From e0c6872cf40896c7be36b11dcc744620f10adf1d Mon Sep 17 00:00:00 2001 From: Norbert Preining Date: Mon, 2 Sep 2019 13:46:59 +0900 Subject: Initial commit --- .../hypertex/tanmoy/ghostview-1.5-hacked/test.ps | 3302 ++++++++++++++++++++ 1 file changed, 3302 insertions(+) create mode 100644 support/hypertex/tanmoy/ghostview-1.5-hacked/test.ps (limited to 'support/hypertex/tanmoy/ghostview-1.5-hacked/test.ps') diff --git a/support/hypertex/tanmoy/ghostview-1.5-hacked/test.ps b/support/hypertex/tanmoy/ghostview-1.5-hacked/test.ps new file mode 100644 index 0000000000..84b87c38fc --- /dev/null +++ b/support/hypertex/tanmoy/ghostview-1.5-hacked/test.ps @@ -0,0 +1,3302 @@ +%!PS-Adobe-3.0 +%%Creator: dvips 5.51 Copyright 1986, 1993 Radical Eye Software +%%Title: contact.dvi +%%CreationDate: Tue Nov 1 16:26:57 1994 +%%Pages: 14 +%%PageOrder: Ascend +%%BoundingBox: 0 0 612 792 +%%EndComments +%DVIPSCommandLine: ./dvips -o contact.ps contact.dvi +%DVIPSSource: TeX output 1994.09.28:1334 +%%BeginProlog +%%BeginProcSet: tex.pro +/TeXDict 250 dict def TeXDict begin /N{def}def /B{bind def}N /S{exch}N /X{S N} +B /TR{translate}N /isls false N /vsize 11 72 mul N /@rigin{isls{[0 -1 1 0 0 0] +concat}if 72 Resolution div 72 VResolution div neg scale isls{Resolution hsize +-72 div mul 0 TR}if Resolution VResolution vsize -72 div 1 add mul TR matrix +currentmatrix dup dup 4 get round 4 exch put dup dup 5 get round 5 exch put +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 +/IE 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 IE N end dup{/foo setfont}2 array copy cvx N load 0 nn +put /ctr 0 N[}B /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 dup definefont setfont}B /ch-width{ch-data +dup length 5 sub get}B /ch-height{ch-data dup length 4 sub get}B /ch-xoff{128 +ch-data dup length 3 sub get sub}B /ch-yoff{ch-data dup length 2 sub get 127 +sub}B /ch-dx{ch-data dup length 1 sub get}B /ch-image{ch-data dup 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 /sf 0 N /CharBuilder{save 3 1 roll S dup /base get 2 index get +S /BitMaps get S get /ch-data X pop /ctr 0 N ch-dx 0 ch-xoff ch-yoff ch-height +sub ch-xoff ch-width add ch-yoff setcachedevice ch-width ch-height true[1 0 0 +-1 -.1 ch-xoff sub ch-yoff .1 add]{ch-image}imagemask restore}B /D{/cc X dup +type /stringtype ne{]}if nn /base get cc ctr put nn /BitMaps get S ctr S sf 1 +ne{dup dup length 1 sub dup 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 dup 1 get dup mul exch 0 get dup mul add +.99 lt{/FV}{/RV}ifelse load def pop}N /eop{SI restore showpage userdict +/eop-hook known{eop-hook}{pop}ifelse}N /@start{userdict /start-hook known{start-hook} +if /VResolution X /Resolution X 1000 div /DVImag X /IE 256 array N 0 1 255{IE +S 1 string dup 0 3 index put cvn put}for 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 /rulex 0 N /ruley +0 N /v{/ruley X /rulex X V}B /V{}B /RV statusdict begin /product where{pop +product dup length 7 ge{0 7 getinterval dup(Display)eq exch 0 4 getinterval +(NeXT)eq or}{pop false}ifelse}{false}ifelse end{{gsave TR -.1 -.1 TR 1 1 scale +rulex ruley false RMat{BDot}imagemask grestore}}{{gsave TR -.1 -.1 TR rulex +ruley scale 1 1 false RMat{BDot}imagemask grestore}}ifelse B /FV{gsave +transform round exch round exch itransform moveto rulex 0 rlineto 0 ruley neg +rlineto rulex neg 0 rlineto fill grestore}B /a{moveto}B /delta 0 N /tail{dup +/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: pdf.pro +/PDFdict 10 dict dup begin +/braindeaddistill 50 def +/rfch % remove first charcter of string +{dup length 1 sub 1 exch getinterval} def +/lookuptarget % str arr lookuptarget arr target true + % or arr false +{exch rfch dup % arr str' str' + /TargetAnchors where + {pop TargetAnchors dup % arr str' str' TargetAnchors TargetAnchors + 3 -1 roll known % arr str' TargetAnchors boolean + {exch get true} % arr target true + {pop (target unknown:)== == false} % arr false + ifelse} + {pop pop % arr + (target dictionary unknown) == false} % arr false + ifelse} +bind def +/initmat matrix currentmatrix def +/pdfmnew % str arr +{exch dup rfch exch 3 -1 roll % str' str arr +lookuptarget % str' arr [target] bool + {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} +bind def +/pdfmold +{exch dup rfch exch 3 -1 roll +lookuptarget + {mark 4 1 roll % put a mark below the source array and the array containing + % the page + % the rectangle array of the destination and the FitH parameter + % and below the Title string + /Title 4 1 roll % put /Title in front of Title string + aload pop % put the array elements on the stack + exch % exchange the FitH parameter and the Rect array + pop % Get rid of the Rect array + /Page 3 1 roll % put a /Page in front of the page number + /View exch % put a /View below the FitH parameter + [ exch /FitH exch ] % put in the /FitH + 5 -1 roll + aload pop pop + 0 3 getinterval + /Rect 3 1 roll + /Border exch + /LNK gsave initmat setmatrix pdfmark grestore} + {pop pop} + ifelse} +bind def +/pdfm +/currentdistillerparams where + {pop + currentdistillerparams + dup /CoreDistVersion known + {/CoreDistVersion get} + {0} + ifelse dup + braindeaddistill le + {(WARNING: switching to old pdfm because version =) == == /pdfmold} + {pop /pdfmnew} + ifelse load + } + {/pdfmark where + {pop + {2 copy mark 3 1 roll + {pdfmnew} stopped + {cleartomark % failure + dup type /marktype eq {pop} if + 2 copy mark 3 1 roll + {pdfmold} stopped + {cleartomark (WARNING: pdfm disabled) == + dup type /marktype eq {pop} if + /pdfm {pop pop} store} + {cleartomark (WARNING: new pdfm failed, switching to old pdfm) == + dup type /marktype eq {pop} if + /pdfm /pdfmold load store} + ifelse} + {cleartomark dup type /marktype eq {pop} if + /pdfm /pdfmnew load store} + ifelse