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1、CERN-TH.7148/94hep-th/9402073LPTENS94/04CPTH-A291.0294UCLA/94/TEP/5ExactSupersymmetricStringSolutionsinCurvedGravitationalBackgroundsI.AntoniadisCentredePhysiqueTh´eorique,EcolePolytechnique,91128Palaiseau,France1S.FerraraandC.Kounnas2TheoreticalPhysicsDivision,CERN
2、,Geneva,SwitzerlandAbstractWeconstructanewclassofexactandstablesuperstringsolutionsbasedonN=4superconformalworld-sheetsymmetry.Inasubclassofthese,thefullspectrumofstringexcitationsisderivedinamodular-invariantway.Intheweakcurvaturelimit,oursolutionsdescribeatargetsp
3、acewithnon-trivialmetricandtopology,andgeneralizethepreviouslyknown(semi)worm-hole.Theeffectivefieldtheorylimitisidentifiedincertaincases,withsolutionsarXiv:hep-th/9402073v21Mar1994oftheN=4andN=8extendedgaugedsupergravities,inwhichthenum-berofspace-timesupersymmetriesi
4、sreducedbyafactorof2becauseofthepresenceofnon-trivialdilaton,gravitationaland/orgaugebackgrounds.Inthecontextofstringtheory,oursolutionscorrespondtostablenon-criticalsuperstringsinthestrongcouplingregion;thesuper-Liouvillefieldcou-plestoaunitarymattersystemwithcentra
5、lcharge5≤cˆM≤9.CERN-TH.7148/94February19941LaboratoirePropreduCNRSUPRA.00142OnleavefromEcoleNormaleSup´erieure,24rueLhomond,75231ParisCedex05,France.1IntroductionThestudyofstringpropagationinnon-trivialgravitationalbackgroundscanprovideabetterunderstandingofquantumg
6、ravitationalphenomenaatshortdistances.Non-trivialclassicalstringbackgroundscanbeobtainedbytwodifferentmethods.Thefirstmakesuseofatwo-dimensionalσ-modelwherethespace-timebackgroundscor-respondtofield-dependentcouplingconstants[1].Thevanishingofthecorrespondingβ-function
7、sisidentifiedwiththebackgroundfieldequationsofmotioninthetargetspace[1]-[3].Thesecondapproachconsistsofreplacingthefreespace-timecoordi-natesbyanon-trivial(super)conformalsystem,which,inthesemiclassicallimit,canbeinterpretedasdescribingastringpropagationinnon-trivials
8、pace-time[4]-[19].Thetwomethodsareusefulandcomplementary.Theσ-modelapproachprovidesacleargeometricinterpretation,butithasthedisadvantageof