]] pdfm 
22 w(and)43 b(3.28)p
 (#equation.3.28) [[388 525 408 537] [1 1 1 [3 3]] [0 0 1]] pdfm 
22 w(of)21 b(the)g(coset)g(manifold)-5 1070 y FE(S)t(T)13
b FH([2)p Fv(;)8 b(n)p FH(].)22 b(In)17 b(this)g(symplectic)c(gauge)18
b(the)f(symplectic)c(transformations)k(of)g(the)g(isometry)e(group)-5
1131 y(are)23 b(the)f(simplest)e(p)q(ossible)i(ones)h(and)g(the)f(en)o
(tire)f(group)i Fv(S)s(O)q FH(\(2)p Fv(;)8 b(n)p FH(\))23
b(is)f(represen)o(ted)f(b)o(y)h(means)-5 1191 y(of)i
Fu(classic)n(al)g FH(transformations)f(that)h(do)g(not)f(mix)f
(electric)f(\014elds)h(with)i(magnetic)d(\014elds.)42
b(The)-5 1251 y(disadv)m(an)o(tage)16 b(of)f(this)g(basis,)g(if)f(an)o
(y)l(,)h(is)g(that)g(there)f(is)h(no)g(holomorphic)f(prep)q(oten)o
(tial.)20 b(T)l(o)15 b(\014nd)h(an)-5 1311 y Fv(F)7 b
FH(\()p Fv(X)t FH(\))16 b(it)g(su\016ces)g(to)g(mak)o(e)f(a)h
(symplectic)e(rotation)i(to)h(a)g(di\013eren)o(t)e(basis.)68
1371 y(If)h(w)o(e)g(set:)487 1470 y Fv(X)531 1450 y FC(1)565
1470 y FH(=)621 1437 y(1)p 621 1459 V 621 1504 a(2)651
1470 y(\(1)11 b(+)g Fv(y)780 1450 y FC(2)800 1470 y FH(\))41
b(=)g FE(\000)983 1437 y FH(1)p 983 1459 V 983 1504 a(2)1013
1470 y(\(1)11 b FE(\000)g Fv(\021)1141 1477 y Ft(ij)1171
1470 y Fv(t)1189 1450 y Ft(i)1203 1470 y Fv(t)1221 1450
y Ft(j)1239 1470 y FH(\))469 1587 y Fv(X)513 1566 y FC(2)547
1587 y FH(=)j Fv(i)621 1553 y FH(1)p 621 1575 V 621 1621
a(2)650 1587 y(\(1)d FE(\000)g Fv(y)780 1566 y FC(2)800
1587 y FH(\))41 b(=)g Fv(t)957 1566 y FC(2)641 1680 y
Fv(X)685 1659 y Ft(a)720 1680 y FH(=)14 b Fv(y)798 1659
y Ft(a)860 1680 y FH(=)41 b Fv(t)957 1659 y FC(2+)p Ft(a)1072
1680 y Fv(a)13 b FH(=)h(1)p Fv(;)8 b(:)g(:)g(:)g(;)g(n)j
FE(\000)g FH(1)590 1772 y Fv(X)634 1751 y Ft(a)p FC(=)p
Ft(n)718 1772 y FH(=)i Fv(y)795 1751 y Ft(n)860 1772
y FH(=)944 1738 y(1)p 944 1760 V 944 1806 a(2)974 1772
y(\(1)e(+)g Fv(\021)1101 1779 y Ft(ij)1132 1772 y Fv(t)1150
1751 y Ft(i)1163 1772 y Fv(t)1181 1751 y Ft(j)1199 1772
y FH(\))532 b(\(C.13\))-5 1874 y(where)489 1934 y Fv(\021)513
1941 y Ft(ij)557 1934 y FH(=)14 b(diag)c(\(+)p Fv(;)e
FE(\000)p Fv(;)g(:)g(:)g(:)f(;)h FE(\000)p FH(\))24 b
Fv(i;)8 b(j)16 b FH(=)e(2)p Fv(;)8 b(:)g(:)g(:)g(;)g(n)j
FH(+)g(1)359 b(\(C.14\))-5 2012 y(Then)17 b(w)o(e)e(can)i(sho)o(w)g
(that)f FE(9)8 b(C)26 b(2)14 b Fv(S)s(p)p FH(\(2)p Fv(n)e
FH(+)f(2)p Fv(;)d FH(I)-9 b(R\))16 b(suc)o(h)g(that:)380
2246 y FE(C)426 2185 y Fs(\022)523 2215 y Fv(X)567 2197
y FC(\003)465 2276 y Fv(S)s(\021)522 2283 y FC(\003\006)582
2276 y Fv(X)626 2258 y FC(\003)661 2185 y Fs(\023)714
2246 y FH(=)22 b(exp[)p Fv(')p FH(\()p Fv(t)p FH(\)])980
2060 y Fs(0)980 2134 y(B)980 2158 y(B)980 2183 y(B)980
2208 y(B)980 2233 y(B)980 2258 y(B)980 2283 y(B)980 2308
y(B)980 2334 y(@)1228 2095 y FH(1)1224 2155 y Fv(S)1224
2215 y(t)1242 2197 y Ft(i)1024 2276 y FH(2)8 b FE(F)17
b(\000)11 b Fv(t)1177 2258 y Ft(i)1208 2256 y(@)p 1195
2264 47 2 v 1195 2293 a(@)r(t)1229 2283 y Fm(i)1247 2276
y FE(F)16 b(\000)11 b Fv(S)1388 2256 y Ft(@)p 1386 2264
24 2 v 1386 2293 a(S)1415 2276 y FE(F)1187 2336 y Fv(S)1226
2316 y Ft(@)p 1224 2324 V 1224 2353 a(S)1253 2336 y FE(F)1209
2376 y Ft(@)p 1196 2384 47 2 v 1196 2413 a(@)r(t)1230
2404 y Fm(i)1248 2396 y FE(F)1464 2060 y Fs(1)1464 2134
y(C)1464 2158 y(C)1464 2183 y(C)1464 2208 y(C)1464 2233
y(C)1464 2258 y(C)1464 2283 y(C)1464 2308 y(C)1464 2334
y(A)1750 2246 y FH(\(C.15\))-5 2476 y(with)533 2575 y
FE(F)5 b FH(\()p Fv(S;)j(t)p FH(\))41 b(=)807 2542 y(1)p
807 2564 25 2 v 807 2609 a(2)845 2575 y Fv(S)11 b(\021)910
2582 y Ft(ij)940 2575 y Fv(t)958 2555 y Ft(i)972 2575
y Fv(t)990 2555 y Ft(j)1022 2575 y FH(=)1079 2542 y(1)p
1079 2564 V 1079 2609 a(2)1116 2575 y Fv(d)1141 2582
y Ft(I)s(J)s(K)1216 2575 y Fv(t)1234 2555 y Ft(I)1254
2575 y Fv(t)1272 2555 y Ft(J)1296 2575 y Fv(t)1314 2555
y Ft(K)644 2668 y Fv(t)662 2647 y FC(1)723 2668 y FH(=)41
b Fv(S)581 2747 y(d)606 2754 y Ft(I)s(J)s(K)723 2747
y FH(=)802 2686 y Fs(\032)842 2722 y Fv(d)867 2729 y
FC(1)p Ft(j)r(k)936 2722 y FH(=)14 b Fv(\021)1012 2729
y Ft(ij)842 2782 y FH(0)33 b(otherwise)1750 2747 y(\(C.16\))916
2892 y(69)p eop
%%Page: 70 71
70 70 bop -5 15 a FH(and)651 93 y Fv(W)697 100 y Ft(I)s(J)s(K)785
93 y FH(=)14 b Fv(d)862 100 y Ft(I)s(J)s(K)951 93 y FH(=)1011
60 y Fv(@)1040 42 y FC(3)1059 60 y FE(F)5 b FH(\()p Fv(S;)j(t)1189
42 y Ft(i)1202 60 y FH(\))p 1008 82 217 2 v 1008 128
a Fv(@)s(t)1055 113 y Ft(I)1074 128 y Fv(@)s(t)1121 113
y Ft(J)1144 128 y Fv(@)s(t)1191 113 y Ft(K)1750 93 y
FH(\(C.17\))-5 193 y(This)17 b(means)f(that)h(in)f(the)h(new)f(basis)h
(the)g(symplectic)c(holomorphic)j(section)g FE(C)s FH(\012)h(can)g(b)q
(e)g(deriv)o(ed)-5 253 y(from)e(the)h(follo)o(wing)g(cubic)g(prep)q
(oten)o(tial:)637 392 y Fv(F)7 b FH(\()p Fv(X)t FH(\))22
b(=)852 358 y(1)p 845 380 38 2 v 845 426 a(3!)901 358
y Fv(d)926 365 y Ft(I)s(J)s(K)1010 358 y Fv(X)1054 340
y Ft(I)1082 358 y Fv(X)1126 340 y Ft(J)1159 358 y Fv(X)1203
340 y Ft(K)p 901 380 337 2 v 1040 426 a Fv(X)1080 433
y FC(0)1750 392 y FH(\(C.18\))-5 522 y(F)l(or)17 b(instance)f(in)g(the)
g(case)g Fv(n)e FH(=)f(1)k(the)f(matrix)f(whic)o(h)g(do)q(es)i(suc)o(h)
f(a)h(job)g(is:)550 773 y FE(C)g FH(=)645 588 y Fs(0)645
661 y(B)645 686 y(B)645 711 y(B)645 736 y(B)645 761 y(B)645
786 y(B)645 811 y(B)645 836 y(B)645 862 y(@)710 623 y
FH(1)90 b(0)70 b FE(\000)p FH(1)52 b(0)70 b(0)90 b(0)710
683 y(0)g(0)f(0)72 b(1)e(0)90 b(1)710 743 y(0)70 b FE(\000)p
FH(1)g(0)i(0)e(0)90 b(0)710 803 y(0)g(0)f(0)1036 784
y FC(1)p 1036 792 18 2 v 1036 821 a(2)1127 803 y FH(0)69
b FE(\000)1264 784 y FC(1)p 1264 792 V 1264 821 a(2)689
864 y FE(\000)733 844 y FC(1)p 733 852 V 733 881 a(2)824
864 y FH(0)f FE(\000)960 844 y FC(1)p 960 852 V 960 881
a(2)1033 864 y FH(0)i(0)90 b(0)710 924 y(0)g(0)f(0)72
b(0)51 b FE(\000)p FH(1)70 b(0)1294 588 y Fs(1)1294 661
y(C)1294 686 y(C)1294 711 y(C)1294 736 y(C)1294 761 y(C)1294
786 y(C)1294 811 y(C)1294 836 y(C)1294 862 y(A)1750 773
y FH(\(C.19\))-5 1055 y Fk(Commen)n(ts)22 b(on)g(the)h
Fj(S)t(T)15 b Fi([2)p Fh(;)10 b Fi(2])24 b Fk(case:)k(S)23
b(dualit)n(y)i(and)e(R)f(symmetry)-5 1147 y FH(T)l(o)f(conclude)e(let)g
(us)h(fo)q(cus)g(on)h(the)e(case)h FE(S)t(T)13 b FH([2)p
Fv(;)8 b FH(2].)31 b(This)20 b(manifold)f(has)h(t)o(w)o(o)g(co)q
(ordinates)h(that)-5 1207 y(w)o(e)d(can)h(either)e(call)h
Fv(S)j FH(and)e Fv(t)p FH(,)g(in)f(the)g(parametrization)f(of)i(eq.)e
(C.16)p
 (#equation.C.16) [[367 477 391 489] [1 1 1 [3 3]] [0 0 1]] pdfm 
19 w(or)i Fv(S)i FH(and)e Fv(y)i FH(in)d(the)g(Calabi)-5
1268 y(Visen)o(tini)c(basis.)22 b(The)16 b(relation)g(b)q(et)o(w)o(een)
g Fv(t)g FH(and)g Fv(y)i FH(simpli\014es)c(enormously)h(in)h(this)g
(case:)814 1397 y Fv(t)29 b FH(=)h Fv(i)951 1363 y(y)13
b FH(+)e(1)p 951 1385 111 2 v 951 1431 a Fv(y)i FE(\000)d
FH(1)1750 1397 y(\(C.20\))-5 1529 y(It)20 b(is)h(then)f(a)h(matter)e
(of)i(c)o(hoice)e(to)i(regard)g(the)g(holomorphic)e(section)h(in)g
(whatev)o(er)g(basis)h(as)h(a)-5 1590 y(function)h(of)g
Fv(y)i FH(or)e(of)h Fv(t)p FH(,)g(in)e(addition)i(to)f
Fv(S)s FH(.)41 b(Indep)q(enden)o(tly)22 b(from)g(this)h(c)o(hoice)f
(the)g(manifold)-5 1650 y FE(S)t(T)13 b FH([2)p Fv(;)8
b FH(2])18 b(emerges)e(as)j Fu(mo)n(duli)g(sp)n(ac)n(e)g(\(at)g(tr)n(e)
n(e{level\))h FH(in)d(a)i(lo)q(cally)e(N=2)h(sup)q(ersymmetric)d(gauge)
-5 1710 y(theory)i(of)h(a)g(rank)f(one)h(gauge)g(group,)g(namely)e
Fv(S)s(U)5 b FH(\(2\).)25 b(The)17 b(t)o(w)o(o)g(\014elds)g(spanning)h
(the)f(manifold)-5 1770 y(ha)o(v)o(e)c(v)o(ery)g(di\013eren)o(t)g(in)o
(terpretations.)19 b(The)14 b(\014eld)f Fv(y)i FH(is)f(the)f(scalar)h
(partner)g(of)g(the)g(gauge)g(\014eld)g(that)-5 1830
y(remains)k(massless)h(after)g(Higgs)h(mec)o(hanism)o(.)28
b(Its)19 b(v)m(acuum)f(exp)q(ectation)h(v)m(alue)g(is)g(the)h(mo)q
(dulus)-5 1891 y(of)g(the)g(gauge)g(theory)l(.)32 b(It)19
b(is)h(the)f(same)g(\014eld)g(that)h(o)q(ccurs)g(also)h(in)e(a)h
(globally)f(sup)q(ersymmetric)-5 1951 y(theory)l(.)h(On)14
b(the)g(other)g(hand)g(the)g(\014eld)f Fv(S)k FH(is)c(the)h
(dilaton{axion.)21 b(It)13 b(pla)o(ys)g(the)h(role)f(of)h(generalized)
-5 2011 y(coupling)f(constan)o(t)h(and)g(generalized)e
Fv(theta)p FH({angle.)19 b(There)13 b(are)g(t)o(w)o(o)g
Fv(S)s(L)p FH(\(2)p Fv(;)8 b FH(I)-9 b(R\))14 b(groups)g(em)o(b)q
(edded)-5 2071 y(in)j Fv(S)s(P)7 b FH(\(6)p Fv(;)h FH(I)-9