pop pop}} + {{pop pop}} + ifelse} +ifelse +bind def +end def +%%EndProcSet +%%EndProlog +%%BeginSetup +%%Feature: *Resolution 400dpi +TeXDict begin + +PDFdict begin +/TargetAnchors +61 dict dup begin +(equation.2.1) [7 [520.02 227.14 535.32 239.14] 427] def +(equation.2.2) [8 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Fc(\))2089 2604 y(0)2165 2587 y Fe(\))2463 +2727 y Fr(\(2)p Fk(:)p Fr(1)q(\))0 2842 y(where)18 b Fk(p)222 +2860 y Fe(1)271 2842 y Fr(=)g Fk(a)376 2860 y Fe(1)406 2842 +y Fr(\(1)9 b Fi(\000)g Fk(f)e Fr(\),)23 b Ff(e)-40 b Fk(p)672 +2860 y Fe(1)720 2842 y Fr(=)17 b Ff(e)-36 b Fk(a)825 2860 y +Fe(1)855 2842 y Fr(\(1)9 b Fi(\000)g Fk(f)e Fr(\),)20 b(and)f +Fk(p)1247 2860 y Fe(2)1296 2842 y Fr(=)f Fk(a)1401 2860 y Fe(2)1431 +2842 y Fr(\(1)9 b Fi(\000)g Fk(f)e Fr(\).)28 b Fk(\033)1710 +2860 y Fh(P)1744 2867 y Fc(0)1793 2842 y Fr(and)19 b Fk(\033)1957 +2860 y Fh(Q)1999 2867 y Fc(0)2047 2842 y Fr(are)g(the)g(equal)g(to)h +Fk(\033)2556 2860 y Fh(P)0 2956 y Fr(and)i Fk(\033)167 2974 +y Fh(Q)234 2956 y Fr(with)g Fk(\032)g Fr(and)g Fk(\034)29 b +Fr(set)22 b(to)g(zero,)f(and)h(rescaled)f(b)n(y)h(a)g(factor)g(of)h +Fk(t)1788 2932 y Fe(2)1817 2956 y Fr(.)30 b(The)22 b(ghost)g(insertions)g +(that)0 3071 y(result)j(from)g(computing)g(the)f(pushforw)n(ards)j(of)e(the)g +(tangen)n(t)g(v)n(ectors)g(asso)r(ciated)g(to)g(the)g(mo)r(duli)0 +3186 y(corresp)r(onding)f(to)g(the)g(lo)r(cations)h(of)g(the)f(p)r(oin)n(ts)g +Fk(P)33 b Fr(and)25 b Fk(Q)f Fr(b)n(y)g(the)g(co)r(ordinate)g(family)h(are)f +(giv)n(en)p 0 3278 800 3 v -66 3434 a Fe(#)6 3460 y Fn(The)j(role)f(of)g +(non-split)g(co)r(ordinate)g(transformations)g(on)f(sup)r(ermo)r(duli)i +(space)f(in)h(this)f(regard)g(w)n(as)g(also)0 3557 y(noted)21 +b(b)n(y)g(H.)g(V)-5 b(erlinde)21 b([15)p + (#reference.15) [[180 78 191 90] [1 1 1 [3 3]] [0 0 1]] pdfm (].)1283 +3719 y Fr(6)p eop +%%Page: 7 8 +7 7 bop 0 66 a Fr(in)25 b([7)p + (#reference.7) [[90 706 96 718] [1 1 1 [3 3]] [0 0 1]] pdfm (].)41 +b(The)24 b(measure)g(is)i(formed)e(b)n(y)i(m)n(ultiplying)g(these)e(six)i +(con)n(tributions)f(together)f(\(including)0 167 y(delta)d(functions)g(for)g +(the)f(insertions)i(for)f Fk(\032)g Fr(and)g Fk(\034)8 b Fr(\).)29 +b(The)21 b(insertions)g(are)g(\(ev)l(aluated)f(at)h Fk(r)f +Fr(=)p 2421 123 32 3 v 19 w Fk(r)g Fr(=)e(0\))189 310 y Fk(B)s +Fr([)p Fk(\033)298 328 y Fd(\003)330 310 y Fr(\()380 266 y +Fk(@)p 364 295 71 3 v 364 356 a(@)t(r)442 310 y Fr(\)])h(=)c +Fi(\000)638 257 y Ff(\000)687 266 y Fr(1)p 676 295 54 3 v 676 +356 a Fk(t)700 337 y Fe(2)738 257 y Ff(\001)769 310 y Fk(b)798 +276 y Fe(\()p Fh(P)7 b Fe(\))798 328 y Fd(\000)p Fe(1)898 310 +y Fr(+)964 217 y Ff(\022)1021 266 y Fr(2)p Fk(p)1087 283 y +Fe(1)1117 266 y Fk(\034)p 1021 295 133 3 v 1061 356 a(t)1085 +337 y Fe(2)1162 217 y Ff(\023)1211 310 y Fk(\014)1253 276 y +Fe(\()p Fh(P)g Fe(\))1249 337 y Fd(\000)1298 320 y Fc(1)p 1298 +328 23 3 v 1298 353 a(2)1352 310 y Fi(\000)1419 257 y Ff(\000)1468 +266 y Fr(1)p 1457 295 54 3 v 1457 356 a Fk(t)1481 337 y Fe(2)1519 +257 y Ff(\001)1549 310 y Fk(b)1578 276 y Fe(\()p Fh(Q)p Fe(\))1578 +328 y Fd(\000)p Fe(1)1679 310 y Fr(+)1746 217 y Ff(\022)1803 +266 y Fr(2)t Ff(e)-41 b Fk(p)1869 283 y Fe(1)1899 266 y Fk(\034)p +1803 295 133 3 v 1842 356 a(t)1866 337 y Fe(2)1944 217 y Ff(\023)1993 +310 y Fk(\014)2035 276 y Fe(\()p Fh(Q)p Fe(\))2031 337 y Fd(\000)2080 +320 y Fc(1)p 2080 328 23 3 v 2080 353 a(2)2135 310 y Fr(+)14 +b Fi(\001)d(\001)g(\001)189 491 y Fk(B)s Fr([)p Fk(\033)298 +509 y Fd(\003)330 491 y Fr(\()380 446 y Fk(@)p 364 476 71 3 +v 364 537 a(@)p 403 493 32 3 v 4 w(r)442 491 y Fr(\)])19 b(=)c +Fi(\000)638 437 y Ff(\000)687 446 y Fr(1)p 676 476 54 3 v 676 +503 24 3 v 676 552 a Fk(t)700 514 y Fe(2)738 437 y Ff(\001)766 +474 y Fr(\026)769 491 y Fk(b)798 457 y Fe(\()p Fh(P)7 b Fe(\))798 +509 y Fd(\000)p Fe(1)898 491 y Fi(\000)964 437 y Ff(\000)1013 +446 y Fr(1)p 1003 476 54 3 v 1003 503 24 3 v 1003 552 a Fk(t)1027 +514 y Fe(2)1064 437 y Ff(\001)1092 474 y Fr(\026)1095 491 y +Fk(b)1124 457 y Fe(\()p Fh(Q)p Fe(\))1124 509 y Fd(\000)p Fe(1)1225 +491 y Fr(+)14 b Fi(\001)d(\001)g(\001)187 677 y Fk(B)s Fr([)p +Fk(\033)296 695 y Fd(\003)327 677 y Fr(\()378 632 y Fk(@)p +361 662 74 3 v 361 723 a(@)t(\032)442 677 y Fr(\)])19 b(=)557 +583 y Ff(\022)606 677 y Fi(\000)675 632 y Fk(\032)p 666 662 +54 3 v 666 723 a(t)690 703 y Fe(2)742 677 y Fr(+)816 632 y(2)p +Fk(\034)p 816 662 70 3 v 839 723 a(t)894 583 y Ff(\023)943 +677 y Fk(b)972 643 y Fe(\()p Fh(P)7 b Fe(\))972 695 y Fd(\000)p +Fe(1)1072 677 y Fr(+)1138 583 y Ff(\022)1195 632 y Fr(2)p 1195 +662 34 3 v 1200 723 a Fk(t)1251 677 y Fr(+)1326 632 y(2)p Fk(p)1392 +650 y Fe(1)1422 632 y Fk(\032\034)p 1326 662 168 3 v 1382 723 +a(t)1406 703 y Fe(2)1501 583 y Ff(\023)1550 677 y Fk(\014)1592 +643 y Fe(\()p Fh(P)g Fe(\))1588 704 y Fd(\000)1637 686 y Fc(1)p +1637 694 23 3 v 1637 720 a(2)1677 677 y Fi(\000)557 769 y Ff(\022)623 +818 y Fk(\032)p 614 848 54 3 v 614 909 a(t)638 889 y Fe(2)675 +769 y Ff(\023)724 863 y Fk(b)753 828 y Fe(\()p Fh(Q)p Fe(\))753 +881 y Fd(\000)p Fe(1)854 863 y Fr(+)921 769 y Ff(\022)978 818 +y Fr(2)p 978 848 34 3 v 983 909 a Fk(t)1034 863 y Fr(+)1108 +818 y(2)t Ff(e)-41 b Fk(p)1174 836 y Fe(1)1204 818 y Fk(\032\034)p +1108 848 168 3 v 1165 909 a(t)1189 889 y Fe(2)1283 769 y Ff(\023)1332 +863 y Fk(\014)1374 828 y Fe(\()p Fh(Q)p Fe(\))1370 890 y Fd(\000)1419 +872 y Fc(1)p 1419 880 23 3 v 1419 906 a(2)1475 863 y Fr(+)14 +b Fi(\001)d(\001)g(\001)197 1049 y Fk(B)s Fr([)p Fk(\033)306 +1067 y Fd(\003)338 1049 y Fr(\()384 1004 y Fk(@)p 372 1034 +63 3 v 372 1095 a(@)t(t)442 1049 y Fr(\)])19 b(=)c Fi(\000)638 +955 y Ff(\022)695 1004 y Fr(2)p 695 1034 34 3 v 700 1095 a +Fk(t)736 955 y Ff(\023)785 1049 y Fk(b)814 1014 y Fe(\()p Fh(P)7 +b Fe(\))814 1067 y Fd(\000)p Fe(1)914 1049 y Fr(+)980 955 y +Ff(\022)1037 1004 y Fr(2)p Fk(\034)p 1037 1034 70 3 v 1060 +1095 a(t)1130 1049 y Fr(+)1204 1004 y(4)p Fk(p)1270 1022 y +Fe(1)1301 1004 y Fk(\034)p 1204 1034 133 3 v 1259 1095 a(t)1345 +955 y Ff(\023)1394 1049 y Fk(\014)1436 1014 y Fe(\()p Fh(P)g +Fe(\))1432 1076 y Fd(\000)1481 1058 y Fc(1)p 1481 1066 23 3 +v 1481 1092 a(2)1536 1049 y Fr(+)14 b Fi(\001)d(\001)g(\001)197 +1235 y Fk(B)s Fr([)p Fk(\033)306 1253 y Fd(\003)338 1235 y +Fr(\()384 1190 y Fk(@)p 372 1220 63 3 v 372 1282 a(@)p 411 +1233 24 3 v 4 w(t)442 1235 y Fr(\)])19 b(=)c Fi(\000)638 1141 +y Ff(\022)695 1190 y Fr(2)p 695 1220 34 3 v 700 1233 24 3 v +700 1282 a Fk(t)736 1141 y Ff(\023)783 1217 y Fr(\026)785 1235 +y Fk(b)814 1200 y Fe(\()p Fh(P)7 b Fe(\))814 1253 y Fd(\000)p +Fe(1)914 1235 y Fr(+)14 b Fi(\001)d(\001)g(\001)185 1416 y +Fk(B)s Fr([)p Fk(\033)294 1434 y Fd(\003)325 1416 y Fr(\()377 +1371 y Fk(@)p 359 1400 76 3 v 359 1461 a(@)t(\034)442 1416 +y Fr(\)])19 b(=)c Fi(\000)638 1362 y Ff(\000)668 1416 y Fk(\034)705 +1362 y Ff(\001)735 1416 y Fk(b)764 1381 y Fe(\()p Fh(P)7 b +Fe(\))764 1433 y Fd(\000)p Fe(1)865 1416 y Fi(\000)931 1362 +y Ff(\000)961 1416 y Fr(2)994 1362 y Ff(\001)1025 1416 y Fk(\014)1067 +1381 y Fe(\()p Fh(P)g Fe(\))1063 1443 y Fd(\000)1112 1425 y +Fc(1)p 1112 1433 23 3 v 1112 1459 a(2)1167 1416 y Fr(+)14 b +Fi(\001)d(\001)g(\001)2463 854 y Fr(\(2)p Fk(:)p Fr(2)q(\))0 +1548 y(where)26 b(the)g(dots)h(represen)n(t)e(higher)i(terms)f(\()p +Fk(b)1209 1566 y Fh(n)1245 1548 y Fk(;)11 b(n)26 b Fi(\025)h +Fr(0)g(and)g Fk(\014)1651 1566 y Fh(n)1686 1548 y Fk(;)11 b(n)27 +b Fi(\025)1868 1522 y Fe(1)p 1868 1533 27 3 v 1868 1571 a(2)1903 +1548 y Fr(\))f(that)h(annihilate)h(strong)0 1648 y(ph)n(ysical)23 +b(states)f(\(SPSs\).)133 1749 y(T)-6 b(o)25 b(insert)f(a)h(SPS)f(at)h +Fk(P)33 b Fr(and)24 b(at)h Fk(Q)p Fr(,)f(there)g(are)g(t)n(w)n(o)g(p)r +(ossible)h(con)n(tributions)g(to)g(the)e(measure)0 1849 y(from)f(the)f(ab)r +(o)n(v)n(e)i(insertions:)195 1973 y Fk(b)224 1939 y Fe(\()p +Fh(P)7 b Fe(\))224 1991 y Fd(\000)p Fe(1)307 1956 y Fr(\026)309 +1973 y Fk(b)338 1939 y Fe(\()p Fh(P)g Fe(\))338 1991 y Fd(\000)p +Fe(1)423 1973 y Fk(\016)s Fr([)p Fk(\014)516 1939 y Fe(\()p +Fh(P)g Fe(\))512 2000 y Fd(\000)561 1982 y Fc(1)p 561 1990 +23 3 v 561 2016 a(2)601 1973 y Fr(])p Fk(b)648 1939 y Fe(\()p +Fh(Q)p Fe(\))648 1991 y Fd(\000)p Fe(1)732 1956 y Fr(\026)734 +1973 y Fk(b)763 1939 y Fe(\()p Fh(Q)p Fe(\))763 1991 y Fd(\000)p +Fe(1)849 1973 y Fk(\016)s Fr([)p Fk(\014)942 1939 y Fe(\()p +Fh(Q)p Fe(\))938 2000 y Fd(\000)987 1982 y Fc(1)p 987 1990 +V 987 2016 a(2)1028 1973 y Fr(])22 b Fk(;)145 b(b)1260 1939 +y Fe(\()p Fh(P)7 b Fe(\))1260 1991 y Fd(\000)p Fe(1)1342 1956 +y Fr(\026)1345 1973 y Fk(b)1374 1939 y Fe(\()p Fh(P)g Fe(\))1374 +1991 y Fd(\000)p Fe(1)1459 1973 y Fk(\016)s Fr([)p Fk(\014)1552 +1939 y Fe(\()p Fh(P)g Fe(\))1548 2000 y Fd(\000)1597 1982 y +Fc(1)p 1597 1990 V 1597 2016 a(2)1636 1973 y Fr(])p Fk(b)1683 +1939 y Fe(\()p Fh(Q)p Fe(\))1683 1991 y Fd(\000)p Fe(1)1768 +1956 y Fr(\026)1770 1973 y Fk(b)1799 1939 y Fe(\()p Fh(Q)p +Fe(\))1799 1991 y Fd(\000)p Fe(1)1885 1973 y Fk(\014)1927 1939 +y Fe(\()p Fh(Q)p Fe(\))1923 2000 y Fd(\000)1972 1982 y Fc(1)p +1972 1990 V 1972 2016 a(2)2013 1973 y Fk(\016)2046 1946 y Fd(0)2064 +1973 y Fr([)p Fk(\014)2124 1939 y Fe(\()p Fh(Q)p Fe(\))2120 +2000 y Fd(\000)2169 1982 y Fc(1)p 2169 1990 V 2169 2016 a(2)2210 +1973 y Fr(])22 b Fk(:)195 b Fr(\(2)p Fk(:)p Fr(3)q(\))0 2098 +y(Using)24 b(the)f(formal)h(iden)n(ti\014cation)g(of)g Fk(\014)t(\016)1068 +2074 y Fd(0)1085 2098 y Fr(\()p Fk(\014)t Fr(\))f(and)g Fi(\000)p +Fk(\016)s Fr(\()p Fk(\014)t Fr(\),)f(w)n(e)h(easily)i(\014nd)e(the)g(con)n +(tribution)h(from)0 2198 y(the)d(insertions)i(in)g(\(2.2)p + (#equation.2.2) [[165 322 180 334] [1 1 1 [3 3]] [0 0 1]] pdfm (\))f(to)h(b) +r(e)853 2277 y Fk(t)p 820 2307 91 3 v 820 2368 a Fi(j)p Fk(t)p +Fi(j)880 2349 y Fe(6)918 2322 y Fk(b)947 2288 y Fe(\()p Fh(P)7 +b Fe(\))947 2340 y Fd(\000)p Fe(1)1030 2305 y Fr(\026)1033 +2322 y Fk(b)1062 2288 y Fe(\()p Fh(P)g Fe(\))1062 2340 y Fd(\000)p +Fe(1)1147 2322 y Fk(\016)s Fr([)p Fk(\014)1240 2288 y Fe(\()p +Fh(P)g Fe(\))1236 2349 y Fd(\000)1285 2331 y Fc(1)p 1285 2339 +23 3 v 1285 2365 a(2)1324 2322 y Fr(])p Fk(b)1371 2288 y Fe(\()p +Fh(Q)p Fe(\))1371 2340 y Fd(\000)p Fe(1)1456 2305 y Fr(\026)1458 +2322 y Fk(b)1487 2288 y Fe(\()p Fh(Q)p Fe(\))1487 2340 y Fd(\000)p +Fe(1)1573 2322 y Fk(\016)s Fr([)p Fk(\014)1666 2288 y Fe(\()p +Fh(Q)p Fe(\))1662 2349 y Fd(\000)1711 2331 y Fc(1)p 1711 2339 +V 1711 2365 a(2)1751 2322 y Fr(])p Fk(;)676 b Fr(\(2)p Fk(:)p +Fr(4)q(\))0 2465 y(where)21 b(there)g(has)h(b)r(een)f(some)h(cancellation)g +(b)r(et)n(w)n(een)e(the)i(t)n(w)n(o)g(di\013eren)n(t)f(con)n(tributions)i(in) +f(\(2.3)p (#equation.2.3) [[510 274 525 286] [1 1 1 [3 3]] [0 0 1]] pdfm +(\).)133 2565 y(Th)n(us)g(w)n(e)g(ha)n(v)n(e)117 2597 y Ff(Z)183 +2634 y(\002)215 2687 y Fr(d)s Fk(r)16 b Fi(^)k Fr(d)p 405 2644 +32 3 v 3 w Fk(r)c Fi(^)k Fr(d)s Fk(t)14 b Fi(^)20 b Fr(d)p +697 2639 24 3 v 3 w Fk(t)p Fi(j)5 b Fr(d)s Fk(\032)g Fr(d)s +Fk(\034)900 2634 y Ff(\003)948 2687 y Fi(h)p Fr(\006)p Fk(;)11 +b(\033)1089 2705 y Fh(P)1134 2687 y Fk(;)g(\033)1201 2705 y +Fh(Q)1247 2687 y Fi(j)g(\001)g(\001)g(\001)i Fk(B)s Fr([)p +Fk(\033)1474 2705 y Fd(\003)1505 2687 y Fr(\()1555 2643 y Fk(@)p +1539 2672 71 3 v 1539 2733 a(@)t(r)1618 2687 y Fr(\)])p Fk(B)s +Fr([)p Fk(\033)1771 2705 y Fd(\003)1803 2687 y Fr(\()1852 2643 +y Fk(@)p 1837 2672 V 1837 2733 a(@)p 1876 2689 32 3 v 4 w(r)1915 +2687 y Fr(\)])p Fk(\016)1992 2634 y Ff(\002)2019 2687 y Fk(B)s +Fr([)p Fk(\033)2128 2705 y Fd(\003)2160 2687 y Fr(\()2211 2643 +y Fk(@)p 2194 2672 74 3 v 2194 2733 a(@)t(\032)2275 