b(R\),)16 b(they)h(act)g(as)g(standard)h(fractional)f(linear)f
(transformations)h(on)g(the)g Fu(dilaton{axion)-5 2131
y Fv(S)24 b FH(and)e(on)g(the)f(sp)q(ecial)g(co)q(ordinate)h
Fv(t)f FH(for)g(the)g(gauge)i(mo)q(dulus.)35 b(Using)21
b(the)h(Calabi{Visen)o(tini)-5 2192 y(section)16 b(of)h(eq.)e(C.7)p
 (#equation.C.7) [[142 241 159 253] [1 1 1 [3 3]] [0 0 1]] pdfm 
16 w(and)i(the)f(em)o(b)q(edding)f(eq.s)g(3.26)p
 (#equation.3.26) [[288 241 309 253] [1 1 1 [3 3]] [0 0 1]] pdfm 
17 w(and)33 b(3.28)p
 (#equation.3.28) [[340 241 360 253] [1 1 1 [3 3]] [0 0 1]] pdfm (,)17
b(w)o(e)f(ha)o(v)o(e)f(that)68 2252 y FD(S{dualit)n(y)h
Fv(S)h FE(\000)-9 b(!)22 b(\000)p FH(1)p Fv(=S)e FH(is)c(generated)g(b)
o(y)g(the)g(symplectic)d(matrix:)513 2506 y Fv(S)543
2513 y Ft(duality)687 2506 y FH(=)763 2321 y Fs(0)763
2394 y(B)763 2419 y(B)763 2444 y(B)763 2469 y(B)763 2494
y(B)763 2518 y(B)763 2543 y(B)763 2568 y(B)763 2595 y(@)827
2356 y FH(0)88 b(0)69 b(0)49 b(1)g(0)69 b(0)827 2416
y(0)88 b(0)69 b(0)49 b(0)g(1)69 b(0)827 2476 y(0)88 b(0)69
b(0)49 b(0)g(0)g FE(\000)p FH(1)808 2536 y FE(\000)p
FH(1)68 b(0)h(0)49 b(0)g(0)69 b(0)827 2596 y(0)g FE(\000)p
FH(1)49 b(0)g(0)g(0)69 b(0)827 2657 y(0)88 b(0)69 b(1)49
b(0)g(0)69 b(0)1323 2321 y Fs(1)1323 2394 y(C)1323 2419
y(C)1323 2444 y(C)1323 2469 y(C)1323 2494 y(C)1323 2518
y(C)1323 2543 y(C)1323 2568 y(C)1323 2595 y(A)1750 2506
y FH(\(C.21\))916 2892 y(70)p eop
%%Page: 71 72
71 71 bop -5 15 a FH(while)16 b FD(T{dualit)n(y)f Fv(t)f
FE(\000)-9 b(!)22 b(\000)p FH(1)p Fv(=t)17 b FH(is)f(generated)g(b)o(y)
g(the)g(symplectic)d(matrix:)465 270 y Fv(R)502 277 y
Ft(sy)q(mmetr)q(y)696 270 y FH(=)773 85 y Fs(0)773 158
y(B)773 183 y(B)773 207 y(B)773 232 y(B)773 257 y(B)773
282 y(B)773 307 y(B)773 332 y(B)773 359 y(@)817 119 y
FE(\000)p FH(1)69 b(0)f(0)h(0)87 b(0)69 b(0)837 179 y(0)f
FE(\000)p FH(1)49 b(0)69 b(0)87 b(0)69 b(0)837 240 y(0)88
b(0)68 b(1)h(0)87 b(0)69 b(0)837 300 y(0)88 b(0)68 b(0)49
b FE(\000)p FH(1)68 b(0)h(0)837 360 y(0)88 b(0)68 b(0)h(0)f
FE(\000)p FH(1)49 b(0)837 420 y(0)88 b(0)68 b(0)h(0)87
b(0)69 b(1)1371 85 y Fs(1)1371 158 y(C)1371 183 y(C)1371
207 y(C)1371 232 y(C)1371 257 y(C)1371 282 y(C)1371 307
y(C)1371 332 y(C)1371 359 y(A)1750 270 y FH(\(C.22\))-5
521 y(If)22 b(w)o(e)h(think)f(of)h(the)f Fv(t)p FH({\014eld)g(as)h(the)
g Fu(mo)n(dulus)f FH(of)h(some)f(compact)f(in)o(ternal)h(manifold)f
(then)h(T{)-5 581 y(dualit)o(y)d(is)g(just)g(the)g(transformation)g
(from)f(small)g(to)h(large)g(compacti\014cation)f(radius.)31
b(Lo)q(oking)-5 642 y(at)20 b(the)f(same)f(transformation)h(in)g(terms)
f(of)h(the)g Fv(y)i FH(v)m(ariable)e(its)g(meaning)f(b)q(ecomes)g(more)
g(clear.)-5 702 y(It)i(is)h Fv(R)p FH({symmetry)d Fv(y)23
b FE(\000)-9 b(!)21 b(\000)p Fv(y)r FH(,)g(an)g(exact)f(global)h
(symmetry)c(of)k(the)f Fu(micr)n(osc)n(opic)g FH(lagrangian.)-5
762 y(The)f(fact)f(that)h(the)f(matrix)e(generating)j(T{dualit)o(y)f
(or)g(R{symmetry)e(is)i(blo)q(c)o(k{diagonal)h(agrees)-5
822 y(with)d(the)f(fact)h(that)g(this)g(is)g(a)g(p)q(erturbativ)o(e)f
(symmetry)-5 b(,)13 b(holding)j(at)g(eac)o(h)f(order)h(in)f(p)q
(erturbation)-5 882 y(theory)g(and)g(nev)o(er)e(exc)o(hanging)i
(electric)d(with)j(magnetic)e(states.)21 b(V)l(ery)13
b(di\013eren)o(t)h(is)h(the)f(nature)h(of)-5 943 y(S{dualit)o(y)l(.)26
b(Since)17 b(it)g(in)o(v)o(erts)g(the)g(coupling)h(constan)o(t)g(it)g
(is)f(b)o(y)h(de\014nition)f(non{p)q(erturbativ)o(e.)26
b(It)-5 1003 y(exc)o(hanges)11 b(strong)h(and)g(w)o(eak)e(coupling)h
(regimes)f(and)h(b)q(ecause)h(of)f(that)g(it)g(is)g(supp)q(osed)h(to)g
(exc)o(hange)-5 1063 y(elemen)o(tary)i(states)j(with)f(soliton)h
(states.)22 b(F)l(or)17 b(this)f(reason)i(it)e(m)o(ust)f(mix)f
(electric)g(with)j(magnetic)-5 1123 y(\014eld)h(strengths)i(and)f(it)f
(is)h(o\013{diagonal.)30 b(These)19 b(symmetri)o(es)d(exist)i(in)g(the)
h(microscopic)d(theory)-5 1183 y(whic)o(h)d(is)g(deriv)o(ed)f(b)o(y)h
Fu(gauging)i FH(the)e(ab)q(elian)g(theories)g(p)q(ossessing)i(con)o
(tin)o(uous)e(dualit)o(y)g(symmetri)o(es)-5 1244 y(\(in)i(this)h(case)f
(the)g(t)o(w)o(o)g Fv(S)s(L)p FH(\(2)p Fv(;)8 b FH(I)-9
b(R\))16 b(groups\).)22 b(After)14 b(gauging)j(the)e(con)o(tin)o(uous)g
(dualit)o(y)g(symmetri)o(es)-5 1304 y(will)f(b)q(e)i(brok)o(en.)k(The)
15 b(question)g(is)g(will)f(the)h(in)o(teger)f(v)m(alued)h(symplectic)d
(generators)k(of)g(S{dualit)o(y)-5 1364 y(and)i(R{symmetry)13
b(surviv)o(e)j(giv)o(en)f(that)i(they)g(resp)q(ect)f(the)g(Dirac)h
(quan)o(tization)f(condition?)23 b(The)-5 1424 y(answ)o(er)14
b(is)g(y)o(es,)g(but)g(in)f(the)h(e\013ectiv)o(e)e(quan)o(tum)h(theory)
g(they)h(will)f(b)q(e)h(represen)o(ted)f(b)o(y)g(new)h(in)o(teger)-5
1484 y(v)m(alued)h(elemen)o(ts)e(of)j Fv(S)s(p)p FH(\(6)p
Fv(;)8 b Fa(Z)-17 b(Z)q FH(\))16 b(not)f(deriv)m(able)g(from)f(the)h
(classical)g(em)o(b)q(edding.)k(Since)14 b(the)i(sp)q(ecial)-5
1544 y(geometry)k(in)h(the)g(e\013ectiv)o(e)e(theory)i(is)g(corrected)f
(b)o(y)h(the)g(instan)o(ton)g(con)o(tributions)g(and)h(has)g(a)-5
1605 y(new)e(complicated)e(transcenden)o(tal)i(structure,)g(the)g
(dualit)o(y)f(generators)h(m)o(ust)f(c)o(hange)h(basis)h(to)-5
1665 y(adapt)16 b(themselv)o(es)11 b(to)k(the)f(new)g(situation)h(and)g
(b)q(e)g(in)o(teger)e(v)m(alued)h(in)g(the)g(new)h(non{p)q(erturbativ)o
(e)-5 1725 y(geometry)l(.)38 b(Alternativ)o(ely)19 b(one)j(can)g(turn)h
(matters)e(around.)40 b(If)21 b(w)o(e)h(kno)o(w)g(the)g(new)g(quan)o
(tum)-5 1785 y(symplectic)17 b(em)o(b)q(edding)h(of)j(the)e(discrete)g
(dualit)o(y)g(group)i(w)o(e)e(ha)o(v)o(e)h(essen)o(tially)e(determined)
f(the)-5 1845 y(non)j(p)q(erturbativ)o(e)e(geometry)l(.)28
b(It)18 b(is)h(this)g(p)q(oin)o(t)g(of)g(view)g(that)g(has)h(pro)o(v)o
(en)e(v)o(ery)g(fruitful)g(in)g(the)-5 1906 y(v)o(ery)d(recen)o(t)g
(literature.)-5 2050 y Fk(C.1)66 b(Momen)n(tum)23 b(maps)f(of)g
Fh(H)5 b(Q)p Fi([)p Fh(m)p Fi(])23 b Fk(and)g(mass)e(matrices)-5
2166 y FH(As)c(w)o(e)g(are)g(just)g(going)h(to)g(see)e(the)h
(quaternionic)g(manifold)e Fv(H)t(Q)p FH([)p Fv(m)p FH(])h(is)h(the)g
(closest)g(quaternionic)-5 2226 y(analogue)f(of)e(a)h(\015at)g(Hyp)q
(erK\177)-24 b(ahler)13 b(manifold)g(and)i(the)g(relev)m(an)o(t)e(form)
o(ulae)g(for)h(the)g(metric)e(and)j(the)-5 2286 y(momen)o(tum)e(maps)i
(are)i(almost)f(iden)o(tical,)e Fu(mutatis)k(mutandis)p
FH(,)e(with)g(the)h(equations)f(surv)o(ey)o(ed)f(in)-5
2347 y(subsection)h(9.3,)f(when)g(w)o(e)g(discussed)h(the)f
(renormalizable)e(microscopic)g(N=2)i(sup)q(er)h(Y)l(ang{Mills)-5
2407 y(lagrangian.)68 2467 y(T)l(o)22 b(describ)q(e)e(the)g(coset)h
(manifold)e Fv(S)s(O)q FH(\(4)p Fv(;)8 b(m)p FH(\))p
Fv(=S)s(O)q FH(\(4\))16 b FE(\002)e Fv(S)s(O)q FH(\()p
Fv(m)p FH(\))21 b(w)o(e)f(use)h(a)g(family)d(of)j(coset)-5
2527 y(represen)o(tativ)o(es)15 b Fv(L)p FH(\()p Fv(q)r
FH(\))e FE(2)h Fv(S)s(O)q FH(\(4)p Fv(;)8 b(m)p FH(\).)22
b(A)16 b(t)o(ypical)e(c)o(hoice)h(is)h(the)g(\(4)c(+)f
Fv(m)p FH(\))g FE(\002)f FH(\(4)i(+)f Fv(m)p FH(\))16
b(matrix:)567 2681 y Fv(L)p FH(\()p Fv(q)r FH(\))22 b(=)744
2595 y Fs(0)744 2670 y(@)788 2595 y(q)p 830 2595 175
2 v 51 x FH(1)-17 b(1)11 b(+)g Fv(q)f(q)977 2632 y Ft(T)1149
2646 y Fv(q)871 2727 y(q)895 2708 y Ft(T)1053 2675 y
Fs(q)p 1094 2675 V 1094 2727 a FH(1)-17 b(1)12 b(+)f
Fv(q)1210 2712 y Ft(T)1245 2727 y Fv(q)1277 2595 y Fs(1)1277
2670 y(A)1750 2681 y FH(\(C.23\))916 2892 y(71)p eop
%%Page: 72 73
72 72 bop -5 15 a FH(function)15 b(of)f(an)i(indep)q(enden)o(t)d(4)8
b FE(\002)g Fv(m)14 b FH(matrix)f Fv(q)r FH(.)20 b(By)14
b(de\014nition)g(of)g(the)h(group)g Fv(S)s(O)q FH(\(4)p
Fv(;)8 b(m)p FH(\))15 b(w)o(e)f(ha)o(v)o(e:)371 125 y
Fv(L)404 105 y Ft(T)440 125 y Fv(\021)c(L)22 b FH(=)g
Fv(\021)99 b FH(;)106 b Fv(\021)24 b FH(=)e(diag)17 b(\(+)p
Fv(;)8 b FH(+)p Fv(;)g FH(+)p Fv(;)g FH(+)p Fv(;)g FE(\000)p
Fv(;)g(:)g(:)g(:)e(;)i FE(\000)p FH(\))240 b(\(C.24\))-5
235 y(W)l(e)16 b(can)g(regard)g(the)g(index)f(range)i(in)e(the)h
(fundamen)o(tal)f(represen)o(tation)g(of)h Fv(S)s(O)q
FH(\(4)p Fv(;)8 b(m)p FH(\))16 b(as)h(split)e(in)-5 296
y(the)h(follo)o(wing)g(w)o(a)o(y:)484 374 y Fv(L)23 b
FH(=)f Fv(L)633 354 y Ft(I)651 387 y(J)870 374 y Fv(I)t(;)8
b(J)18 b FH(=)1015 314 y Fs(\032)1054 344 y Fv(a;)8 b(b)13
b FH(=)h(0)p Fv(;)8 b FH(1)p Fv(;)g FH(2)p Fv(;)g FH(3)1054
404 y Fv(t;)g(s)13 b FH(=)h(1)p Fv(;)8 b FH(2)p Fv(;)g(:)g(:)g(:)16
b(m)1750 374 y FH(\(C.25\))-5 480 y(and)h(in)o(tro)q(ducing)f(the)g
(left)g(in)o(v)m(arian)o(t)f(one{form:)806 590 y Fv(L)839
569 y FB(\000)p FC(1)895 590 y Fv(dL)22 b FE(\021)g FH(\002)676
b(\(C.26\))-5 700 y(w)o(e)16 b(can)h(split)e(it)h(in)o(to)g(the)g
(vielb)q(ein)e(and)j(the)f(connections)g(on)h(the)f(coset)g(manifold:)
322 866 y(\002)d(=)425 793 y Fs( )518 836 y Fv(\022)542
818 y Ft(ab)658 836 y Fv(E)697 818 y Ft(at)479 896 y
FH(\()p Fv(E)537 878 y Ft(T)564 896 y FH(\))583 878 y
Ft(ta)659 896 y FH(\001)700 878 y Ft(st)752 793 y Fs(!)911
766 y(8)911 804 y(>)911 816 y(<)911 891 y(>)911 903 y(:)969
806 y Fv(\022)993 787 y Ft(ab)1083 806 y FH(SO\(4\))j(connection)969
866 y Fv(E)1008 848 y Ft(at)1083 866 y FH(Vielb)q(ein)e(on)j(the)f
(coset)969 926 y(\001)1010 908 y Ft(st)1083 926 y FH(SO\(m\))f
(connection.)1750 866 y(\(C.27\))-5 1033 y(F)l(rom)g(the)h(v)o(ery)f
(de\014nition)h(of)h(\002)f(one)g(immedi)o(ately)d(obtains)k(the)f
(Maurer-Cartan)h(equations:)341 1099 y Fs(8)341 1137
y(>)341 1149 y(<)341 1224 y(>)341 1236 y(:)399 1138 y
Fv(\016)r(E)462 1120 y Ft(at)506 1138 y FH(+)11 b Fv(\022)579
1120 y Ft(ab)626 1138 y FE(^)g Fv(E)709 1120 y Ft(bt)750
1138 y FE(\000)g FH(\001)841 1120 y Ft(ts)883 1138 y
FE(^)g Fv(E)966 1120 y Ft(as)1017 1138 y FH(=)j(0)67
b(T)l(orsion)17 b(equation)399 1198 y Fv(\016)r(\022)447
1180 y Ft(ab)493 1198 y FH(+)11 b Fv(\022)566 1180 y
Ft(ac)614 1198 y FE(^)g Fv(\022)682 1180 y Ft(cb)728
1198 y FH(=)j FE(\000)p Fv(E)858 1180 y Ft(as)906 1198
y FE(^)d Fv(E)989 1180 y Ft(bs)1160 1198 y FH(SO\(4\))17
b(curv)m(ature)399 1259 y Fv(\016)r FH(\001)464 1241
y Ft(ts)505 1259 y FE(\000)11 b FH(\001)596 1241 y Ft(tr)638
1259 y FE(^)h FH(\001)724 1241 y Ft(r)q(s)773 1259 y
FH(=)h Fv(E)863 1241 y Ft(at)908 1259 y FE(^)e Fv(E)991
1241 y Ft(as)1042 1259 y FH(=)j(0)42 b(SO\(m\))15 b(curv)m(ature)1750
1199 y(\(C.28\))-5 1369 y(Notice)f(that)h(the)f(vielb)q(ein)f
Fv(E)552 1351 y Ft(at)599 1369 y FH(=)h Fv(E)690 1351
y Ft(at)687 1382 y(u)724 1369 y Fv(dq)773 1351 y Ft(u)809
1369 y FH(carries)g(a)h(v)o(ector)f(index)g Fv(a)f FH(=)h(0)p
Fv(;)8 b FH(1)p Fv(;)g FH(2)p Fv(;)g FH(3)16 b(of)e(SO\(4\))h(and)h(an)
-5 1429 y(index)g Fv(t)h FH(in)f(the)g(v)o(ector)g(represen)o(tation)g
(of)h(SO\(m\))f(just)h(as)g(it)f(do)q(es)i(the)e(co)q(ordinate)i
FD(q)e FH(of)h(the)g(\015at)-5 1490 y(Hyp)q(erK\177)-24
b(ahler)12 b(manifold)g(discussed)h(in)g(eq.)f(10.42)p
 (#equation.10.42) [[269 409 295 421] [1 1 1 [3 3]] [0 0 1]] pdfm (.)21
b(Accordingly)12 b(the)g(quaternionic)h(generalization)-5
1550 y(of)k(eq.)e(10.42)p
 (#equation.10.42) [[103 395 129 407] [1 1 1 [3 3]] [0 0 1]] pdfm 
17 w(is)h(obtained)h(b)o(y)f(setting:)841 1660 y FD(l)41
b FE(\021)g Fv(L)1011 1639 y Ft(a)p FB(j)p Ft(t)820 1732
y FD(E)g FE(\021)g Fv(E)1017 1712 y Ft(a)p FB(j)p Ft(t)1750
1732 y FH(\(C.29\))-5 1842 y(The)16 b(quaternionic)f(metric)e(and)j
(the)g(corresp)q(onding)g(triplet)f(of)h(Hyp)q(erK\177)-24
b(ahler)15 b(2{forms)g(are)h(giv)o(en)-5 1903 y(b)o(y:)465
2013 y Fv(ds)513 1992 y FC(2)574 2013 y FE(\021)41 b
Fv(h)682 2020 y Ft(uv)732 2013 y Fv(dq)781 1992 y Ft(u)811
2013 y Fv(dq)860 1992 y Ft(v)902 2013 y FH(=)23 b FD(E)1000
1992 y Ft(T)1043 2013 y FH(\(1)-17 b(1)1094 2020 y FC(4)p
FB(\002)p FC(4)1170 2013 y FE(\012)11 b FH(1)-17 b(1)1252
2020 y Ft(m)p FB(\002)p Ft(m)1343 2013 y FH(\))17 b FD(E)466
2091 y Fv(K)511 2071 y Ft(x)574 2091 y FH(=)42 b FD(E)691
2071 y Ft(T)738 2091 y FE(^)791 2043 y Fs(\020)815 2091
y Fv(J)847 2071 y FC(+)p FB(j)p Ft(x)917 2091 y FE(\012)11
b FH(1)-17 b(1)999 2098 y Ft(m)p FB(\002)p Ft(m)1091
2043 y Fs(\021)1132 2091 y FD(E)16 b Fv(;)551 b FH(\(C.30\))-5
2201 y(whic)o(h)15 b(is)g(the)g(quaternionic)f(coun)o(terpart)h(of)h
(eq.)e(10.47)p
 (#equation.10.47) [[297 239 324 251] [1 1 1 [3 3]] [0 0 1]] pdfm 
16 w(Alternativ)o(ely)e(in)j(the)g(ab)q(o)o(v)o(e)g(form)o(ula)f(one)-5
2262 y(can)j(use)g(the)f(triplet)f(of)i(an)o(tiself)f(dual)g(t'Ho)q
(oft)h(matrices)e(to)i(de\014ne)f(the)g(Hyp)q(erK\177)-24
b(ahler)16 b(structure.)-5 2322 y(Using)24 b(the)f(iden)o(tities)45
b(10.48)p
 (#equation.10.48) [[185 210 212 222] [1 1 1 [3 3]] [0 0 1]] pdfm 
24 w(and)24 b(rearranging)h(the)e(4)p Fv(m)h FH(vielb)q(ein)d
Fv(E)1385 2304 y Ft(a)p FB(j)p Ft(t)1452 2322 y FH(in)o(to)i(an)h
Fv(m)p FH(-v)o(ector)f(of)-5 2382 y(quaternions:)652
2554 y FD(QE)f FH(=)813 2406 y Fs(0)813 2479 y(B)813
2504 y(B)813 2529 y(B)813 2554 y(B)813 2579 y(B)813 2605
y(@)857 2433 y Fv(QE)935 2415 y FC(1)977 2433 y FH(=)g
Fv(E)1076 2415 y Ft(a)p FB(j)p FC(1)1132 2433 y Fv(e)1155
2440 y Ft(a)857 2493 y Fv(QE)935 2475 y FC(2)977 2493
y FH(=)g Fv(E)1076 2475 y Ft(a)p FB(j)p FC(2)1132 2493
y Fv(e)1155 2500 y Ft(a)988 2554 y Fv(:)8 b(:)g(:)862
2614 y(QE)940 2596 y Ft(t)977 2614 y FH(=)22 b Fv(E)1076
2596 y Ft(a)p FB(j)p Ft(t)1128 2614 y Fv(e)1151 2621
y Ft(a)988 2674 y Fv(:)8 b(:)g(:)1184 2406 y Fs(1)1184
2479 y(C)1184 2504 y(C)1184 2529 y(C)1184 2554 y(C)1184
2579 y(C)1184 2605 y(A)1750 2554 y FH(\(C.31\))916 2892
y(72)p eop
%%Page: 73 74
73 73 bop -5 15 a FH(whic)o(h)17 b(is)h(the)g(quaternionic)f(coun)o
(terpart)h(of)g(eq.)f(10.49)p
 (#equation.10.49) [[302 763 328 775] [1 1 1 [3 3]] [0 0 1]] pdfm (,)i
(eq.s)e(C.30)p
 (#equation.C.30) [[360 763 383 775] [1 1 1 [3 3]] [0 0 1]] pdfm 
18 w(can)h(b)q(e)g(rewritten)f(in)h(a)g(form)-5 76 y(completely)c
(analogous)k(to)e(eq.s)g(10.50)p
 (#equation.10.50) [[221 749 248 761] [1 1 1 [3 3]] [0 0 1]] pdfm (:)
505 200 y Fv(ds)553 179 y FC(2)614 200 y FH(=)699 166
y(1)p 699 188 25 2 v 699 234 a(2)740 200 y(tr)795 152
y Fs(\020)820 200 y FD(QE)899 179 y FB(y)925 200 y FH(1)-17
b(1)956 207 y Ft(m)p FB(\002)p Ft(m)1048 200 y FD(QE)1127
152 y Fs(\021)528 316 y Fv(K)45 b FH(=)707 283 y(1)p
707 305 V 707 351 a(2)745 316 y FD(QE)823 295 y Ft(T)870
316 y FE(^)20 b FH(1)-17 b(1)955 323 y Ft(m)p FB(\002)p
Ft(m)p 1047 277 79 2 v 1047 316 a FD(QE)22 b FH(=)1213
283 y(1)p 1213 305 25 2 v 1213 351 a(2)1250 316 y Fv(K)1295
296 y Ft(x)1326 316 y Fv(e)1349 296 y Ft(T)1349 329 y(x)1750
316 y FH(\(C.32\))-5 434 y(Just)13 b(as)f(in)g(the)g(\015at)g(Hyp)q
(erk\177)-24 b(ahler)11 b(case)h(the)g(action)g(of)h(the)e(gauge)i
(group)g FE(G)i FH(on)e(the)e(h)o(yp)q(erm)o(ultiplets)-5
494 y(is)16 b(assumed)g(to)h(b)q(e)f(linear)f(and)i(b)q(e)g(generated)f
(b)o(y)g(a)g(set)g(of)h(4)p Fv(m)11 b FE(\002)g FH(4)p
Fv(m)16 b FH(matrices)f Fv(T)1561 501 y Ft(I)1580 494
y FH(:)568 599 y Fv(\016)590 606 y Ft(I)609 599 y FD(l)22
b FH(=)g Fv(T)736 606 y Ft(I)764 599 y FD(l)70 b FE(\000)-8
b(!)62 b Fv(k)1020 578 y Ft(u)1018 611 y(I)1065 599 y
FH(=)22 b(\()p Fv(T)1173 606 y Ft(I)1192 599 y FH(\))1211
575 y Ft(u)1232 613 y(v)1269 599 y Fv(q)1293 578 y Ft(v)1750
599 y FH(\(C.33\))-5 704 y(In)d(order)h(for)g(this)f(action)h(to)g(b)q
(e)f(an)h(isometry)e(of)i(the)f(Euclidean)g(diagonal)h(metric)37
b(10.47)p
 (#equation.10.47) [[473 598 499 610] [1 1 1 [3 3]] [0 0 1]] pdfm 
20 w(it)19 b(is)-5 764 y(necessary)g(and)h(su\016cien)o(t)e(that)i(the)
f(matrices)e Fv(T)943 771 y Ft(I)982 764 y FH(b)q(elong)j(to)f(the)g
(linearly)f(realized)g(part)i(of)f(the)-5 824 y(isometry)c(algebra)h
Fv(S)s(O)q FH(\(4)p Fv(;)8 b(m)p FH(\),)17 b(namely)d
Fv(S)s(O)q FH(\(4\))e FE(\002)f Fv(S)s(O)q FH(\()p Fv(m)p
FH(\).)21 b(namely:)563 929 y Fv(T)592 936 y Ft(I)634
929 y FE(2)h Fv(S)s(O)q FH(\(4\))12 b FE(\002)f Fv(S)s(O)q
FH(\()p Fv(m)p FH(\))22 b FE(\032)g Fv(S)s(O)q FH(\(4)p
Fv(;)8 b(m)p FH(\))433 b(\(C.34\))-5 1033 y(The)16 b(action)g(of)g
FE(G)i FH(ho)o(w)o(ev)o(er)c(is)i(not)g(only)f(required)g(to)h(b)q(e)g
(isometrical)d(but)j(also)g(to)g(b)q(e)g(triholomor-)-5
1094 y(phic.)21 b(This)16 b(means:)567 1154 y Fv(`)587
1161 y Ft(I)616 1154 y Fv(K)661 1133 y Ft(x)705 1154
y FE(\021)22 b FD(i)782 1161 y Ft(I)810 1154 y Fv(dK)880
1133 y Ft(x)921 1154 y FH(+)e Fv(d)8 b FD(i)1028 1161
y Ft(I)1056 1154 y Fv(K)1101 1133 y Ft(x)1145 1154 y
FH(=)14 b FE(r)p Fv(W)1292 1133 y Ft(x)1285 1166 y(I)1750
1154 y FH(\(C.35\))-5 1239 y(where)h Fv(W)181 1246 y
Ft(x)217 1239 y FH(is)g(the)f(in\014nitesimal)e(parameter)i(of)h(some)e
Fv(S)s(U)5 b FH(\(2\))15 b(transformation)g(A)f(straigh)o(tforw)o(ard)
-5 1299 y(calculation)19 b(sho)o(ws)h(that)g(the)f(triholomorphicit)o
(y)d(condition)k(is)f(that)h(the)f(generators)h Fv(T)1708