2687 y +Fr(\)])2319 2634 y Ff(\003)331 2864 y Fi(\002)h Fk(B)s Fr([)p +Fk(\033)506 2882 y Fd(\003)538 2864 y Fr(\()583 2819 y Fk(@)p +572 2848 63 3 v 572 2909 a(@)t(t)642 2864 y Fr(\)])p Fk(B)s +Fr([)p Fk(\033)795 2882 y Fd(\003)827 2864 y Fr(\()873 2819 +y Fk(@)p 861 2848 V 861 2910 a(@)p 900 2862 24 3 v 4 w(t)932 +2864 y Fr(\)])p Fk(\016)1009 2810 y Ff(\002)1036 2864 y Fk(B)s +Fr([)p Fk(\033)1145 2882 y Fd(\003)1177 2864 y Fr(\()1229 2819 +y Fk(@)p 1211 2848 76 3 v 1211 2909 a(@)t(\034)1294 2864 y +Fr(\)])1338 2810 y Ff(\003)1366 2864 y Fi(j)p Fk( )r Fi(i)1455 +2836 y Fh(P)1515 2864 y Fi(\012)g(j)p Fk( )r Fi(i)1670 2836 +y Fh(Q)1735 2864 y Fr(=)117 2940 y Ff(Z)183 2976 y(\002)215 +3030 y Fr(d)s Fk(r)i Fi(^)k Fr(d)p 405 2986 32 3 v 3 w Fk(r)c +Fi(^)k Fr(d)s Fk(t)14 b Fi(^)20 b Fr(d)p 697 2981 24 3 v 3 +w Fk(t)p Fi(j)5 b Fr(d)s Fk(\032)g Fr(d)s Fk(\034)900 2976 +y Ff(\003)948 3030 y Fi(h)p Fr(\006)p Fk(;)11 b(\033)1089 3048 +y Fh(P)1123 3055 y Fc(0)1153 3030 y Fk(;)g(\033)1220 3048 y +Fh(Q)1262 3055 y Fc(0)1291 3030 y Fi(j)331 3201 y(\002)397 +3148 y Ff(\000)427 3201 y Fr(1)k(+)g Fk(\032\034)8 b(tL)682 +3167 y Fe(\()p Fh(P)f Fe(\))682 3219 y Fd(\000)p Fe(1)782 3201 +y Fr(+)15 b Fk(\032\034)920 3148 y Ff(\000)958 3157 y Fr(2)p +Fk(p)1024 3174 y Fe(2)1069 3157 y Fi(\000)g Fk(p)1169 3174 +y Fe(1)p 958 3186 241 3 v 1067 3247 a Fk(t)1207 3148 y Ff(\001)1237 +3201 y Fk(L)1282 3167 y Fe(\()p Fh(P)7 b Fe(\))1282 3219 y(0)1383 +3201 y Fr(+)15 b(2)1483 3148 y Ff(\000)1513 3201 y Fk(\032)g +Fi(\000)g Fk(\034)8 b(t)1690 3148 y Ff(\001)1720 3201 y Fk(G)1772 +3167 y Fe(\()p Fh(P)f Fe(\))1772 3228 y Fd(\000)1821 3211 y +Fc(1)p 1821 3219 23 3 v 1821 3244 a(2)1858 3148 y Ff(\001)331 +3366 y Fi(\002)397 3313 y Ff(\000)427 3366 y Fr(1)15 b Fi(\000)550 +3322 y Fk(\032\034)c Ff(e)-40 b Fk(p)654 3339 y Fe(1)p 550 +3351 135 3 v 605 3412 a Fk(t)692 3366 y(L)737 3332 y Fe(\()p +Fh(Q)p Fe(\))737 3384 y(0)838 3366 y Fr(+)15 b(2)p Fk(\032G)1024 +3332 y Fe(\()p Fh(Q)p Fe(\))1024 3393 y Fd(\000)1074 3376 y +Fc(1)p 1074 3384 23 3 v 1074 3409 a(2)1111 3313 y Ff(\001)1142 +3366 y Fk(t)1166 3339 y Fe(2\()p Fh(L)1249 3315 y Fc(\()p Fb(P)6 +b Fc(\))1249 3355 y(0)1324 3339 y Fe(+)p Fh(L)1401 3315 y Fc(\()p +Fb(Q)p Fc(\))1401 3355 y(0)1476 3339 y Fe(\))p 1500 3318 24 +3 v 1500 3366 a Fk(t)1524 3329 y Fe(2\()1577 3317 y(\026)1571 +3329 y Fh(L)1607 3304 y Fc(\()p Fb(P)h Fc(\))1607 3345 y(0)1682 +3329 y Fe(+)1729 3317 y(\026)1723 3329 y Fh(L)1759 3304 y Fc(\()p +Fb(Q)p Fc(\))1759 3345 y(0)1834 3329 y Fe(\))331 3524 y Fi(\002)397 +3471 y Ff(\000)469 3479 y Fk(t)p 435 3509 91 3 v 435 3570 a +Fi(j)p Fk(t)p Fi(j)495 3551 y Fe(6)534 3471 y Ff(\001)564 3524 +y Fk(b)593 3490 y Fe(\()p Fh(P)g Fe(\))593 3542 y Fd(\000)p +Fe(1)676 3507 y Fr(\026)679 3524 y Fk(b)708 3490 y Fe(\()p +Fh(P)g Fe(\))708 3542 y Fd(\000)p Fe(1)793 3524 y Fk(\016)s +Fr([)p Fk(\014)886 3490 y Fe(\()p Fh(P)g Fe(\))882 3551 y Fd(\000)931 +3534 y Fc(1)p 931 3542 23 3 v 931 3567 a(2)970 3524 y Fr(])p +Fk(b)1017 3490 y Fe(\()p Fh(Q)p Fe(\))1017 3542 y Fd(\000)p +Fe(1)1102 3507 y Fr(\026)1104 3524 y Fk(b)1133 3490 y Fe(\()p +Fh(Q)p Fe(\))1133 3542 y Fd(\000)p Fe(1)1219 3524 y Fk(\016)s +Fr([)p Fk(\014)1312 3490 y Fe(\()p Fh(Q)p Fe(\))1308 3551 y +Fd(\000)1357 3534 y Fc(1)p 1357 3542 V 1357 3567 a(2)1397 3524 +y Fr(])p Fi(j)p Fk( )r Fi(i)1504 3497 y Fh(P)1565 3524 y Fi(\012)14 +b(j)p Fk( )r Fi(i)1720 3497 y Fh(Q)1766 3524 y Fk(:)2463 3108 +y Fr(\(2)p Fk(:)p Fr(5)q(\))1283 3719 y(7)p eop +%%Page: 8 9 +8 8 bop 0 66 a Fr(The)21 b(state)h Fk(b)328 84 y Fd(\000)p +Fe(1)396 49 y Fr(\026)399 66 y Fk(b)428 84 y Fd(\000)p Fe(1)499 +66 y Fk(\016)s Fr([)p Fk(\014)588 84 y Fd(\000)636 67 y Fc(1)p +636 75 23 3 v 636 100 a(2)670 66 y Fr(])p Fi(j)p Fk( )r Fi(i)h +Fr(has)g Fk(L)964 84 y Fe(0)1012 66 y Fr(=)1090 40 y Fe(1)p +1090 51 27 3 v 1090 89 a(2)1147 66 y Fr(and)1284 50 y(\026)1276 +66 y Fk(L)1321 84 y Fe(0)1369 66 y Fr(=)18 b(1)23 b(and)f(th)n(us,)g(pic)n +(king)h(o\013)f(the)f(term)g(prop)r(or-)0 171 y(tional)i Fk(\032\034)8 +b Fr(,)23 b(\(2.5)p + (#equation.2.5) [[131 687 146 699] [1 1 1 [3 3]] [0 0 1]] pdfm (\))f(b)r +(ecomes)672 254 y Ff(Z)739 291 y(\002)771 345 y Fr(d)s Fk(r)16 +b Fi(^)k Fr(d)p 961 301 32 3 v 3 w Fk(r)c Fi(^)k Fr(d)s Fk(t)14 +b Fi(^)20 b Fr(d)p 1253 296 24 3 v 3 w Fk(t)p Fi(j)5 b Fr(d)s +Fk(\032)g Fr(d)s Fk(\034)1456 291 y Ff(\003)377 525 y Fi(h)p +Fr(\006)p Fk(;)11 b(\033)518 543 y Fh(P)552 550 y Fc(0)582 +525 y Fk(;)g(\033)649 543 y Fh(Q)691 550 y Fc(0)720 525 y Fi(j)q +Fk(\032\034)810 431 y Ff(\022)859 525 y Fk(tL)928 490 y Fe(\()p +Fh(P)c Fe(\))928 542 y Fd(\000)p Fe(1)1028 525 y Fr(+)1103 +480 y(\(2)p Fk(a)1197 498 y Fe(2)1241 480 y Fi(\000)15 b Fk(a)1343 +498 y Fe(1)1388 480 y Fi(\000)e Ff(e)-36 b Fk(a)1489 498 y +Fe(1)1519 480 y Fr(\)\(1)14 b Fi(\000)h Fk(f)7 b Fr(\))p 1103 +509 648 3 v 1398 570 a(2)p Fk(t)1773 525 y Fr(+)15 b(4)p Fk(tG)1949 +490 y Fe(\()p Fh(Q)p Fe(\))1949 552 y Fd(\000)1998 534 y Fc(1)p +1998 542 23 3 v 1998 568 a(2)2036 525 y Fk(G)2088 490 y Fe(\()p +Fh(P)7 b Fe(\))2088 552 y Fd(\000)2137 534 y Fc(1)p 2137 542 +V 2137 568 a(2)2174 431 y Ff(\023)754 713 y Fi(\002)820 659 +y Ff(\000)858 668 y Fi(j)p Fk(t)p Fi(j)918 644 y Fe(2)p 858 +698 91 3 v 892 759 a Fk(t)957 659 y Ff(\001)987 713 y Fk(b)1016 +679 y Fe(\()p Fh(P)g Fe(\))1016 731 y Fd(\000)p Fe(1)1099 696 +y Fr(\026)1102 713 y Fk(b)1131 679 y Fe(\()p Fh(P)g Fe(\))1131 +731 y Fd(\000)p Fe(1)1216 713 y Fk(\016)s Fr([)p Fk(\014)1309 +679 y Fe(\()p Fh(P)g Fe(\))1305 740 y Fd(\000)1354 722 y Fc(1)p +1354 730 23 3 v 1354 756 a(2)1393 713 y Fr(])p Fk(b)1440 679 +y Fe(\()p Fh(Q)p Fe(\))1440 731 y Fd(\000)p Fe(1)1525 696 y +Fr(\026)1527 713 y Fk(b)1556 679 y Fe(\()p Fh(Q)p Fe(\))1556 +731 y Fd(\000)p Fe(1)1642 713 y Fk(\016)s