1306 y Ft(I)1747 1299 y FH(should)-5 1359 y(comm)o(ute)d(with)j(the)f
(tensor)h(pro)q(duct)h(of)f(the)g('t)f(Ho)q(oft)h(matrices)e(with)i
(the)g(unit)f(matrix)f(in)i Fv(m)p FH({)-5 1419 y(dimensions.)g(When)c
(this)g(last)h(condition)f(is)g(v)o(eri\014ed)f(w)o(e)g(can)i(write)f
(the)g(momen)o(tum)c(maps)j(as:)665 1524 y FE(P)704 1503
y Ft(x)700 1536 y(I)748 1524 y FH(=)22 b FD(l)824 1503
y Ft(T)859 1524 y Fv(J)891 1503 y FC(+)p FB(j)p Ft(x)961
1524 y FE(\012)11 b FH(1)-17 b(1)1043 1531 y Ft(m)p FB(\002)p
Ft(m)1143 1524 y Fv(T)1172 1531 y Ft(I)1200 1524 y FD(l)534
b FH(\(C.36\))-5 1629 y(Using)18 b(these)f(ingredien)o(ts)g(the)g(mass)
g(matrices)f(and)i(the)g(scalar)g(p)q(oten)o(tial)f(can)h(b)q(e)f
(written)h(do)o(wn)-5 1689 y(without)26 b(an)o(y)f(further)h
(di\016cult)o(y)l(.)47 b(The)25 b(quaternionic)g(vielb)q(ein)f(is)h
(giv)o(en)f(in)i(full)e(analogy)j(to)-5 1749 y(eq.s)16
b(10.61)p
 (#equation.10.61) [[94 347 120 359] [1 1 1 [3 3]] [0 0 1]] pdfm (,)h
(10.62)p
 (#equation.10.62) [[128 347 154 359] [1 1 1 [3 3]] [0 0 1]] pdfm (,)g
(b)o(y)583 1809 y FE(U)619 1789 y Ft(A\013)692 1809 y
FE(\021)22 b(U)789 1789 y Ft(A\013)784 1822 y(b)p FB(j)p
Ft(s)848 1809 y Fv(dq)897 1789 y Ft(b)p FB(j)p Ft(s)963
1809 y FH(=)8 b(=)22 b Fv(E)1108 1789 y Ft(a)p FB(j)p
Ft(t)1160 1809 y FH(\()p Fv(e)1202 1816 y Ft(a)1222 1809
y FH(\))1241 1789 y Ft(A)1267 1822 y(B)1750 1809 y FH(\(C.37\))-5
1894 y(and,)16 b(as)h(b)q(efore,)f(w)o(e)f(iden)o(tify)g(the)h
(symplectic)c(index)k Fv(\013)g FH(running)g(on)h(2)p
Fv(m)f FH(v)m(alues)g(with)g(the)g(pair)g(of)-5 1954
y(indices)f Fv(B)s(;)8 b(t)16 b FH(\()g Fv(B)g FH(=)e(1)p
Fv(;)8 b FH(2;)17 b Fv(t)c FH(=)h(1)p Fv(;)8 b(:)g(:)g(:)g(;)g(m)p
FH(\).)-5 2120 y Fw(App)r(endix)26 b(D:)h(Normalizations)f(and)h(con)n
(v)n(en)n(tions)-5 2230 y Fu(Minkowski)19 b(metric)p
FH(:)718 2290 y Fv(\021)742 2297 y Ft(ab)792 2290 y FE(\021)14
b FH(\(1)p Fv(;)8 b FE(\000)p FH(1)p Fv(;)g FE(\000)p
FH(1)p Fv(;)g FE(\000)p FH(1\))588 b(\(C.38\))68 2375
y Fu(De\014nition)19 b(of)f(the)f(R)o(iemann)h(tensor)p
FH(:)441 2499 y Fv(R)478 2478 y Ft(\026)499 2511 y(\027)543
2499 y FH(=)k Fv(d)p FH(\000)658 2478 y Ft(\026)680 2511
y(\027)713 2499 y FH(+)11 b(\000)792 2478 y Ft(\026)813
2511 y(\032)845 2499 y FE(^)g FH(\000)919 2478 y Ft(\032)937
2511 y(\027)973 2499 y FE(\021)22 b(\000)1086 2465 y
FH(1)p 1086 2487 V 1086 2533 a(2)1115 2499 y Fv(R)1152
2478 y Ft(\026)1173 2511 y(\027)r(\032\033)1234 2499
y Fv(dx)1287 2478 y Ft(\032)1319 2499 y FE(^)11 b Fv(dx)1416
2478 y Ft(\033)1750 2499 y FH(\(C.39\))68 2619 y Fu(De)n(c)n(omp)n
(osition)17 b(of)g(tensors)h(in)g(self{dual)g(and)g(antiself{dual)h(p)n
(arts)d(\()p Fv(\017)1419 2626 y FC(0123)1514 2619 y
FE(\021)21 b FH(1)p Fu(\))p FH(:)642 2747 y Fv(T)678
2726 y FB(\007)671 2759 y Ft(\026\027)735 2747 y FH(=)800
2713 y(1)p 800 2735 V 800 2781 a(2)838 2686 y Fs(\022)868
2747 y Fv(T)897 2754 y Ft(\026\027)948 2747 y FE(\007)1005
2713 y FH(i)p 1000 2735 V 1000 2781 a(2)1029 2747 y Fv(\017)1049
2754 y Ft(\026\027)r(\032\033)1131 2747 y Fv(T)1167 2726
y Ft(\032\033)1208 2686 y Fs(\023)1750 2747 y FH(\(C.40\))916
2892 y(73)p eop
%%Page: 74 75
74 74 bop 68 15 a Fu(Cli\013or)n(d)17 b(A)o(lgebr)n(a)p
FH(:)173 125 y FE(f)p Fv(\015)223 132 y Ft(a)244 125
y Fv(;)8 b(\015)291 132 y Ft(b)308 125 y FE(g)51 b FH(=)f(2)8
b Fv(\021)528 132 y Ft(ab)196 198 y FH([)o Fv(\015)234
205 y Ft(a)255 198 y Fv(;)g(\015)302 205 y Ft(b)320 198
y FH(])50 b(=)g(2)8 b Fv(\015)529 205 y Ft(ab)288 270
y Fv(\015)313 277 y FC(5)383 270 y FE(\021)41 b(\000)8
b FH(i)g Fv(\015)557 277 y FC(0)577 270 y Fv(\015)602
277 y FC(1)622 270 y Fv(\015)647 277 y FC(2)667 270 y
Fv(\015)692 277 y FC(3)288 343 y Fv(\015)316 319 y FB(y)313
354 y FC(0)384 343 y FH(=)50 b Fv(\015)497 350 y FC(0)517
343 y FH(;)203 b Fv(\015)759 350 y FC(0)779 343 y Fv(\015)807
319 y FB(y)804 354 y Ft(i)824 343 y Fv(\015)849 350 y
FC(0)892 343 y FH(=)22 b Fv(\015)977 350 y Ft(i)1089
343 y FH(\()p Fv(i)13 b FH(=)h(1)p Fv(;)8 b FH(2)p Fv(;)g
FH(3\);)204 b Fv(\015)1571 319 y FB(y)1568 354 y FC(5)1610
343 y FH(=)23 b Fv(\015)1696 350 y FC(5)181 415 y Fv(\017)201
422 y Ft(abcd)270 415 y Fv(\015)298 395 y Ft(cd)384 415
y FH(=)50 b(2)8 b(i)g Fv(\015)551 422 y Ft(ab)587 415
y Fv(\015)612 422 y FC(5)1750 415 y FH(\(C.41\))68 525
y Fu(De)n(c)n(omp)n(osition)17 b(of)g(fermions)h(in)f(chir)n(al)g(and)h
(antichir)n(al)g(p)n(arts)p FH(:)-5 585 y(the)e(indices)f(of)i(the)f
(spinors)h(also)g(\014x)f(their)f(c)o(hiralit)o(y)f(according)j(to)f
(the)g(follo)o(wing)g(con)o(v)o(en)o(tions:)666 751 y
Fv(\015)691 758 y FC(5)719 653 y Fs(0)719 726 y(B)719
753 y(@)776 690 y Fv(\025)804 672 y Ft(iA)788 750 y Fv(\020)809
757 y Ft(\013)781 811 y Fv( )813 818 y Ft(A)866 653 y
Fs(1)866 726 y(C)866 753 y(A)925 751 y FH(=)985 653 y
Fs(0)985 726 y(B)985 753 y(@)1042 690 y Fv(\025)1070
672 y Ft(iA)1053 750 y Fv(\020)1074 757 y Ft(\013)1046
811 y Fv( )1078 818 y Ft(A)1132 653 y Fs(1)1132 726 y(C)1132
753 y(A)1192 751 y Fv(;)544 b FH(\(C.42\))664 985 y Fv(\015)689
992 y FC(5)718 887 y Fs(0)718 960 y(B)718 986 y(@)776
924 y Fv(\025)804 906 y Ft(i)816 894 y Fm(?)804 937 y
Ft(A)781 984 y Fv(\020)806 966 y Ft(\013)775 1045 y Fv( )809
1026 y Ft(A)858 887 y Fs(1)858 960 y(C)858 986 y(A)916
985 y FH(=)22 b FE(\000)1031 887 y Fs(0)1031 960 y(B)1031
986 y(@)1089 924 y Fv(\025)1117 906 y Ft(i)1129 894 y
Fm(?)1117 937 y Ft(A)1095 984 y Fv(\020)1120 966 y Ft(\013)1089
1045 y Fv( )1123 1026 y Ft(A)1171 887 y Fs(1)1171 960
y(C)1171 986 y(A)1750 985 y FH(\(C.43\))68 1128 y Fu(Major)n(ana)17
b(c)n(onventions)p FH(:)-5 1188 y(F)l(or)g(an)o(y)f(fermion)e
Fv(\036)i FH(:)p 750 1208 29 2 v 750 1248 a Fv(\036)22
b FE(\021)g Fv(\036)891 1227 y FB(y)908 1248 y Fv(\015)933
1255 y FC(0)976 1248 y FH(=)g Fv(\036)1065 1227 y Ft(T)1092
1248 y Fv(C)623 b FH(\(C.44\))68 1335 y Fu(Fierz)18 b(r)n(e)n(arr)n
(angements)-5 1395 y FH(Let)j(us)h(denote)e(b)o(y)h(a)g(lo)o(w)o(er)f
(or)i(upp)q(er)f(dot)g(righ)o(t)g(and)g(left)f(c)o(hiralit)o(y)f(resp)q
(ectiv)o(ely)l(.)33 b(Then:)e Fu(for)-5 1455 y(0{form)17
b(spinors)g Fv(\037;)8 b(\030)r FH(:)633 1584 y Fv(\037)664
1591 y FB(\017)p 683 1545 24 2 v 683 1584 a Fv(\030)707
1596 y FB(\017)749 1584 y FH(=)22 b FE(\000)861 1550
y FH(1)p 861 1572 25 2 v 861 1618 a(2)p 899 1545 24 2
v 899 1584 a Fv(\030)922 1596 y FB(\017)942 1584 y Fv(\037)973
1591 y FB(\017)1012 1584 y FH(+)1074 1550 y(1)p 1074
1572 25 2 v 1074 1618 a(8)1112 1584 y Fv(\015)1137 1591
y Ft(ab)p 1173 1545 24 2 v 1173 1584 a Fv(\030)1196 1596
y FB(\017)1216 1584 y Fv(\015)1244 1564 y Ft(ab)1280
1584 y Fv(\037)1311 1591 y FB(\017)633 1701 y Fv(\037)664
1708 y FB(\017)p 683 1661 V 683 1701 a Fv(\030)707 1671
y FB(\017)749 1701 y FH(=)g FE(\000)861 1667 y FH(1)p
861 1689 25 2 v 861 1735 a(2)899 1701 y Fv(\015)924 1708
y Ft(a)p 945 1661 24 2 v 945 1701 a Fv(\030)968 1671
y FB(\017)988 1701 y Fv(\015)1016 1680 y Ft(a)1037 1701
y Fv(\037)1068 1708 y FB(\017)1750 1701 y FH(\(C.45\))-5
1829 y Fu(for)17 b(1{form)g(spinors)g Fv( )443 1836 y
Ft(A)471 1829 y Fv(;)8 b( )527 1811 y Ft(B)556 1829 y
FH(:)611 1958 y Fv( )643 1965 y Ft(A)p 671 1918 34 2
v 671 1958 a Fv( )704 1970 y Ft(B)757 1958 y FH(=)822
1924 y(1)p 822 1946 25 2 v 822 1992 a(2)p 859 1918 34
2 v 859 1958 a Fv( )893 1970 y Ft(B)923 1958 y Fv( )955
1965 y Ft(A)1003 1958 y FE(\000)1066 1924 y FH(1)p 1066
1946 25 2 v 1066 1992 a(8)1104 1958 y Fv(\015)1129 1965
y Ft(ab)p 1165 1918 34 2 v 1165 1958 a Fv( )1198 1970
y Ft(B)1229 1958 y Fv(\015)1257 1937 y Ft(ab)1293 1958
y Fv( )1325 1965 y Ft(A)611 2074 y Fv( )643 2081 y Ft(A)p
671 2035 V 671 2074 a Fv( )704 2045 y Ft(B)757 2074 y
FH(=)822 2041 y(1)p 822 2063 25 2 v 822 2109 a(2)859
2074 y Fv(\015)884 2081 y Ft(a)p 906 2035 34 2 v 906
2074 a Fv( )939 2045 y Ft(B)969 2074 y Fv(\015)997 2054
y Ft(a)1018 2074 y Fv( )1050 2081 y Ft(A)1750 2074 y
FH(\(C.46\))68 2197 y Fu(Char)n(ge)17 b(c)n(onjugation)i(matrix)e(pr)n
(op)n(erties)p FH(:)131 2319 y Fv(C)170 2298 y FC(2)212
2319 y FH(=)22 b FE(\000)p FH(1;)105 b Fv(C)493 2298
y Ft(T)543 2319 y FH(=)22 b FE(\000)8 b Fv(C)t FH(;)105
b(\()p Fv(C)t(\015)894 2298 y Ft(a)914 2319 y FH(\))933
2295 y Ft(T)982 2319 y FH(=)23 b Fv(C)t(\015)1110 2298
y Ft(a)1130 2319 y FH(;)1249 2271 y Fs(\020)1274 2319
y Fv(C)t(\015)1341 2298 y Ft(ab)1376 2271 y Fs(\021)1401