Fr([)p Fk(\014)1735 +679 y Fe(\()p Fh(Q)p Fe(\))1731 740 y Fd(\000)1780 722 y Fc(1)p +1780 730 V 1780 756 a(2)1820 713 y Fr(])p Fi(j)p Fk( )r Fi(i)1927 +686 y Fh(P)1988 713 y Fi(\012)14 b(j)p Fk( )r Fi(i)2143 686 +y Fh(Q)2189 713 y Fk(:)2463 523 y Fr(\(2)p Fk(:)p Fr(6)q(\))0 +876 y(A)n(t)26 b(\014rst)g(sigh)n(t,)i(the)d(term)g(prop)r(ortional)i(to)f +(\(1)17 b Fi(\000)g Fk(f)7 b Fr(\))26 b(lo)r(oks)h(lik)n(e)f(bad)g(news,)h +(since)f(it)g(dep)r(ends)f(on)0 980 y(the)k(shap)r(e)f(of)i(the)f(function)g +Fk(f)7 b Fr(,)31 b(and)e(hence)f(on)h(the)g(details)h(of)g(the)e(co)r +(ordinate)h(family)h(c)n(hosen.)0 1084 y(Actually)-6 b(,)29 +b(the)d(co)r(e\016cien)n(ts)f Fk(a)782 1102 y Fh(i)831 1084 +y Fr(and)h Ff(e)-36 b Fk(a)1000 1102 y Fh(i)1048 1084 y Fr(are)27 +b(not)f(to)h(b)r(e)f(tak)n(en)g(to)g(b)r(e)g(arbitrary)-6 b(.)45 +b(As)26 b(discussed)h(in)0 1188 y([7)p + (#reference.7) [[75 504 81 516] [1 1 1 [3 3]] [0 0 1]] pdfm (],)c(a)e +(unique)g(c)n(hoice)f(for)h(the)f(co)r(e\016cien)n(ts)g(is)i(singled)g(out)e +(b)n(y)h(demanding)g(that)f(dilaton)i(insertions)0 1292 y(b)r(eha)n(v)n(e)j +(correctly)-6 b(.)40 b(There)25 b(one)g(found)h(that)f Fk(a)1224 +1310 y Fe(1)1279 1292 y Fr(=)f Fk(a)1390 1310 y Fe(2)1444 1292 +y Fr(=)f Ff(e)-36 b Fk(a)1555 1310 y Fe(1)1609 1292 y Fr(=)24 +b Fi(\000)o Ff(e)-36 b Fk(a)1772 1310 y Fe(2)1826 1292 y Fr(=)24 +b Fi(\000)p Fr(1)p Fk(=)p Fr(4.)41 b(\(Actually)-6 b(,)28 b(the)c +Ff(e)-36 b Fk(a)2578 1310 y Fh(i)0 1396 y Fr(w)n(ere)18 b(not)h(determined)e +(in)i([7)p (#reference.7) [[198 467 204 479] [1 1 1 [3 3]] [0 0 1]] pdfm +(],)i(but)e(a)g(calculation)h(exactly)e(analogous)j(to)e(the)f(ones)h(presen) +n(ted)e(there)0 1500 y(\014xes)24 b(these)f(co)r(e\016cien)n(ts)g(as)h(w)n +(ell.\))36 b(With)25 b(these)e(v)l(alues)h(for)h(the)e(co)r(e\016cien)n(ts,)h +(the)f(o\013ending)h(term)0 1604 y(v)l(anishes,)e(and)e(all)h(dep)r(endence)d +(on)i(the)f(shap)r(e)h(of)h(the)e(co)r(ordinate)h(family)h(c)n(hosen)f(drops) +g(out.)30 b Fl(A)n(ny)0 1709 y Fr(co)r(ordinate)19 b(family)i(whic)n(h)f(in)n +(terp)r(olates)g(to)f(the)h(asymptotic)f(b)r(eha)n(vior)h(\(1.5)p + (#equation.1.5) [[414 410 429 422] [1 1 1 [3 3]] [0 0 1]] pdfm (\),\(1.6)p + (#equation.1.6) [[441 410 456 422] [1 1 1 [3 3]] [0 0 1]] pdfm (\))h(giv)n +(es)g(the)e(same)0 1813 y(result)j(for)h(the)e(measure)131 +1880 y Ff(Z)197 1916 y(\002)230 1970 y Fr(d)s Fk(r)16 b Fi(^)k +Fr(d)p 420 1926 32 3 v 3 w Fk(r)c Fi(^)j Fr(d)s Fk(t)c Fi(^)k +Fr(d)p 711 1921 24 3 v 3 w Fk(t)p Fi(j)5 b Fr(d)s Fk(\032)g +Fr(d)s Fk(\034)914 1916 y Ff(\003)963 1970 y Fi(h)p Fr(\006)p +Fk(;)11 b(\033)1104 1988 y Fh(P)1138 1995 y Fc(0)1167 1970 +y Fk(;)g(\033)1234 1988 y Fh(Q)1276 1995 y Fc(0)1306 1970 y +Fi(j)p Fk(\032\034)1395 1916 y Ff(\000)1425 1970 y Fk(L)1470 +1936 y Fe(\()p Fh(P)c Fe(\))1470 1988 y Fd(\000)p Fe(1)1571 +1970 y Fr(+)14 b(4)p Fk(G)1722 1936 y Fe(\()p Fh(Q)p Fe(\))1722 +1997 y Fd(\000)1772 1979 y Fc(1)p 1772 1987 23 3 v 1772 2013 +a(2)1810 1970 y Fk(G)1862 1936 y Fe(\()p Fh(P)7 b Fe(\))1862 +1997 y Fd(\000)1911 1979 y Fc(1)p 1911 1987 V 1911 2013 a(2)1948 +1916 y Ff(\001)955 2123 y Fi(\002)15 b(j)p Fk(t)p Fi(j)1082 +2096 y Fe(2)1112 2123 y Fk(b)1141 2089 y Fe(\()p Fh(P)7 b Fe(\))1141 +2141 y Fd(\000)p Fe(1)1224 2106 y Fr(\026)1227 2123 y Fk(b)1256 +2089 y Fe(\()p Fh(P)g Fe(\))1256 2141 y Fd(\000)p Fe(1)1341 +2123 y Fk(\016)s Fr([)p Fk(\014)1434 2089 y Fe(\()p Fh(P)g +Fe(\))1430 2150 y Fd(\000)1479 2132 y Fc(1)p 1479 2140 V 1479 +2166 a(2)1518 2123 y Fr(])p Fk(b)1565 2089 y Fe(\()p Fh(Q)p +Fe(\))1565 2141 y Fd(\000)p Fe(1)1650 2106 y Fr(\026)1652 2123 +y Fk(b)1681 2089 y Fe(\()p Fh(Q)p Fe(\))1681 2141 y Fd(\000)p +Fe(1)1767 2123 y Fk(\016)s Fr([)p Fk(\014)1860 2089 y Fe(\()p +Fh(Q)p Fe(\))1856 2150 y Fd(\000)1905 2132 y Fc(1)p 1905 2140 +V 1905 2166 a(2)1945 2123 y Fr(])p Fi(j)p Fk( )r Fi(i)2052 +2096 y Fh(P)2113 2123 y Fi(\012)14 b(j)p Fk( )r Fi(i)2268 2096 +y Fh(Q)2314 2123 y Fk(:)2463 2039 y Fr(\(2)p Fk(:)p Fr(7)q(\))133 +2279 y(Our)23 b(demand)g(that)h(the)f(co)r(ordinate)g(family)i(exhibit)f(a)g +(certain)f(asymptotic)h(b)r(eha)n(vior)g(as)g(w)n(e)0 2383 +y(approac)n(h)18 b(the)e(b)r(oundary)i(of)g(mo)r(duli)f(space)g(has)h(b)r +(oth)f(a)h(ph)n(ysical)h(motiv)l(ation)f(\(it)f(giv)n(es)i(the)d(correct)0 +2487 y(b)r(eha)n(vior)i(for)g(dilaton)g(correlation)g(functions\))f(and)h(a)f +(mathematical)g(motiv)l(ation.)29 b(When)17 b(w)n(e)g(think)0 +2592 y(ab)r(out)26 b(the)f(plum)n(bing)h(construction)g(as)g(gluing)h(a)f +(certain)g Fl(\014xtur)m(e)f Fr({)h(a)g(3-punctured)e(sphere)h +Fl(with)0 2696 y Fr(co)r(ordinates)j({)g(on)n(to)g(the)f(rest)h(of)g(the)f +(surface,)i(it)g(mak)n(es)e(sense)g(to)h(demand)f(that)g(the)h(resulting)0 +2800 y(sewn)h(surface)g(b)r(e)f(the)h(same,)h(regardless)g(of)f(whic)n(h)g +(puncture)f(w)n(e)h(c)n(hose)g(to)g(attac)n(h)g(to)g(the)f(rest)0 +2904 y(of)k(the)f(surface.)57 b(In)32 b(other)f(w)n(ords,)j(w)n(e)d(demand)g +(in)n(v)l(ariance)h(under)e(\(a)i(subgroup)g(of)5 b(\))32 b(m\033bius)0 +3008 y(transformations)24 b(of)f(the)f(3-punctures)g(sphere.)32 +b(As)23 b(in)g(the)f(b)r(osonic)h(string)h([6)p + (#reference.6) [[434 177 440 189] [1 1 1 [3 3]] [0 0 1]] pdfm (,16)p + (#reference.16) [[443 177 455 189] [1 1 1 [3 3]] [0 0 1]] pdfm (],)h(this)f +(leads)f(to)g(a)0 3112 y(de\014nite)f(c)n(hoice)h(for)h(the)e(\014rst)h(few)g +(co)r(e\016cien)n(ts)f(in)i(\(1.5)p + (#equation.1.5) [[316 158 331 170] [1 1 1 [3 3]] [0 0 1]] pdfm (\),\(1.6)p + (#equation.1.6) [[344 158 359 170] [1 1 1 [3 3]] [0 0 1]] pdfm (\).)35 +b(Still,)25 b(one)e(migh)n(t)g(b)r(e)f(puzzled)g(that)0 3216 +y(the)d(measure)g(formed)g(with)h(SPSs)g(should)h(b)r(e)e(sensitiv)n(e)h(at)g +(all)h(to)f(the)g(asymptotic)f(b)r(eha)n(vior)h(of)h(the)0 +3320 y(co)r(ordinate)h(family)-6 b(.)31 b(W)-6 b(e)22 b(will)i(defer)d(a)i +(discussion)g(of)f(this)h(p)r(oin)n(t)f(to)g(section)g(3.)133 +3425 y(Of)k(the)g(t)n(w)n(o)h(terms)f(in)h(\(2.7)p + (#equation.2.7) [[212 102 227 114] [1 1 1 [3 3]] [0 0 1]] pdfm (\),)h(the)e +Fk(G)1105 3390 y Fe(\()p Fh(Q)p Fe(\))1105 3452 y Fd(\000)1155 +3434 y Fc(1)p 1155 3442 V 1155 3468 a(2)1192 3425 y Fk(G)1244 +3390 y Fe(\()p Fh(P)7 b Fe(\))1244 3452 y Fd(\000)1294 3434 +y Fc(1)p 1294 3442 V 1294 3468 a(2)1357 3425 y Fr(is)27 b(precisely)f(what)h +(is)g(exp)r(ected)d(from)j(a)g(na)-7 b(\177)-26 b(\020v)n(e)0 +3544 y(analysis)18 b(of)f(the)f(collision)i(of)f(t)n(w)n(o)g(v)n(ertex)f(op)r +(erators.)28 b(Indeed,)17 b(the)e Fk(G)1766 3509 y Fe(\()p +Fh(P)7 b Fe(\))1766 3571 y Fd(\000)1816 3553 y Fc(1)p 1816 +3561 V 1816 3587 a(2)1869 3544 y Fr(com)n(bines)16 b(with)g(the)g +Fk(\016)s Fr([)p Fk(\014)2497 3509 y Fe(\()p Fh(P)7 b Fe(\))2493 +3571 y Fd(\000)2542 3553 y Fc(1)p 2542 3561 V 2542 3587 a(2)2582 +3544 y Fr(])1283 3719 y(8)p eop +%%Page: 9 10 +9 9 bop 0 66 a Fr(to)24 b(form)g(a)g(picture-c)n(hanging)g(op)r(erator,)h +(whic)n(h)f(con)n(v)n(erts)g(the)f(state)h(at)g Fk(P)33 b Fr(from)24 +b(the)f(\()p Fi(\000)p Fr(1\))h(to)g(the)0 172 y(\(0\))f(picture)f(\(and)h +(similarly)h(for)g(the)e(state)h(at)g Fk(Q)p Fr(\).)31 b(The)23 +b Fk(L)1537 138 y Fe(\()p Fh(P)7 b Fe(\))1537 190 y Fd(\000)p +Fe(1)1646 172 y Fr(term)21 b(is)j(new)e(and,)i(as)g(w)n(e)e(shall)i(see,)0 +278 y(pla)n(ys)f(the)e(role)i(of)f(the)g(\\con)n(tact)f(term")g(p)r +(ostulated)h(b)n(y)h(Green)e(and)h(Seib)r(erg.)133 384 y(First,)i(let)f(us)g +(see)g(that)f(it)i(mak)n(es)e(sense)g(b)n(y)i(examining)f(the)f +(transformation)i(of)f(the)f(measure)0 490 y(under)16 b(the)f(co)r(ordinate)h +(transformation)h(in)f(\(1.10)p + (#equation.1.10) [[280 630 301 642] [1 1 1 [3 3]] [0 0 1]] pdfm (\).)29 +b(There)15 b(are)h(three)g(con)n(tributions)g(to)h(the)e(c)n(hange.)0 +596 y(The)21 b(\014rst)h(is)g(the)f(ho)n(w)h(the)f(in)n(tegration)i(measure)d +([)5 b(d)t Ff(e)-38 b Fk(r)16 b Fi(^)j Fr(d)p 1513 540 32 3 +v 4 w Ff(e)-38 b Fk(r)q Fi(j)5 b Fr(d)i Ff(e)-41 b Fk(\032)p +Fr(])22 b(transforms)g(to)g([)5 b(d)s Fk(t)14 b Fi(^)19 b Fr(d)p +2297 547 24 3 v 3 w Fk(t)o Fi(j)5 b Fr(d)s Fk(\034)j Fr(].)30 +b(The)0 702 y(c)n(hange)22 b(of)g(v)l(ariables)i(requires)d(the)h(in)n(tro)r +(duction)g(of)h(a)f(Jacobian)h(\(Berezinian\),)514 917 y([)5 +b(d)t Ff(e)-38 b Fk(r)17 b Fi(^)j Fr(d)p 728 861 32 3 v 4 w +Ff(e)-38 b Fk(r)q Fi(j)5 b Fr(d)i Ff(e)-41 b Fk(\032)p Fr(])19 +b(=)f(sdet)1092 823 y Ff(\022)1162 847 y Fh(@)p Ff(e)-34 b +Fh(r)p 1162 858 58 3 v 1165 896 a(@)s(t)1305 844 y(@)r Ff(e)e +Fh(\032)p 1305 858 59 3 v 1309 896 a(@)s(t)1162 955 y(@)p Ff(e)i +Fh(r)p 1160 965 62 3 v 1160 1004 a(@)s(\034)1305 951 y(@)r +Ff(e)e Fh(\032)p 1304 965 V 1304 1004 a(@)s(\034)1384 823 y +Ff(\023)1433 917 y Fr(det)1536 823 y Ff(\022)1593 872 y Fk(@)p +1632 816 32 3 v 5 w Ff(e)e Fk(r)p 1593 901 71 3 v 1597 963 +a(@)p 1636 915 24 3 v 4 w(t)1672 823 y Ff(\023)1721 917 y Fr([)5 +b(d)s Fk(t)14 b Fi(^)20 b Fr(d)p 1926 868 V 3 w Fk(t)o Fi(j)5 +b Fr(d)s Fk(\034)j Fr(])p Fk(:)378 b Fr(\(2)p Fk(:)p Fr(8)q(\))0 +1131 y(Using)23 b(\(1.10)p + (#equation.1.10) [[110 514 131 526] [1 1 1 [3 3]] [0 0 1]] pdfm (\),)g(this) +g(results)f(in)692 1330 y([)5 b(d)t Ff(e)-38 b Fk(r)17 b Fi(^)i +Fr(d)p 905 1274 32 3 v 4 w Ff(e)-38 b Fk(r)r Fi(j)5 b Fr(d)i +Ff(e)-41 b Fk(\032)p Fr(])19 b(=)1149 1285 y(4)p Fi(j)p Fk(t)p +Fi(j)1242 1261 y Fe(2)p 1149 1315 124 3 v 1199 1376 a Fk(t)1281 +1276 y Ff(\000)1311 1330 y Fr(1)c(+)1433 1285 y Fk(\032\034)p +1433 1315 71 3 v 1440 1376 a Fr(2)p Fk(t)1512 1276 y Ff(\001)1543 +1330 y Fr([)5 b(d)s Fk(t)14 b Fi(^)20 b Fr(d)p 1748 1281 24 +3 v 3 w Fk(t)p Fi(j)5 b Fr(d)s Fk(\034)j Fr(])p Fk(:)555 b +Fr(\(2)p Fk(:)p Fr(9)q(\))0 1513 y(But)31 b(the)f Fk(B)35 b +Fr(insertions)d(\(2.2)p + (#equation.2.2) [[195 446 210 458] [1 1 1 [3 3]] [0 0 1]] pdfm (\))f(also)h +(c)n(hange,)h(in)n(tro)r(ducing)f(a)f(comp)r(ensating)f(Jacobian)i(in)f +(\(2.4)p (#equation.2.4) [[517 446 532 458] [1 1 1 [3 3]] [0 0 1]] pdfm +(\).)0 1619 y(Finally)-6 b(,)25 b(c)n(hanging)e(v)l(ariables)g(to)f +Fk(t)g Fr(and)g Fk(\034)30 b Fr(also)23 b(c)n(hanges)f(the)f(state)h +Fi(h)p Fr(\006)p Fi(j)p Fr(.)30 b(Equation)23 b(\(1.3)p + (#equation.1.3) [[471 427 486 439] [1 1 1 [3 3]] [0 0 1]] pdfm (\))g(giv)n +(es)117 1783 y Fi(h)p Fr(\006)p Fk(;)11 b(z)18 b Fi(\000)e +Ff(e)-39 b Fk(r)17 b Fr(+)i Ff(e)-42 b Fk(\032)q(\022)r Fi(j)19 +b Fr(=)o Fi(h)p Fr(\006)p Fk(;)11 b(z)18 b Fi(\000)e Ff(e)-38 +b Fk(r)r Fi(j)873 1729 y Ff(\000)903 1783 y Fr(1)15 b Fi(\000)g +Fr(2)t Ff(e)-41 b Fk(\032G)1137 1801 y Fd(\000)1187 1783 y +Fc(1)p 1187 1791 23 3 v 1187 1817 a(2)1221 1729 y Ff(\001)1270 +1783 y Fr(=)18 b Fi(h)p Fr(\006)p Fk(;)11 b(z)18 b Fi(\000)c +Fr(\()p Fk(r)j Fr(+)d Fk(t)1721 1755 y Fe(2)1751 1783 y Fr(\))g +Fi(\000)h Fk(t\032\034)22 b Fi(\000)15 b Fr(\()p Fk(\032)g +Fi(\000)f Fk(t\034)8 b Fr(\))p Fk(\022)r Fi(j)553 1909 y Fr(=)o +Fi(h)p Fr(\006)p Fk(;)j(z)18 b Fi(\000)d Fr(\()p Fk(r)h Fr(+)f +Fk(t)986 1881 y Fe(2)1015 1909 y Fr(\))p Fi(j)1059 1855 y Ff(\000)1090 +1909 y Fr(1)g(+)f Fk(t\032\034)8 b(L)1344 1927 y Fd(\000)p +Fe(1)1431 1909 y Fr(+)14 b(2\()p Fk(\032)h Fi(\000)g Fk(t\034)8 +b Fr(\))p Fk(G)1811 1927 y Fd(\000)1860 1909 y Fc(1)p 1860 +1917 V 1860 1943 a(2)1893 1855 y Ff(\001)1924 1909 y Fk(:)2430 +1848 y Fr(\(2)p Fk(:)p Fr(10)q(\))0 2076 y(In)23 b(this)h(form)n(ula,)h(w)n +(e)e(see)f(the)h(consequences)e(of)j(the)f(non-split)h(nature)f(of)h(\(1.10)p + (#equation.1.10) [[430 344 451 356] [1 1 1 [3 3]] [0 0 1]] pdfm (\).)35 +b(The)22 b Fk(L)2368 2094 y Fd(\000)p Fe(1)2463 2076 y Fr(term)0 +2182 y(w)n(ould)30 b(not)f(b)r(e)f(there)g(for)h(some)f(split)i +(transformation.)51 