2282 y Ft(T)1451 2319 y FH(=)f Fv(C)t(\015)1578 2298
y Ft(ab)1750 2319 y FH(\(C.47\))68 2428 y Fu(Hermiticity)c(of)f(curr)n
(ents)-5 2489 y FH(for)g(0{form)f(spinors:)607 2598 y(\()p
626 2571 31 2 v Fv(\037)657 2610 y FB(\017)676 2598 y
Fv(\030)697 2605 y FB(\017)717 2598 y FH(\))736 2574
y FB(y)776 2598 y FH(=)p 836 2558 24 2 v 22 w Fv(\030)860
2568 y FB(\017)880 2598 y Fv(\037)911 2577 y FB(\017)952
2598 y FH(=)p 1012 2571 31 2 v 22 w Fv(\037)1043 2577
y FB(\017)1062 2598 y Fv(\030)1085 2577 y FB(\017)1750
2598 y FH(\(C.48\))607 2671 y(\()p 626 2644 V Fv(\037)657
2682 y FB(\017)676 2671 y Fv(\015)704 2650 y Ft(a)725
2671 y Fv(\030)748 2650 y FB(\017)769 2671 y FH(\))787
2646 y FB(y)827 2671 y FH(=)p 887 2631 24 2 v 22 w Fv(\030)911
2682 y FB(\017)931 2671 y Fv(\015)959 2650 y Ft(a)980
2671 y Fv(\037)1011 2650 y FB(\017)1052 2671 y FH(=)22
b FE(\000)p 1159 2644 31 2 v 8 w Fv(\037)1190 2650 y
FB(\017)1210 2671 y Fv(\015)1238 2650 y Ft(a)1258 2671
y Fv(\030)1279 2678 y FB(\017)1750 2671 y FH(\(C.49\))607
2711 y Fs(\020)p 632 2733 V 48 x Fv(\037)662 2771 y FB(\017)682
2759 y Fv(\015)710 2739 y Ft(ab)746 2759 y Fv(\030)767
2766 y FB(\017)787 2711 y Fs(\021)812 2723 y FB(y)852
2759 y FH(=)g FE(\000)p 959 2720 24 2 v 8 w Fv(\030)983
2730 y FB(\017)1002 2759 y Fv(\015)1030 2739 y Ft(ab)1066
2759 y Fv(\037)1097 2739 y FB(\017)1139 2759 y FH(=)p
1199 2733 31 2 v 22 w Fv(\037)1229 2739 y FB(\017)1249
2759 y Fv(\015)1277 2739 y Ft(ab)1313 2759 y Fv(\030)1336
2739 y FB(\017)1750 2759 y FH(\(C.50\))916 2892 y(74)p
eop
%%Page: 75 76
75 75 bop -5 15 a FH(for)17 b(1{form)f(spinors:)559 91
y Fs(\020)p 583 99 34 2 v 583 139 a Fv( )617 151 y Ft(A)645
139 y Fv( )677 146 y Ft(B)707 91 y Fs(\021)732 102 y
FB(y)772 139 y FH(=)22 b FE(\000)p 879 99 V 8 w Fv( )913
109 y Ft(B)943 139 y Fv( )977 118 y Ft(A)1027 139 y FH(=)p
1087 99 V 22 w Fv( )1121 109 y Ft(A)1149 139 y Fv( )1183
118 y Ft(B)1750 139 y FH(\(C.51\))559 195 y Fs(\020)p
583 203 V 583 243 a Fv( )617 213 y Ft(A)645 243 y Fv(\015)673
222 y Ft(a)694 243 y Fv( )726 250 y Ft(B)756 195 y Fs(\021)781
203 y FB(y)821 243 y FH(=)g FE(\000)p 928 203 V 8 w Fv( )962
213 y Ft(B)992 243 y Fv(\015)1020 222 y Ft(a)1041 243
y Fv( )1073 250 y Ft(A)1123 243 y FH(=)g FE(\000)p 1230
203 V 8 w Fv( )1264 254 y Ft(A)1292 243 y Fv(\015)1320
222 y Ft(a)1341 243 y Fv( )1375 222 y Ft(B)1750 243 y
FH(\(C.52\))559 298 y Fs(\020)p 583 307 V 583 347 a Fv( )617
317 y Ft(A)645 347 y Fv(\015)673 326 y Ft(ab)709 347
y Fv( )743 326 y Ft(B)773 298 y Fs(\021)798 307 y FB(y)838
347 y FH(=)p 898 307 V 22 w Fv( )931 358 y Ft(B)962 347
y Fv(\015)990 326 y Ft(ab)1026 347 y Fv( )1058 354 y
Ft(A)1108 347 y FH(=)p 1168 307 V 22 w Fv( )1202 358
y Ft(A)1230 347 y Fv(\015)1258 326 y Ft(ab)1294 347 y
Fv( )1326 354 y Ft(B)1750 347 y FH(\(C.53\))68 457 y
Fu(Conventions)e(on)d(K\177)-25 b(ahler)18 b(ge)n(ometry)p
FH(:)k(The)16 b(hermitean)e(metric)g(is)i(lo)q(cally)f(giv)o(en)h(b)o
(y:)801 567 y Fv(g)824 574 y Ft(ij)852 565 y Fm(?)887
567 y FH(=)e Fv(@)965 574 y Ft(i)978 567 y Fv(@)1004
574 y Ft(j)1020 565 y Fm(?)1040 567 y FE(K)672 b FH(\(C.54\))-5
677 y(where)18 b(the)h(real)f(function)g FE(K)g FH(=)g
FE(K)666 659 y Ft(?)703 677 y FH(=)f FE(K)q FH(\()p Fv(z)r(;)8
b(z)888 659 y FB(\003)907 677 y FH(\))18 b(is)h(named)e(the)h
Fu(K\177)-25 b(ahler)20 b(p)n(otential)p FH(.)29 b(It)18
b(is)g(de\014ned)-5 737 y(up)f(to)f(the)g(real)g(part)h(of)f(a)h
(holomorphic)e(function)h Fv(f)5 b FH(\()p Fv(z)r FH(\).)22
b(Indeed)15 b(one)i(sees)f(that)616 847 y FE(K)655 826
y FB(0)667 847 y FH(\()p Fv(z)r(;)8 b(z)758 826 y Ft(i)770
815 y Fm(?)789 847 y FH(\))14 b(=)g FE(K)q FH(\()p Fv(z)r(;)8
b(z)1004 826 y Ft(i)1016 815 y Fm(?)1035 847 y FH(\))j(+)g(Re)p
Fv(f)5 b FH(\()p Fv(z)r FH(\))486 b(\(C.55\))-5 957 y(giv)o(es)14
b(rise)g(to)h(the)f(same)g(metric)e Fv(g)635 964 y Ft(ij)663
955 y Fm(?)698 957 y FH(as)j FE(K)q FH(.)20 b(The)15
b(transformation)f(in)g(eq.)g(C.55)p
 (#equation.C.55) [[405 537 429 549] [1 1 1 [3 3]] [0 0 1]] pdfm 
15 w(is)g(named)f(a)i Fu(K\177)-25 b(ahler)-5 1017 y(tr)n(ansformation)
p FH(.)68 1077 y(T)l(o)16 b(\014x)f(our)h(notations)g(w)o(e)f(write)f
(the)h(form)o(ulae)e(for)j(the)f(Levi{Civita)f(connection)h(1{form)f
(and)-5 1137 y(Riemann)h(curv)m(ature)h(2{form)g(on)h(a)f(K\177)-24
b(ahler)16 b(manifold:)386 1233 y(\000)416 1215 y Ft(i)416
1246 y(j)491 1233 y FH(=)143 b(\000)702 1215 y Ft(i)702
1246 y(k)q(j)740 1233 y Fv(dz)790 1215 y Ft(k)954 1233
y FH(;)72 b(\000)1070 1215 y Ft(i)1070 1246 y(k)q(j)1181
1233 y FH(=)54 b Fv(g)1298 1215 y Ft(i`)1324 1204 y Fn(\003)1345
1233 y FH(\()p Fv(@)1390 1240 y Ft(j)1408 1233 y Fv(g)1431
1240 y Ft(k)q(`)1464 1232 y Fn(\003)1485 1233 y FH(\))377
1294 y(\000)407 1276 y Ft(i)419 1265 y Fn(\003)407 1307
y Ft(j)423 1297 y Fn(\003)491 1294 y FH(=)116 b(\000)675
1276 y Ft(i)687 1265 y Fn(\003)675 1307 y Ft(k)694 1297
y Fn(\003)713 1307 y Ft(j)729 1297 y Fn(\003)749 1294
y Fv(d)p 774 1268 25 2 v(z)799 1276 y Ft(k)818 1265 y
Fn(\003)954 1294 y FH(;)54 b(\000)1052 1276 y Ft(i)1064
1265 y Fn(\003)1052 1307 y Ft(k)1071 1297 y Fn(\003)1090
1307 y Ft(j)1106 1297 y Fn(\003)1181 1294 y FH(=)41 b
Fv(g)1285 1276 y Ft(i)1297 1265 y Fn(\003)1315 1276 y
Ft(`)1332 1294 y FH(\()p Fv(@)1377 1301 y Ft(j)1393 1292
y Fn(\003)1413 1294 y Fv(g)1436 1301 y Ft(k)1455 1292
y Fn(\003)1473 1301 y Ft(`)1490 1294 y FH(\))380 1355
y FE(R)422 1337 y Ft(i)422 1368 y(j)491 1355 y FH(=)51
b FE(R)622 1337 y Ft(i)622 1368 y(j)r(k)657 1358 y Fn(\003)675
1368 y Ft(`)692 1355 y Fv(d)p 717 1329 V(z)742 1337 y
Ft(k)761 1325 y Fn(\003)793 1355 y FE(^)11 b Fv(dz)887
1337 y Ft(`)954 1355 y FH(;)50 b FE(R)1060 1337 y Ft(i)1060
1368 y(j)r(k)1095 1358 y Fn(\003)1114 1368 y Ft(`)1181
1355 y FH(=)101 b Fv(@)1346 1362 y Ft(k)1365 1353 y Fn(\003)1386
1355 y FH(\000)1416 1337 y Ft(i)1416 1368 y(j)r(`)371
1416 y FE(R)413 1398 y Ft(i)425 1386 y Fn(\003)413 1429
y Ft(j)429 1419 y Fn(\003)491 1416 y FH(=)42 b FE(R)613
1398 y Ft(i)625 1386 y Fn(\003)613 1429 y Ft(j)629 1419
y Fn(\003)647 1429 y Ft(k)q(`)680 1419 y Fn(\003)701
1416 y Fv(dz)751 1398 y Ft(k)784 1416 y FE(^)11 b Fv(d)p
853 1390 V(z)878 1398 y Ft(`)892 1386 y Fn(\003)954 1416
y FH(;)41 b FE(R)1051 1398 y Ft(i)1063 1386 y Fn(\003)1051
1429 y Ft(j)1067 1419 y Fn(\003)1086 1429 y Ft(k)q(`)1119
1419 y Fn(\003)1181 1416 y FH(=)92 b Fv(@)1337 1423 y
Ft(k)1359 1416 y FH(\000)1389 1398 y Ft(i)1401 1386 y
Fn(\003)1389 1429 y Ft(j)1405 1419 y Fn(\003)1423 1429
y Ft(`)1437 1419 y Fn(\003)1750 1326 y FH(\(C.56\))68
1526 y Fv(S)s(U)5 b FH(\(2\))18 b Fu(and)g Fv(S)s(p)p
FH(\(2)p Fv(n)p FH(\))g Fu(metrics)p FH(:)519 1636 y
Fv(\017)539 1616 y Ft(AB)604 1636 y Fv(\017)624 1643
y Ft(B)r(C)703 1636 y FH(=)k FE(\000)8 b Fv(\016)834
1616 y Ft(A)832 1649 y(C)862 1636 y FH(;)203 b Fv(\017)1099
1616 y Ft(AB)1178 1636 y FH(=)22 b FE(\000)8 b Fv(\017)1305
1616 y Ft(B)r(A)1750 1636 y FH(\(C.57\))p 519 1746 2
33 v 506 1746 a(C)541 1725 y Ft(\013\014)p 604 1746 V
591 1746 a FH(C)627 1753 y Ft(\014)r(\015)692 1746 y
FH(=)22 b FE(\000)8 b Fv(\016)823 1726 y Ft(\013)821
1759 y(\015)848 1746 y FH(;)p 1073 1746 V 198 w(C)1095
1725 y Ft(\013\014)1164 1746 y FH(=)22 b FE(\000)p 1279
1746 V 3 w FH(C)1301 1725 y Ft(\014)r(\013)1348 1746
y FH(;)388 b(\(C.58\))-5 1833 y(F)l(or)17 b(an)o(y)f
Fv(S)s(U)5 b FH(\(2\))17 b(v)o(ector)e Fv(P)502 1840
y Ft(A)547 1833 y FH(w)o(e)h(ha)o(v)o(e:)513 1943 y Fv(\017)533
1950 y Ft(AB)597 1943 y Fv(P)635 1923 y Ft(B)688 1943
y FH(=)22 b Fv(P)779 1950 y Ft(A)808 1943 y FH(;)203
b Fv(\017)1045 1923 y Ft(AB)1110 1943 y Fv(P)1141 1950
y Ft(B)1194 1943 y FH(=)22 b FE(\000)8 b Fv(P)1339 1923
y Ft(A)1750 1943 y FH(\(C.59\))-5 2053 y(and)17 b(equiv)m(alen)o(tly)d
(for)j Fv(S)s(p)p FH(\(2)p Fv(n)p FH(\))g(v)o(ectors)e
Fv(P)797 2060 y Ft(\013)822 2053 y FH(:)p 531 2163 V
518 2163 a(C)553 2170 y Ft(\013\014)608 2163 y Fv(P)646
2143 y Ft(\014)692 2163 y FH(=)22 b Fv(P)783 2170 y Ft(\013)808
2163 y FH(;)p 1033 2163 V 198 w(C)1056 2143 y Ft(\013\014)1110
2163 y Fv(P)1141 2170 y Ft(\014)1187 2163 y FH(=)g FE(\000)8
b Fv(P)1332 2143 y Ft(\013)1750 2163 y FH(\(C.60\))68
2273 y Fu(R)n(e)n(ality)17 b(c)n(ondition)h(for)f Fv(S)s(U)5
b FH(\(2\))18 b Fu(value)n(d)g(matric)n(es)f Fv(H)1061
2255 y Ft(AB)1118 2273 y FH(:)p 698 2341 139 2 v 698
2383 a(\()p Fv(H)761 2369 y Ft(AB)818 2383 y FH(\))22
b(=)g Fv(\017)939 2363 y Ft(AC)1003 2383 y Fv(\017)1023
2363 y Ft(B)r(D)1083 2383 y Fv(H)1127 2363 y Ft(?)1123
2396 y(C)r(D)1750 2383 y FH(\(C.61\))916 2892 y(75)p
eop
%%Page: 76 77
76 76 bop 379 645 a FH(T)l(able)16 b(1:)22 b Fg(Homogeneous)16
b(Symme)o(tric)d(Sp)q(ecial)i(Manifolds)p 228 661 1425
2 v 227 721 2 61 v 296 703 a FH(n)p 390 721 V 399 721
V 262 w Fv(G=H)p 876 721 V 885 721 V 223 w(S)s(p)p FH(\(2)p
Fv(n)d FH(+)f(2\))p 1167 721 V 1176 721 V 118 w(symp)k(rep)h(of)h(G)p
1652 721 V 228 723 1425 2 v 227 783 2 61 v 390 783 V
399 783 V 876 783 V 885 783 V 1167 783 V 1176 783 V 1652
783 V 227 857 2 74 v 297 831 a(1)p 390 857 V 399 857
V 577 808 a Ft(S)r(U)t FC(\(1)p Ft(;)p FC(1\))p 577 820
124 2 v 602 848 a Ft(U)t FC(\(1\))p 876 857 2 74 v 884
857 V 967 831 a Fv(S)s(p)p FH(\(4\))p 1167 857 V 1176
857 V 315 w FD(4)p 1401 838 29 2 v 1652 857 2 74 v 227
917 2 61 v 390 917 V 399 917 V 876 917 V 885 917 V 1167
917 V 1176 917 V 1652 917 V 228 918 1425 2 v 227 979
2 61 v 390 979 V 399 979 V 876 979 V 885 979 V 1167 979
V 1176 979 V 1652 979 V 227 1039 V 390 1039 V 399 1039
V 876 1039 V 885 1039 V 1167 1039 V 1176 1039 V 1652
1039 V 227 1112 2 74 v 295 1087 a Fv(n)p 390 1112 V 399
1112 V 575 1064 a Ft(S)r(U)t FC(\(1)p Ft(;n)p FC(\))p
538 1075 200 2 v 538 1104 a Ft(S)r(U)t FC(\()p Ft(n)p
FC(\))p FB(\002)p Ft(U)t FC(\(1\))p 876 1112 2 74 v 884
1112 V 910 1087 a Fv(S)s(p)p FH(\(2)p Fv(n)12 b FH(+)f(2\))p
1167 1112 V 1176 1112 V 122 w FD(n)g FH(+)g FD(1)p 1265
1097 120 2 v 11 w FE(\010)g FD(n)g FH(+)g FD(1)p 1445
1097 V 1652 1112 2 74 v 227 1173 2 61 v 390 1173 V 399
1173 V 876 1173 V 885 1173 V 1167 1173 V 1176 1173 V
1652 1173 V 228 1174 1425 2 v 227 1235 2 61 v 390 1235
V 399 1235 V 876 1235 V 885 1235 V 1167 1235 V 1176 1235
V 1652 1235 V 227 1308 2 74 v 253 1283 a Fv(n)g FH(+)g(1)p
390 1308 V 399 1308 V 429 1259 a Ft(S)r(U)t FC(\(1)p
Ft(;)p FC(1\))p 429 1271 124 2 v 455 1300 a Ft(U)t FC(\(1\))569
1283 y FE(\012)672 1259 y Ft(S)r(O)q FC(\(2)p Ft(;n)p
FC(\))p 623 1271 224 2 v 623 1300 a Ft(S)r(O)q FC(\(2\))p
FB(\002)p Ft(S)r(O)q FC(\()p Ft(n)p FC(\))p 876 1308
2 74 v 884 1308 V 910 1283 a Fv(S)s(p)p FH(\(2)p Fv(n)h
FH(+)f(4\))p 1167 1308 V 1176 1308 V 58 w FD(2)p 1201
1290 29 2 v 12 w FE(\012)f FH(\()p FD(n)i FH(+)f FD(2)p
1309 1293 120 2 v 11 w FE(\010)f FD(n)i FH(+)f FD(2)p
1489 1293 V FH(\))p 1652 1308 2 74 v 227 1368 2 61 v
390 1368 V 399 1368 V 876 1368 V 885 1368 V 1167 1368
V 1176 1368 V 1652 1368 V 228 1370 1425 2 v 227 1430
2 61 v 390 1430 V 399 1430 V 876 1430 V 885 1430 V 1167
1430 V 1176 1430 V 1652 1430 V 227 1504 2 74 v 297 1478
a(6)p 390 1504 V 399 1504 V 575 1455 a Ft(S)r(p)p FC(\(6)p
Ft(;)p FC(I)-9 b(R)o(\))p 540 1467 196 2 v 540 1496 a
Ft(S)r(U)t FC(\(3\))p FB(\002)p Ft(U)t FC(\(1\))p 876
1504 2 74 v 884 1504 V 955 1478 a Fv(S)s(p)p FH(\(14\))p
1167 1504 V 1176 1504 V 289 w FD(14)p 1387 1485 57 2
v 1652 1504 2 74 v 227 1564 2 61 v 390 1564 V 399 1564
V 876 1564 V 885 1564 V 1167 1564 V 1176 1564 V 1652
1564 V 228 1566 1425 2 v 228 1574 V 227 1634 2 61 v 390
1634 V 399 1634 V 876 1634 V 885 1634 V 1167 1634 V 1176
1634 V 1652 1634 V 227 1708 2 74 v 297 1682 a FH(9)p
390 1708 V 399 1708 V 577 1659 a Ft(S)r(U)t FC(\(3)p
Ft(;)p FC(3\))p 527 1671 224 2 v 527 1700 a Ft(S)r FC(\()p
Ft(U)t FC(\(3\))p FB(\002)p Ft(U)t FC(\(3\)\))p 876 1708
2 74 v 884 1708 V 955 1682 a Fv(S)s(p)p FH(\(20\))p 1167
1708 V 1176 1708 V 289 w FD(20)p 1387 1689 57 2 v 1652
1708 2 74 v 227 1768 2 61 v 390 1768 V 399 1768 V 876
1768 V 885 1768 V 1167 1768 V 1176 1768 V 1652 1768 V
228 1770 1425 2 v 227 1830 2 61 v 390 1830 V 399 1830
V 876 1830 V 885 1830 V 1167 1830 V 1176 1830 V 1652
1830 V 227 1903 2 74 v 285 1878 a FH(15)p 390 1903 V
399 1903 V 572 1855 a Ft(S)r(O)623 1843 y Fm(?)641 1855
y FC(\(12\))p 540 1866 196 2 v 540 1895 a Ft(S)r(U)t
FC(\(6\))p FB(\002)p Ft(U)t FC(\(1\))p 876 1903 2 74
v 884 1903 V 955 1878 a Fv(S)s(p)p FH(\(32\))p 1167 1903
V 1176 1903 V 289 w FD(32)p 1387 1885 57 2 v 1652 1903
2 74 v 227 1964 2 61 v 390 1964 V 399 1964 V 876 1964
V 885 1964 V 1167 1964 V 1176 1964 V 1652 1964 V 228
1965 1425 2 v 227 2026 2 61 v 390 2026 V 399 2026 V 876
2026 V 885 2026 V 1167 2026 V 1176 2026 V 1652 2026 V
227 2102 2 77 v 285 2077 a FH(27)p 390 2102 V 399 2102
V 585 2048 a Ft(E)611 2055 y Fr(7\()p Fn(\000)p Fr(6\))p
555 2065 167 2 v 555 2094 a Ft(E)581 2099 y Fr(6)598
2094 y FB(\002)p Ft(S)r(O)q FC(\(2\))p 876 2102 2 77
v 884 2102 V 955 2077 a Fv(S)s(p)p FH(\(56\))p 1167 2102
V 1176 2102 V 289 w FD(56)p 1387 2084 57 2 v 1652 2102
2 77 v 227 2162 2 61 v 390 2162 V 399 2162 V 876 2162
V 885 2162 V 1167 2162 V 1176 2162 V 1652 2162 V 228
2164 1425 2 v 916 2892 a FH(76)p eop
%%Page: 77 78
77 77 bop 328 96 a FH(T)l(able)16 b(2:)22 b Fg(Homogeneous)16
b(symmetr)o(ic)d(quaternionic)i(manifolds)p 691 111 500
2 v 690 171 2 61 v 720 153 a FH(m)p 788 171 V 797 171
V 178 w Fv(G=H)p 1189 171 V 691 173 500 2 v 690 233 2
61 v 788 233 V 797 233 V 1189 233 V 690 307 2 74 v 719
281 a(m)p 788 307 V 797 307 V 912 258 a Ft(S)r(p)p FC(\(2)p
Ft(m)p FC(+2\))p 873 270 241 2 v 873 299 a Ft(S)r(p)p
FC(\(2\))p FB(\002)p Ft(S)r(P)5 b FC(\(2)p Ft(m)p FC(\))p
1189 307 2 74 v 690 367 2 61 v 788 367 V 797 367 V 1189
367 V 691 369 500 2 v 690 429 2 61 v 788 429 V 797 429
V 1189 429 V 690 503 2 74 v 719 477 a Fv(m)p 788 503
V 797 503 V 925 454 a Ft(S)r(U)t FC(\()p Ft(m;)p FC(2\))p
827 465 333 2 v 827 494 a Ft(S)r(U)t FC(\()p Ft(m)p FC(\))p
FB(\002)p Ft(S)r(U)t FC(\(2\))p FB(\002)p Ft(U)t FC(\(1\))p
1189 503 2 74 v 690 563 2 61 v 788 563 V 797 563 V 1189
563 V 691 564 500 2 v 690 625 2 61 v 788 625 V 797 625
V 1189 625 V 690 698 2 74 v 719 673 a Fv(m)p 788 698
V 797 698 V 925 650 a Ft(S)r(O)q FC(\(4)p Ft(;m)p FC(\))p
877 661 234 2 v 877 690 a Ft(S)r(O)q FC(\(4\))p FB(\002)p
Ft(S)r(O)q FC(\()p Ft(m)p FC(\))p 1189 698 2 74 v 690
758 2 61 v 788 758 V 797 758 V 1189 758 V 691 760 500
2 v 691 768 V 690 829 2 61 v 788 829 V 797 829 V 1189
829 V 690 896 2 68 v 728 871 a FH(2)p 788 896 V 797 896
V 971 851 a Ft(G)998 856 y Fr(2)p 951 859 87 2 v 951
888 a Ft(S)r FC(0\(4\))p 1189 896 2 68 v 690 957 2 61
v 788 957 V 797 957 V 1189 957 V 691 958 500 2 v 690
1018 2 61 v 788 1018 V 797 1018 V 1189 1018 V 690 1086
2 68 v 728 1061 a FH(7)p 788 1086 V 797 1086 V 974 1041
a Ft(F)996 1046 y Fr(4)p 894 1049 200 2 v 894 1078 a
Ft(S)r(p)p FC(\(6\))p FB(\002)p Ft(S)r(p)p FC(\(2\))p
1189 1086 2 68 v 690 1146 2 61 v 788 1146 V 797 1146
V 1189 1146 V 691 1148 500 2 v 690 1208 2 61 v 788 1208
V 797 1208 V 1189 1208 V 690 1276 2 68 v 715 1251 a FH(10)p
788 1276 V 797 1276 V 972 1231 a Ft(E)998 1236 y Fr(6)p
896 1239 196 2 v 896 1268 a Ft(S)r(U)t FC(\(6\))p FB(\002)p
Ft(U)t FC(\(1\))p 1189 1276 2 68 v 690 1336 2 61 v 788
1336 V 797 1336 V 1189 1336 V 691 1338 500 2 v 690 1398
2 61 v 788 1398 V 797 1398 V 1189 1398 V 690 1466 2 68
v 715 1440 a FH(16)p 788 1466 V 797 1466 V 972 1421 a
Ft(E)998 1426 y Fr(7)p 880 1429 227 2 v 880 1458 a Ft(S)r
FC(0\(12\))p FB(\002)p Ft(S)r(U)t FC(\(2\))p 1189 1466
2 68 v 690 1526 2 61 v 788 1526 V 797 1526 V 1189 1526
V 691 1528 500 2 v 690 1588 2 61 v 788 1588 V 797 1588
V 1189 1588 V 690 1656 2 68 v 715 1630 a FH(28)p 788
1656 V 797 1656 V 972 1611 a Ft(E)998 1616 y Fr(8)p 910
1619 167 2 v 910 1647 a Ft(E)936 1652 y Fr(7)954 1647
y FB(\002)p Ft(S)r(U)t FC(\(2\))p 1189 1656 2 68 v 690
1716 2 61 v 788 1716 V 797 1716 V 1189 1716 V 691 1718
500 2 v -5 1902 a Fw(Ac)n(kno)n(wledgemen)n(ts)-5 2011
y FH(A.C.)17 b(and)i(S.)f(F.)f(w)o(ould)h(lik)o(e)e(to)j(thank)f(the)g
(Institute)f(for)h(Theoretical)g(Ph)o(ysics)f(at)h(U.)g(C.)f(San)o(ta)
-5 2071 y(Barbara)g(for)g(its)f(kind)g(hospitalit)o(y)f(and)i(where)f
(part)g(of)h(this)f(w)o(ork)g(w)o(as)h(completed.)-5
2237 y Fw(References)20 2346 y FH([1])24 b(N.)13 b(Seib)q(erg)h(and)g
(E.)g(Witten,)g(Nucl.)e(Ph)o(ys.)i(B426)h(\(1994\))g(19;)h(Nucl.)c(Ph)o
(ys.)i(B431)h(\(1994\))g(484.)20 2447 y([2])24 b(A.)14
b(Klemm)o(,)e(W.)j(Lerc)o(he,)g(S.)g(Theisen)g(and)h(S.)e(Y)l(ankielo)o
(vicz,)f(Ph)o(ys.)i(Lett.)f(B344)j(\(1995\))f(169;)96
2507 y(P)l(.)f(Argyres)h(and)h(A.)e(F)l(araggi,)i(Ph)o(ys.)f(Rev.)f
(Lett.)h(74)h(\(1995\))h(3931.)20 2607 y([3])24 b(A.)12
b(Ceresole,)i(R.)f(D'Auria)g(and)i(S.)e(F)l(errara,)h(Ph)o(ys.)f(Lett.)