b(So,)32 b(though)c(the)h(measure)e(is)j(p)r(erfectly)0 +2288 y(con)n(tin)n(uous,)24 b(the)f(app)r(earance)e(of)j(the)f(extra)f(term)g +(in)i(\(2.7)p (#equation.2.7) [[332 306 348 318] [1 1 1 [3 3]] [0 0 1]] pdfm +(\))f(is)h(a)f(consequence)e(of)j(expanding)f(it)h(in)0 2394 +y(co)r(ordinates)i(appropriate)g(to)g(the)f(neigh)n(b)r(orho)r(o)r(d)h(of)g +(the)f(b)r(oundary)h(of)g(mo)r(duli)g(space)g(when)f(the)0 +2500 y(t)n(w)n(o)d(punctures)f(collide.)133 2606 y(Recall)16 +b(that)g(our)g(goal)i(is)e(to)h(p)r(erform)e(an)h(op)r(erator)g(pro)r(duct)g +(expansion,)i(whic)n(h)e(in)g(this)h(con)n(text)0 2712 y(amoun)n(ts)e(to)g +(rewriting)h(the)e(state)h(that)f(arises)i(from)f(the)g(collision)h(of)g(t)n +(w)n(o)g(op)r(erators)f(as)g(the)g(insertion)0 2818 y(of)25 +b(a)g(single)g(op)r(erator)f(at)h(the)f(collision)i(p)r(oin)n(t.)38 +b(The)24 b(result)g(in)h(Green)f(and)g(Seib)r(erg)g(w)n(as)h(that)g(the)0 +2924 y(na)-7 b(\177)-26 b(\020v)n(e)29 b(OPE)g(resulted)g(in)g(a)g(state)g +(that)g(w)n(as)g(not)g(the)g(highest)g(comp)r(onen)n(t)e(of)j(a)f(sup)r +(er\014eld)f(and)0 3030 y(hence)18 b(violated)j(sup)r(ersymmetry)-6 +b(.)28 b(Restoring)20 b(sup)r(ersymmetry)e(required)h(adding)i(a)g(con)n +(tact)e(term.)0 3136 y(Ho)n(w)n(ev)n(er,)33 b(as)f(w)n(e)e(will)j(shortly)e +(see,)i(the)d(state)h(that)g(w)n(e)f(\014nd)h Fl(is)h Fr(the)e(highest)h +(comp)r(onen)n(t)e(of)j(a)0 3242 y(sup)r(er\014eld)16 b(inserted)g(at)g(the)g +(collision)j(p)r(oin)n(t,)f(and)f(th)n(us,)h(no)f(con)n(tact)f(term)f(is)i +(needed.)27 b(It)16 b(is)h(precisely)0 3348 y(the)23 b(\\extra")i +Fk(L)402 3366 y Fd(\000)p Fe(1)497 3348 y Fr(term)e(that)h(restores)g(sup)r +(ersymmetry)-6 b(.)34 b(The)23 b(k)n(ey)h(p)r(oin)n(t)h(is)g(to)f(appreciate) +f(what)0 3454 y(\\taking)31 b(the)e(OPE")h(means)f(in)i(the)e(op)r(erator)g +(formalism:)46 b(tak)n(e)30 b(the)f(t)n(w)n(o)i(states)e(at)h +Fk(P)39 b Fr(and)30 b Fk(Q)p Fr(,)0 3560 y(con)n(tract)c(them)f(with)i(the)f +(state)h(asso)r(ciated)g(to)g(the)f(3-punctured)f(sphere,)j(and)f(insert)f +(the)g(state)1283 3719 y(9)p eop +%%Page: 10 11 +10 10 bop 0 66 a Fr(that)20 b(results)f(at)h(the)f(nec)n(k)g(where)g(the)g +(3-punctured)f(sphere)h(is)i(joined)f(on)n(to)g(the)f(rest)g(of)h(the)f +(surface)0 166 y(\(Fig.)24 b(1\).)31 b(In)22 b(doing)h(so,)h(it)e(is)h(vital) +h(to)e(use)h(the)e(co)r(ordinates)i(appropriate)f(to)h(this)f(sup)r +(erconformal)0 266 y(geometry)-6 b(.)28 b(In)18 b(particular,)i(to)e(see)g +(that)g(the)g(state)g(inserted)f(at)i(the)e(nec)n(k)h(is)h(the)e(highest)i +(comp)r(onen)n(t)0 366 y(of)25 b(a)f(sup)r(er\014eld,)h(w)n(e)f(need)f(to)h +(use)g(a)g(con)n(tour-deformation,)h(or)g(more)e(p)r(edan)n(tically)-6 +b(,)26 b(to)f(mak)n(e)e(use)0 466 y(of)k(the)f(Borel-am)n(biguit)n(y)i(asso)r +(ciated)e(to)h(the)f(3-punctured)f(sphere.)43 b(F)-6 b(rom)27 +b(the)f(Nev)n(eu-Sc)n(h)n(w)n(artz)0 566 y(algebra,)d(w)n(e)f(ha)n(v)n(e)859 +666 y Fk(L)904 684 y Fd(\000)p Fe(1)994 666 y Fr(=)c(2)p Fi(f)p +Fk(G)1182 684 y Fd(\000)1233 666 y Fc(1)p 1233 674 23 3 v 1233 +700 a(2)1266 666 y Fk(;)11 b(G)1347 684 y Fd(\000)1398 666 +y Fc(1)p 1398 674 V 1398 700 a(2)1432 666 y Fi(g)18 b Fr(=)g(4)p +Fk(G)1638 639 y Fe(2)1638 688 y Fd(\000)1688 671 y Fc(1)p 1688 +679 V 1688 704 a(2)1722 666 y Fk(:)0 787 y Fr(Th)n(us,)23 b(\(2.7)p + (#equation.2.7) [[110 576 125 588] [1 1 1 [3 3]] [0 0 1]] pdfm (\))f(b)r +(ecomes)160 833 y Ff(Z)226 870 y(\002)258 924 y Fr(d)s Fk(r)16 +b Fi(^)k Fr(d)p 448 880 32 3 v 3 w Fk(r)c Fi(^)k Fr(d)s Fk(t)14 +b Fi(^)20 b Fr(d)p 740 875 24 3 v 3 w Fk(t)p Fi(j)5 b Fr(d)s +Fk(\032)g Fr(d)s Fk(\034)943 870 y Ff(\003)991 924 y Fr(4)p +Fk(\032\034)j Fi(j)p Fk(t)p Fi(j)1155 896 y Fe(2)1186 924 y +Fi(h)p Fr(\006)p Fk(;)j(\033)1327 941 y Fh(P)1361 948 y Fc(0)1391 +924 y Fk(;)g(\033)1458 941 y Fh(Q)1500 948 y Fc(0)1529 924 +y Fi(j)1547 870 y Ff(\000)1578 924 y Fk(G)1630 889 y Fe(\()p +Fh(P)c Fe(\))1630 951 y Fd(\000)1680 933 y Fc(1)p 1680 941 +23 3 v 1680 967 a(2)1731 924 y Fr(+)14 b Fk(G)1849 889 y Fe(\()p +Fh(Q)p Fe(\))1849 951 y Fd(\000)1899 933 y Fc(1)p 1899 941 +V 1899 967 a(2)1936 870 y Ff(\001)1966 924 y Fk(G)2018 889 +y Fe(\()p Fh(P)7 b Fe(\))2018 951 y Fd(\000)2068 933 y Fc(1)p +2068 941 V 2068 967 a(2)984 1077 y Fi(\002)14 b Fk(b)1079 1042 +y Fe(\()p Fh(P)7 b Fe(\))1079 1094 y Fd(\000)p Fe(1)1162 1059 +y Fr(\026)1165 1077 y Fk(b)1194 1042 y Fe(\()p Fh(P)g Fe(\))1194 +1094 y Fd(\000)p Fe(1)1279 1077 y Fk(\016)s Fr([)p Fk(\014)1372 +1042 y Fe(\()p Fh(P)g Fe(\))1368 1104 y Fd(\000)1417 1086 y +Fc(1)p 1417 1094 V 1417 1120 a(2)1456 1077 y Fr(])p Fk(b)1503 +1042 y Fe(\()p Fh(Q)p Fe(\))1503 1094 y Fd(\000)p Fe(1)1588 +1059 y Fr(\026)1590 1077 y Fk(b)1619 1042 y Fe(\()p Fh(Q)p +Fe(\))1619 1094 y Fd(\000)p Fe(1)1705 1077 y Fk(\016)s Fr([)p +Fk(\014)1798 1042 y Fe(\()p Fh(Q)p Fe(\))1794 1104 y Fd(\000)1843 +1086 y Fc(1)p 1843 1094 V 1843 1120 a(2)1883 1077 y Fr(])p +Fi(j)p Fk( )r Fi(i)1990 1049 y Fh(P)2051 1077 y Fi(\012)14 +b(j)p Fk( )r Fi(i)2206 1049 y Fh(Q)2252 1077 y Fk(:)2430 993 +y Fr(\(2)p Fk(:)p Fr(11)q(\))0 1218 y(The)28 b(factor)h(of)g(\()p +Fk(G)500 1184 y Fe(\()p Fh(P)7 b Fe(\))500 1245 y Fd(\000)550 +1228 y Fc(1)p 550 1236 V 550 1261 a(2)605 1218 y Fr(+)19 b +Fk(G)728 1184 y Fe(\()p Fh(Q)p Fe(\))728 1245 y Fd(\000)778 +1228 y Fc(1)p 778 1236 V 778 1261 a(2)815 1218 y Fr(\))29 b(is)g(equiv)l +(alen)n(t)g(\(up)f(to)h(the)f(Borel-am)n(biguit)n(y)i(asso)r(ciated)f(to)g +(the)0 1337 y(3-punctured)23 b(sphere\))h(to)h(an)f(insertion)i +Fk(G)1118 1303 y Fe(\()p Fh(N)5 b Fe(\))1118 1364 y Fd(\000)1167 +1347 y Fc(1)p 1167 1355 V 1167 1380 a(2)1210 1337 y Fr(,)25 +b(on)g(the)f(nec)n(k)g(of)h(the)f(sphere)g(that)g(is)i(pinc)n(hing)f(o\013.)0 +1437 y(E\013ectiv)n(ely)-6 b(,)20 b(w)n(e)f(can)f(replace)g(the)g(sum)h(of)g +(t)n(w)n(o)g(con)n(tours)g(surrounding)h Fk(P)27 b Fr(and)19 +b Fk(Q)g Fr(with)g(one)f(con)n(tour)0 1537 y(surrounding)23 +b(b)r(oth)f(and)g(deformed)f(this)h(con)n(tour)g(on)n(to)g(the)g(nec)n(k)f +(\(Fig.)i(2\).)266 2161 y(Fig.)g(2:Con)n(tour)g(manipulations.)133 +2315 y(The)c Fk(b)g Fr(and)g Fk(\016)s Fr(\()p Fk(\014)t Fr(\))e(insertions)k +(ha)n(v)n(e)e(remo)n(v)n(ed)f(the)h(ghost)h(dep)r(endence)c(in)k(our)g(SPSs)g +(and)f(w)n(e)g(are)0 2415 y(left)j(with)h(a)f(state)g Fi(j)516 +2398 y Ff(e)504 2415 y Fk( )s Fi(i)576 2433 y Fh(M)657 2415 +y Fr(in)g(the)f(matter)g(theory)-6 b(,)23 b(inserted)e(on)i(the)e(nec)n(k,)h +(giv)n(en)g(b)n(y)622 2538 y Fi(j)653 2520 y Ff(e)640 2538 +y Fk( )t Fi(i)713 2556 y Fh(M)790 2538 y Fr(=)c Fk(G)912 2503 +y Fe(\()p Fh(N)5 b Fe(\))912 2565 y Fd(\000)962 2547 y Fc(1)p +962 2555 V 962 2581 a(2)1004 2538 y Fi(j)p Fk(\033)1060 2556 +y Fh(N)1111 2538 y Fi(ih)p Fk(\033)1201 2556 y Fh(P)1245 2538 +y Fk(;)11 b(\033)1312 2556 y Fh(Q)1357 2538 y Fi(j)p Fk(G)1427 +2503 y Fe(\()p Fh(P)c Fe(\))1427 2565 y Fd(\000)1477 2547 y +Fc(1)p 1477 2555 V 1477 2581 a(2)1514 2538 y Fi(j)p Fk( )r +Fi(i)1603 2510 y Fh(P)1603 2556 y(M)1677 2538 y Fi(\012)15 +b(j)p Fk( )r Fi(i)1833 2506 y Fh(Q)1833 2557 y(M)1959 2538 +y Fk(:)453 b Fr(\(2)p Fk(:)p Fr(12)q(\))0 2661 y(Here)19 b +Fi(j)p Fk(\033)211 2678 y Fh(N)262 2661 y Fi(ih)p Fk(\033)352 +2678 y Fh(P)396 2661 y Fk(;)11 b(\033)463 2678 y Fh(Q)509 2661 +y Fi(j)21 b Fr(is)g(the)f(state)g(asso)r(ciated)h(to)f(the)g(3-punctured)g +(sphere,)g(view)n(ed)g(as)h(an)g(elemen)n(t)0 2760 y(of)f Fi(H)11 +b(\012)f(H)259 2736 y Fd(\003)299 2760 y Fi(\012)g(H)418 2736 +y Fd(\003)449 2760 y Fr(.)29 b(Since)19 b Fi(j)697 2743 y Ff(e)685 +2760 y Fk( )s Fi(i)757 2778 y Fh(M)836 2760 y Fr(is)h(the)f(highest)h(comp)r +(onen)n(t)e(of)j(a)f(sup)r(er\014eld)f(\()p Fl(i.e.)h Fr(it)g(is)g +Fk(G)2319 2778 y Fd(\000)2369 2761 y Fc(1)p 2369 2769 V 2369 +2794 a(2)2423 2760 y Fr(acting)0 2860 y(on)i(the)g(lo)n(w)n(est)g(comp)r +(onen)n(t)f(of)h(a)h(sup)r(er\014eld\),)e(it)i(is)f(sup)r(ersymmetric.)133 +2960 y(Th)n(us)e(w)n(e)g(ha)n(v)n(e)h(main)n(tained)f(w)n(orld-sheet)g(sup)r +(ersymmetry)e Fl(without)i Fr(adding)h(an)g(explicit)f(con-)0 +3060 y(tact)26 b(term)g(when)g(the)g(t)n(w)n(o)h(v)n(ertex)f(op)r(erators)h +(coincide.)43 b(The)27 b(correction)f(to)g(the)h(\\na)-7 b(\177)-26 +b(\020v)n(e")27 b(result)0 3160 y(\(of)20 b(taking)g(the)f(OPE)h(of)g(t)n(w)n +(o)g(\(0\)-picture)f(v)n(ertex)g(op)r(erators\))g(arises)h(not)g(from)f(an)h +(explicit)g(con)n(tact)0 3260 y(term,)h(but)g(rather)h(from)f(a)h(prop)r(er)g +(accoun)n(t)f(of)h(the)f(sup)r(erconformal)g(geometry)g(asso)r(ciated)h(to)g 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b(the)e(in)n(tegration)0 2157 y(am)n(biguit)n(y)j(w)n(as)g(not)f +(really)h(an)g(am)n(biguit)n(y)g(in)g(the)e(measure)g([20)p + (#reference.20) [[369 330 381 342] [1 1 1 [3 3]] [0 0 1]] pdfm (],)30 +b(but)c(rather,)h(an)g(am)n(biguit)n(y)g(in)0 2265 y(the)21 +b(region)h(of)g(in)n(tegration.)31 b(Here)20 b(the)h(region)h(of)g(in)n +(tegration)h(\(de\014ned)d(b)n(y)i(some)f(cuto\013)f Fi(j)p +Fk(t)p Fi(j)g Fk(>)e(\017)p Fr(\))j(is)0 2373 y(the)f(same;)h(it)g(is)h +(really)f(the)f(measure)g(that)g(su\013ers)h(from)f(a)h(p)r(oten)n(tial)g(am) +n(biguit)n(y)-6 b(.)31 b(W)-6 b(e)21 b(b)r(eliev)n(e)f(that)0 +2481 y(there)c(is,)j(in)e(fact,)i(no)e(am)n(biguit)n(y)g(so)h(long)f(as)h +(one)e(restricts)h(oneself)g(to)g(co)r(ordinate)g(families)h(with)f(the)0 +2589 y(correct)i(asymptotic)g(b)r(eha)n(vior)h(at)g(in\014nit)n(y)h(\()p +Fl(i.e.)f Fr(co)r(ordinate)f(families)i(whic)n(h)f(also)h(giv)n(e)f(the)f +(correct)0 2697 y(dilaton)k(insertions\).)31 b(A)21 b(more)h(careful)g(in)n 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Fe(1)623 279 y Fk(;)g(\032)686 297 y Fe(2)717 279 y Fr(\))26 +b(and)g(those)g(appropriate)g(near)g(the)f(b)r(oundary)i(m)n(ust)e(in)n(v)n +(olv)n(e)i(a)g(non-)0 385 y(split)h(transformation)f(for)g(at)g(least)g(one)f +(of)h(the)f(comp)r(onen)n(ts)f(of)i(the)f(b)r(oundary)-6 b(.)44 +b(In)27 b(the)f(case)g(at)0 491 y(hand,)34 b(it)e(is)g Fk(r)k +Fi(!)f Fr(0)c(whic)n(h)h(in)n(v)n(olv)n(es)h(the)e(nonsplit)h(transformation) +g(but,)i(ho)n(w)n(ev)n(er)d(w)n(e)g(c)n(ho)r(ose)0 598 y(to)i(co)r +(ordinatize)f(the)g(in)n(terior)i(of)f(sup)r(ermo)r(duli)f(space,)k(it)d(is)g +(imp)r(ossible)g(to)g(a)n(v)n(oid)h(a)f(nonsplit)0 704 y(transformation)d +(somewhere)e([20)p + (#reference.20) [[220 591 232 603] [1 1 1 [3 3]] [0 0 1]] pdfm (].)52 +b(In)30 b(constructing)f(the)f(corresp)r(onding)h(string)h(measure,)h(this)0 +810 y(nonsplit)i(transformation)f(manifests)g(itself)h(as)f(a)g(correction)f +(to)h(the)f(\\na)-7 b(\177)-26 b(\020v)n(e")33 b(measure,)g(whic)n(h)0 +917 y(restores)18 b(the)f(sup)r(erconformal)h(W)-6 b(ard)19 +b(iden)n(tities.)29 b(The)18 b(calculation)h(of)g(the)e(measure)g(in)i(the)e +(in)n(terior)0 1023 y(of)23 b(mo)r(duli)g(space)f(is)h(easily)g(translated)g +(in)n(to)g(the)f(con)n(v)n(en)n(tional)h(picture-c)n(hanging)g(language.)32 +b(The)0 1129 y(v)n(ertex)19 b(op)r(erators)g(at)g(1)p Fk(;)11 +b Fi(1)21 b Fr(are)e(in)h(the)f(\(0\)-picture,)g(while)h(the)e(v)n(ertex)h +(op)r(erators)g(at)h(0)p Fk(;)11 b(r)22 b Fr(are)d(in)h(the)0 +1235 y(\()p Fi(\000)p Fr(1\)-picture.)34 b(But)23 b(the)h(picture-c)n +(hanging)f(is)i(to)r(o)e(na)-7 b(\177)-26 b(\020v)n(e,)25 b(and)f(in)g(need)f +(of)h(corrections)g(when)f(the)0 1342 y(t)n(w)n(o)f(\()p Fi(\000)p +Fr(1\)-picture)f(v)n(ertex)h(op)r(erators)g(run)g(in)n(to)g(eac)n(h)g(other.) +133 1448 y(The)i(real)i(p)r(oin)n(t)f(of)h(this)g(is)f(that,)i(in)e(general,) +h(w)n(e)f(need)f(to)h(cut)g(o\013)g(the)g(in)n(tegration)g(b)r(ecause)0 +1554 y(the)30 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