h(339B)g(\(1994\))i(71,)e(hep-th/9408036)p
 [[441 141 520 153] [1 1 1 [3 3]] [0 0 1]] (http://ru.arXiv.org/abs/hep-th/9408036) pdfm 
(.)20 2707 y([4])24 b(A.)18 b(Ceresole,)g(R.)g(D'Auria,)h(S.)f(F)l
(errara)h(and)h(A.)e(V)l(an)h(Pro)q(ey)o(en,)f(Nucl.)g(Ph)o(ys.)g(B444)
i(\(1995\))96 2768 y(92,)f(hep-th/9502072)p
 [[114 103 194 115] [1 1 1 [3 3]] [0 0 1]] (http://ru.arXiv.org/abs/hep-th/9502072) pdfm 
(;)j(\\On)d(Electromagnetic)d(Dualit)o(y)h(in)h(Lo)q(cally)g(Sup)q
(ersymmetric)d(N=2)916 2892 y(77)p eop
%%Page: 78 79
78 78 bop 96 15 a FH(Y)l(ang-Mills)14 b(Theory",)i(hep-th/9412200)p
 [[203 763 282 775] [1 1 1 [3 3]] [0 0 1]] (http://ru.arXiv.org/abs/hep-th/9412200) pdfm 
(,)i(Pro)q(ceedings)e(of)g(the)f(W)l(orkshop)h(on)g(Ph)o(ysics)f(from)
96 76 y(the)h(Planc)o(k)f(Scale)h(to)g(Electromagnetic)e(Scale,)i(W)l
(arsa)o(w)h(1994.)20 177 y([5])24 b(C.)16 b(M.)f(Hull)g(and)i(P)l(.K.)e
(T)l(o)o(wnsend,)i(Nucl.)d(Ph)o(ys.)i(B438)h(\(1995\))h(109,)f
(hep-th/9410167)p
 [[415 725 494 737] [1 1 1 [3 3]] [0 0 1]] (http://ru.arXiv.org/abs/hep-th/9410167) pdfm 
(.)20 279 y([6])24 b(E.)f(Witten,)i(\\String)f(Theory)g(Dynamics)e(in)i
(V)l(arious)g(Dimensions",)g(Nucl.)e(Ph)o(ys.)h(B443)96
339 y(\(1995\))17 b(85,)g(hep-th/9503124)p
 [[150 686 229 698] [1 1 1 [3 3]] [0 0 1]] (http://ru.arXiv.org/abs/hep-th/9503124) pdfm 
(.)20 441 y([7])24 b(M.)29 b(J.)g(Du\013,)34 b(Nucl.)28
b(Ph)o(ys.)h(B442)i(\(1995\))g(47;)37 b(for)30 b(a)g(recen)o(t)f
(review)f(see)i(also)g(\\Elec-)96 501 y(tric/Magnetic)15
b(Dualit)o(y)g(and)i(its)f(Stringy)g(Origins",)g(hep-th/9509106)p
 [[342 647 421 659] [1 1 1 [3 3]] [0 0 1]] (http://ru.arXiv.org/abs/hep-th/9509106) pdfm 
(.)20 603 y([8])24 b(A.)c(Sen,)i(Nucl.)d(Ph)o(ys)i(B388)h(\(1992\))h
(457)f(and)g(Ph)o(ys.)e(Lett.)h(B303)h(\(1993\))h(22;)h(A)c(Sen)h(and)
96 663 y(J.H.)e(Sc)o(h)o(w)o(arz,)g(Nucl.)g(Ph)o(ys.)h(B411)h(\(1994\))
h(35;)g(Ph)o(ys.)e(Lett.)g(B312)h(\(1993\))h(105)f(;)h(A.)e(Sen,)96
723 y(\\Strong{W)l(eak)g(coupling)f(dualit)o(y)f(in)h(F)l
(our{dimensional)f(String)h(Theory",)h(preprin)o(t)e(hep-)p
 [[502 593 524 605] [1 1 1 [3 3]] [0 0 1]] (http://ru.arXiv.org/abs/hep-th/9402002) pdfm 
96 783 a(th/9402002)p
 [[71 579 152 591] [1 1 1 [3 3]] [0 0 1]] (http://ru.arXiv.org/abs/hep-th/9402002) pdfm 
(.)20 885 y([9])24 b(A.)17 b(Strominger,)h(\\Massless)h(blac)o(k)f
(holes)h(and)g(conifolds)f(in)h(string)g(theories",)f(Nucl.)g(Ph)o(ys.)
96 945 y(B451)e(\(1995\))i(96,)f(hep-th/9504090)p
 [[180 540 259 552] [1 1 1 [3 3]] [0 0 1]] (http://ru.arXiv.org/abs/hep-th/9504090) pdfm 
(;)-5 1047 y([10])25 b(B.)15 b(Greene,)g(D.)h(Morrison)h(and)f(A.)g
(Strominger,)e(\\Blac)o(k)h(hole)h(condensation)h(and)g(the)f(uni\014-)
96 1107 y(cation)g(of)g(string)h(v)m(acua",)g(Nucl.)d(Ph)o(ys.)i(B451)h
(\(1995\))h(109,)f(hep-th/9504145)p
 [[372 501 452 513] [1 1 1 [3 3]] [0 0 1]] (http://ru.arXiv.org/abs/hep-th/9504145) pdfm 
(.)-5 1209 y([11])25 b(S.)e(F)l(errara,)j(J.)e(A.)f(Harv)o(ey)l(,)i(A.)
e(Strominger)g(and)i(C.)f(V)l(afa,)i(\\Second-quan)o(tized)e(Mirror)96
1269 y(Symme)o(try",)13 b(Ph)o(ys.)j(Lett.)g(B361)h(\(1995\))h(59,)e
(hep-th/9505162)p
 [[306 462 386 474] [1 1 1 [3 3]] [0 0 1]] (http://ru.arXiv.org/abs/hep-th/9505162) pdfm 
(.)-5 1371 y([12])25 b(S.)f(Kac)o(hru)h(and)g(C.)g(V)l(afa,)i(\\Exact)e
(Results)g(for)g(N=2)g(Compacti\014cations)f(of)i(Heterotic)96
1431 y(Strings",)16 b(Nucl.)f(Ph)o(ys.)g(B450)i(\(1995\))h(69,)f
(hep-th/9505105)p
 [[292 424 371 436] [1 1 1 [3 3]] [0 0 1]] (http://ru.arXiv.org/abs/hep-th/9505105) pdfm 
(.)-5 1533 y([13])25 b(M.)11 b(Bill\023)-24 b(o,)11 b(R.)g(D'Auria,)h
(S.)f(F)l(errara,)i(P)l(.)e(F)l(r)o(\022)-23 b(e,)12
b(P)l(.)f(Soriani)h(and)h(A.)e(V)l(an)h(Pro)q(ey)o(en,)g(\\R-symmetry)
96 1593 y(and)f(the)g(top)q(ological)h(t)o(wist)f(of)h(N=2)f
(e\013ectiv)o(e)e(sup)q(ergra)o(vities)i(of)g(heterotic)f(strings",)j
(preprin)o(t)96 1653 y(hep-th)j(9505123)p
 [[95 370 172 382] [1 1 1 [3 3]] [0 0 1]] (http://ru.arXiv.org/abs/hep-th/9505123) pdfm 
(.)-5 1755 y([14])25 b(A.)10 b(Klemm)o(,)f(W.)i(Lerc)o(he)g(and)h(S.)f
(Theisen,)h(\\Nonp)q(erturbativ)o(e)f(E\013ectiv)o(e)f(Actions)h(of)g
(N=2)h(Su-)96 1815 y(p)q(ersymmetri)o(c)i(Gauge)19 b(Theories",)f
(preprin)o(t)f(CERN-TH/95-104,)j(LMU-TPW)e(95-7,)h(hep-)p
 [[502 331 524 343] [1 1 1 [3 3]] [0 0 1]] (http://ru.arXiv.org/abs/hep-th/9505150) pdfm 
96 1875 a(th/9505150)p
 [[71 317 152 329] [1 1 1 [3 3]] [0 0 1]] (http://ru.arXiv.org/abs/hep-th/9505150) pdfm 
(.)-5 1977 y([15])25 b(C.)16 b(Gomez)e(and)j(E.)f(Lop)q(ez,)h(Ph)o(ys.)
f(Lett.)f(B356)i(\(1995\))h(487,)f(hep-th/9506024)p
 [[377 293 456 305] [1 1 1 [3 3]] [0 0 1]] (http://ru.arXiv.org/abs/hep-th/9506024) pdfm 
(.)-5 2079 y([16])25 b(I.)17 b(An)o(toniadis,)g(S.)g(F)l(errara,)h(E.)g
(Ga)o(v)m(a,)h(K.S.)e(Narain)g(and)i(T.R.)e(T)l(a)o(ylor,)h(Nucl.)e(Ph)
o(ys.)h(B447)96 2139 y(\(1995\))g(35,)g(hep-th/9504034)p
 [[150 254 229 266] [1 1 1 [3 3]] [0 0 1]] (http://ru.arXiv.org/abs/hep-th/9504034) pdfm 
19 w(\(1995\).)-5 2240 y([17])25 b(B.)11 b(de)i(Wit,)g(V.)f(Kapluno)o
(vsky)l(,)g(J.)h(Louis)g(and)g(D.)g(L)q(\177)-26 b(ust,)15
b(Nucl.)c(Ph)o(ys.)h(B451)i(\(1995\))g(53,)g(hep-th)p
 [[491 229 524 241] [1 1 1 [3 3]] [0 0 1]] (http://ru.arXiv.org/abs/hep-th/9504006) pdfm 
96 2301 a(9504006)p
 [[71 215 135 227] [1 1 1 [3 3]] [0 0 1]] (http://ru.arXiv.org/abs/hep-th/9504006) pdfm 
19 w(\(1995\).)-5 2402 y([18])25 b(M.)18 b(Bill\023)-24
b(o,)19 b(A.)g(Ceresole,)g(R.)g(D'Auria,)g(S.)h(F)l(errara,)g(P)l(.)f
(F)l(r)o(\022)-23 b(e,)19 b(T.)h(Regge,)g(P)l(.)f(Soriani)h(and)g(A.)96
2463 y(V)l(an)i(Pro)q(ey)o(en,)i(\\A)f(Searc)o(h)f(for)h(non-p)q
(erturbativ)o(e)g(Dualities)f(of)h(Lo)q(cal)g(N=2)g(Y)l(ang-Mills)96
2523 y(Theories)13 b(from)g(Calabi-Y)l(au)h(Threefolds",)g(preprin)o(t)
f(hep-th/9506075)p
 [[340 161 420 173] [1 1 1 [3 3]] [0 0 1]] (http://ru.arXiv.org/abs/hep-th/9506075) pdfm 
(,)k(to)d(app)q(ear)h(on)f(Class.)96 2583 y(and)i(Quan)o(tum)g(Gra)o
(v.)-5 2685 y([19])25 b(A.)15 b(Klemm)o(,)e(W.)j(Lerc)o(he)g(and)g(P)l
(.)g(Ma)o(yr,)g(Ph)o(ys.)f(Lett.)h(B357)h(\(1995\))h(313,)f
(hep-th/9506112)p
 [[435 123 514 135] [1 1 1 [3 3]] [0 0 1]] (http://ru.arXiv.org/abs/hep-th/9506112) pdfm 
(.)916 2892 y(78)p eop
%%Page: 79 80
79 79 bop -5 15 a FH([20])25 b(A.)e(Ceresole,)h(R.)g(D'Auria)f(and)i
(S.)e(F)l(errara,)j(\\The)e(Symplectic)d(Structure)i(of)i(N=2)f(Su-)96
76 y(p)q(ergra)o(vit)o(y)c(and)i(its)f(Cen)o(tral)g(Extension",)h
(Nucl.)e(Ph)o(ys.)h(B46)h(\(Pro)q(c.)f(Suppl.\))g(\(1996\))i(67,)96
136 y(hep-th/9509160)p
 [[95 734 174 746] [1 1 1 [3 3]] [0 0 1]] (http://ru.arXiv.org/abs/hep-th/9509160) pdfm 
(.)-5 238 y([21])i(J.)15 b(Bagger)i(and)g(E.)f(Witten,)f(Nucl.)g(Ph)o
(ys.)32 b(B222)17 b(\(1983\))g(1.)-5 339 y([22])25 b(N.)14
b(J.)h(Hitc)o(hin,)e(A.)i(Karlhede,)f(U.)h(Lindstrom)g(and)h(M.)f(Ro)q
(cek,)f(\\Hyp)q(erK\177)-24 b(ahler)15 b(Metrics)f(and)96
399 y(Sup)q(ersymmetry)o(",)g(Comm)o(un.)f(math.)i(Ph)o(ys.)h(108)h
(\(1987\))h(535.)-5 501 y([23])25 b(K.)15 b(Galic)o(ki,)f(Comm.)g
(Math.)i(Ph)o(ys.)g(108)h(\(1987\))h(117.)-5 603 y([24])25
b(R.)15 b(D'Auria,)g(S.)h(F)l(errara)h(and)g(P)l(.)e(F)l(r)o(\023)-23
b(e,)16 b(Nucl.)e(Ph)o(ys.)i(B359)h(\(1991\))h(705.)-5
705 y([25])25 b(D.)17 b(Anselmi)d(and)k(P)l(.)f(F)l(r)o(\023)-23
b(e,)17 b(Nucl.)f(Ph)o(ys.)g(B392)i(\(1993\))h(401;)g(Nucl.)d(Ph)o(ys.)
g(B404)j(\(1993\))f(288;)96 765 y(Nucl.)c(Ph)o(ys.)i(B416)h(\(1994\))h
(255;)f(Ph)o(ys.)e(Lett.)h(B347)h(\(1995\))h(247.)-5
866 y([26])25 b(B.)15 b(de)h(Wit,)f(P)l(.)h(G.)g(Lau)o(w)o(ers)h(and)g
(A.)e(V)l(an)h(Pro)q(ey)o(en)g(Nucl.)f(Ph)o(ys.)h(B255)h(\(1985\))h
(569.)-5 968 y([27])25 b(L.)11 b(Castellani,)h(R.)g(D'Auria)f(and)i(S.)
e(F)l(errara,)i(Ph)o(ys.)e(Lett.)g(241B)i(\(1990\))g(57;)h(Class.)e
(Quan)o(tum)96 1028 y(Gra)o(v.)j(7)i(\(1990\))h(1767.)-5
1130 y([28])25 b(E.)14 b(Cremmer,)d(S.)k(F)l(errara,)f(L.)h(Girardello)
f(and)h(A.)f(V)l(an)h(Pro)q(ey)o(en,)f(Nucl.)f(Ph)o(ys.)h(B212)i
(\(1983\))96 1190 y(413.)-5 1292 y([29])25 b(S.)18 b(F)l(errara,)i(L.)f
(Girardello)g(and)g(M.)g(P)o(orrati,)g(\\Minimal)e(Higgs)j(Branc)o(h)e
(for)i(the)f(Breaking)96 1352 y(of)i(Half)g(of)g(the)g(Sup)q
(ersymmetry)d(in)j(N=2)g(Sup)q(ergra)o(vit)o(y",)h(preprin)o(t)e
(CERN-TH/95-268,)96 1412 y(hep-th/9510074)p
 [[95 428 174 440] [1 1 1 [3 3]] [0 0 1]] (http://ru.arXiv.org/abs/hep-th/9510074) pdfm 
(.)-5 1514 y([30])25 b(J.)17 b(P)o(olc)o(hinski)g(and)i(A.)e
(Strominger,)g(\\New)i(v)m(acua)f(for)h(T)o(yp)q(e)f(I)q(I)g(String)g
(Theory",)h(preprin)o(t)96 1574 y(hep-th/9510227)p
 [[95 389 174 401] [1 1 1 [3 3]] [0 0 1]] (http://ru.arXiv.org/abs/hep-th/9510227) pdfm 
(.)-5 1676 y([31])25 b(L.)f(Castellani,)h(R.)f(D'Auria)g(and)g(P)l(.)g
(F)l(r)o(\023)-23 b(e,)26 b(\\Sup)q(ergra)o(vit)o(y)e(and)h(Sup)q
(erstring)f(Theory:)38 b(a)96 1736 y(Geometric)14 b(P)o(ersp)q(ectiv)o
(e",)g(W)l(orld)i(Scien)o(ti\014c)f(\(1991\))i(,)f(V)l(olumes)e(1,)j
(2,)f(3.)-5 1838 y([32])25 b(I.)12 b(An)o(toniadis,)h(H.)f(P)o(artouc)o
(he)h(and)h(T.)f(R.)f(T)l(a)o(ylor,)i(\\Sp)q(on)o(taneous)h(Breaking)d
(of)i(N=2)f(Global)96 1898 y(Sup)q(ersymmetry)o(",)h(preprin)o(t)h
(hep-th/9512006)p
 [[234 311 313 323] [1 1 1 [3 3]] [0 0 1]] (http://ru.arXiv.org/abs/hep-th/9512006) pdfm 
(.)-5 2000 y([33])25 b(L.)d(Andrianop)q(oli,)h(M.)f(Bertolini,)f(A.)h
(Ceresole,)g(R.)g(D'Auria,)h(S.)f(F)l(errara)g(and)h(P)l(.)f(F)l(r)o
(\023)-23 b(e,)23 b(\\)96 2060 y(General)15 b(Matter)h(Coupled)h(N=2)f
(Sup)q(ergra)o(vit)o(y",)f(preprin)o(t)h(hep-th/9603004)p
 [[375 273 455 285] [1 1 1 [3 3]] [0 0 1]] (http://ru.arXiv.org/abs/hep-th/9603004) pdfm 
(.)-5 2162 y([34])25 b(B.)12 b(de)h(Wit,)f(P)l(.G.)h(Lau)o(w)o(ers,)h
(R.)e(Philipp)q(e,)h(Su)g(S.Q.)f(and)i(A.)e(V)l(an)h(Pro)q(ey)o(en,)g
(Ph)o(ys.)g(Lett.)f(134B)96 2222 y(\(1984\))k(37;)f(S.)g(J.)f(Gates,)h
(Nucl.)f(Ph)o(ys.)g(B238)h(\(1984\))i(349;)f(B.)e(de)g(Wit)h(and)g(A.)f
(V)l(an)h(Pro)q(ey)o(en,)96 2282 y(Nucl.)f(Ph)o(ys.)i(B245)h(\(1984\))h
(89.)-5 2384 y([35])25 b(J.)15 b(P)l(.)h(Derendinger,)g(S.)f(F)l
(errara)i(and)g(A.)e(Masiero,)h(Ph)o(ys.)g(Lett.)f(143B)i(\(1984\))h
(133.)-5 2485 y([36])25 b(E.)15 b(Cremmer,)e(C.)i(Kounnas,)i(A.)e(V)l
(an)h(Pro)q(ey)o(en,)g(J.P)l(.)f(Derendinger,)g(S.)h(F)l(errara,)f(B.)g
(De)h(Wit)96 2546 y(and)g(L.)h(Girardello,)e(Nucl.)g(Ph)o(ys.)g(B250)i
(\(1985\))h(385.)-5 2647 y([37])25 b(B.)15 b(de)h(Wit)g(and)h(H.)e
(Nicolai,)f(Nucl.)h(Ph)o(ys.)h(B208)h(\(1982\))h(323.)-5
2749 y([38])25 b(S.)15 b(F)l(errara,)h(J.)g(Sc)o(herk)f(and)i(B.)f
(Zumino,)e(Nucl.)h(Ph)o(ys.)g(B121)i(\(1977\))h(393.)916
2892 y(79)p eop
%%Page: 80 81
80 80 bop -5 15 a FH([39])25 b(S.)15 b(F)l(errara)i(and)g(L.)f(Maiani,)
g(Pro)q(c.)g(V)g(Silarg)g(Symp.,)e(W)l(orld)i(Scien)o(ti\014c)f
(\(1986\);)i(S.)f(Cecotti,)96 76 y(L.)f(Girardello)f(and)h(M.)g(P)o
(orrati,)f(Nucl.)g(Ph)o(ys.)g(B268)i(\(1986\))g(295;)g(A.)f(Ceresole,)f
(R.)g(D'Auria,)96 136 y(S.)h(F)l(errara,)h(P)l(.)g(F)l(r)o(\023)-23
b(e)16 b(and)h(E.)f(Maina,)g(Nucl.)e(Ph)o(ys.)i(B268)h(\(1986\))h(317.)
-5 238 y([40])25 b(S.)15 b(F)l(errara,)h(C.)g(Kounnas,)h(M.)f(P)o
(orrati)g(and)h(F.)f(Zwirner,)f(Nucl.)g(Ph)o(ys.)g(B318)i(\(1989\))h
(75.)-5 339 y([41])25 b(I.)15 b(An)o(toniadis,)g(Ph)o(ys.)h(Lett.)g
(B246)h(\(1990\))h(377.)-5 441 y([42])25 b(E.)18 b(Cremmer,)e(C.)j
(Kounnas,)h(S.)f(F)l(errara)g(and)g(D.)g(Nanop)q(oulos,)i(Ph)o(ys.)d
(Lett.)h(133B)h(\(1983\))96 501 y(61.)-5 603 y([43])25
b(C.)16 b(Zac)o(hos)g(Ph)o(ys.)g(Lett.)g(76B)g(\(1978\))i(329.)-5
705 y([44])25 b(D.Z.)15 b(F)l(reedman,)f(A.)h(Das)j(Nucl.)c(Ph)o(ys.)i
(B120)h(\(1977\))h(221)-5 806 y([45])25 b(P)l(.S.)15
b(Aspin)o(w)o(all)g(hep{th/9510142)-5 908 y([46])25 b(M.K:)15
b(Gaillard,)g(B.)g(Zumino,)g(Nucl.)f(Ph)o(ys.)32 b(B193)17
b(\(1981\))h(221)-5 1010 y([47])25 b(P)l(.)15 b(F)l(r)o(\023)-23
b(e)16 b(Lectures)g(giv)o(en)g(at)g(the)g(T)l(rieste)g(1995)h(Spring)g
(sc)o(ho)q(ol,)f(preprin)o(t)f(hep-th/9512043)p
 [[428 525 508 537] [1 1 1 [3 3]] [0 0 1]] (http://ru.arXiv.org/abs/hep-th/9512043) pdfm 
1 w(.)-5 1111 y([48])25 b(S.)15 b(F)l(errara,)h(A.)g(V)l(an)g(Pro)q(ey)
o(en)g(Class.)g(Quan)o(tum)g(Gra)o(v.)f(2)i(\(1989\))h(124.)-5
1213 y([49])25 b(B.)15 b(Zumino,)f(Ph)o(ys.)i(Lett.)32
b(B87)17 b(\(1979\))g(203)-5 1315 y([50])25 b(E.)19 b(Cremmer,)e(B.)i
(Julia,)i(J.)e(Sc)o(herk,)g(S.)h(F)l(errara,)h(L.)f(Girardello,)f(P)l
(.)h(v)m(an)g(Nieu)o(w)o(enh)o(uizen,)96 1375 y(Nucl.)14
b(Ph)o(ys.)32 b(B147)17 b(\(1979\))h(105.)-5 1477 y([51])25
b(E.)14 b(Cremmer,)e(B.)i(Julia,)g(J.)h(Sc)o(herk,)f(S.)h(F)l(errara,)f
(P)l(.)h(v)m(an)h(Nieu)o(w)o(enh)o(uizen,)c(Ph)o(ys.)i(Lett.)30
b(B79)96 1537 y(\(1978\))17 b(231.)-5 1639 y([52])25
b(D.Z.)14 b(F)l(reedman,)e(S.)j(F)l(errara,)g(P)l(.)f(v)m(an)i(Nieu)o
(w)o(enh)o(uize)o(n)c(Ph)o(ys.)j(Rev.)e(Lett.)i(D13)h(\(1976\))g(3214.)
-5 1740 y([53])25 b(S.)15 b(Deser,)h(B.)f(Zumino,)g(Ph)o(ys.)h(Lett.)f
(B62)i(\(1976\))h(335.)-5 1842 y([54])25 b(E.)14 b(Cremmer,)d(S.)k(F)l
(errara,)f(L.)h(Girardello)f(and)h(A.)f(V)l(an)h(Pro)q(ey)o(en,)f
(Nucl.)f(Ph)o(ys.)h(B212)i(\(1983\))96 1902 y(413)-5
2004 y([55])25 b(J.)15 b(Bagger,)i(E.)f(Witten,)f(Ph)o(ys.)g(Lett.)h
(B115)h(\(1982\))h(202.)-5 2106 y([56])25 b(J.)15 b(Bagger,)i(E.)f
(Witten,)f(Nucl.)f(Ph)o(ys.)i(B222)h(\(1983\))h(1.)-5
2207 y([57])25 b(B.)15 b(de)h(Wit)g(and)h(A.)e(V)l(an)h(Pro)q(ey)o(en,)
g(Nucl.)e(Ph)o(ys.)32 b(B245)17 b(\(1984\))h(89;)-5 2309
y([58])25 b(E.)15 b(Cremmer,)d(C.)j(Kounnas,)i(A.)d(V)l(an)i(Pro)q(ey)o
(en,)f(J.)g(P)l(.)g(Derendinger,)g(S.)g(F)l(errara,)g(B.)g(de)g(Wit)96
2369 y(and)h(L.)h(Girardello,)e(Nucl.)g(Ph)o(ys.)g(B250)i(\(1985\))h
(385;)-5 2471 y([59])25 b(A.)15 b(Strominger,)f(Comm.)g(Math.)i(Ph)o
(ys.)g(133)h(\(1990\))h(163.)-5 2573 y([60])25 b(P)l(.)18
b(F)l(r)o(\023)-23 b(e)18 b(and)i(P)l(.)e(Soriani,)h(The)g(N=2)g(W)l
(onderland:)27 b(from)17 b(Calabi{Y)l(au)j(manifolds)d(to)j(top)q(o-)96
2633 y(logical)15 b(\014eld)h(theories,)f(W)o(ORLD)i(SCIENTIFIC,)e
(Singap)q(ore)i(1995.)-5 2734 y([61])25 b(E.)16 b(Cremme)o(r)e(and)i
(A.)g(V)l(an)g(Pro)q(ey)o(en)g(Class.)g(Quan)o(tum)g(Gra)o(v.)f(2)i
(\(1985\))h(445.)916 2892 y(80)p eop
%%Page: 81 82
81 81 bop -5 15 a FH([62])25 b(D.V.)15 b(Alekseevskii,)d(Math.)k(USSR)g
(Izv)o(estija)f(9)i(\(1975\))g(297.)-5 117 y([63])25
b(S.)17 b(Cecotti,)h(S.)g(F)l(errara)h(and)f(L.)h(Girardello,)f(Ph)o
(ys.)f(Lett.)h(213B)h(\(1988\))h(443;)g(In)o(t.)d(J.)h(Mo)q(d.)96
177 y(Ph)o(ys.)d(A4\(1989\))j(2475.)-5 279 y([64])25
b(S.)15 b(F)l(errara,)h(S:)g(Sabharw)o(al,)h(Nucl.)e(Ph)o(ys.)g(B332)i
(\(1990\))h(317.)-5 381 y([65])25 b(B.)15 b(de)h(Wit,)f(F.)h(V)l
(anderseyp)q(en)g(and)h(A.)e(V)l(an)h(Pro)q(ey)o(en)g(Nucl.)f(Ph)o(ys.)
32 b(B400)17 b(\(1993\))h(463.)-5 482 y([66])25 b(B.)15
b(de)h(Wit,)f(A.)h(V)l(an)g(Pro)q(ey)o(en,)g(Isometries)e(of)i(sp)q
(ecial)g(manifolds,)f(hep-th/9505097)p
 [[405 651 484 663] [1 1 1 [3 3]] [0 0 1]] (http://ru.arXiv.org/abs/hep-th/9505097) pdfm 
(.)-5 584 y([67])25 b(S.)15 b(F)l(errara,)h(J.)g(Sc)o(herk)f(and)i(B.)f
(Zumino,)e(Nucl.)h(Ph)o(ys.)32 b(B121)17 b(\(1977\))g(393.)-5
686 y([68])25 b(E.)16 b(Calabi)g(and)h(E.)f(Visen)o(tini,)e(Ann.)h(of)i
(Math.)f(71)h(\(1960\))g(472.)-5 788 y([69])25 b(C.)16
b(Zac)o(hos)g(Ph)o(ys.)g(Lett.)32 b(76B)17 b(\(1978\))g(329)-5
889 y([70])25 b(A.)15 b(Ceresole,)h(R.)g(D'Auria,)g(S.)g(F)l(errara,)g
(W.)g(Lerc)o(he)g(and)h(J.)g(Louis)g(In)o(t.)f(J.)g(Mo)q(d.)g(Ph)o(ys.)
33 b(A8)96 949 y(\(1993\))17 b(79.)-5 1051 y([71])25
b(L.J.)12 b(Dixon,)h(V.)f(S.)g(Kapluno)o(vsky)h(and)g(J.)g(Louis,)g
(Nucl.)f(Ph)o(ys.)g(B329)h(\(1990\))i(27;)f(P)l(.)e(Candelas)96
1111 y(and)18 b(X.C.)e(De)i(La)g(Ossa,)g(Nucl.)f(Ph)o(ys.)g(B355)h
(\(1991\))h(455;)g(S.)e(F)l(errara)h(and)g(J.)f(Louis,)i(Ph)o(ys.)96
1172 y(Lett.)c(B278)i(\(1992\))h(240.)916 2892 y(81)p
eop
%%Trailer
end 
end

userdict /end-hook known{end-hook}if
%%EOF