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1、CERN-TH.6799/93FOUR-DIMENSIONALGRAVITATIONALBACKGROUNDSBASEDONN=4,cˆ=4,SUPERCONFORMALSYSTEMSCostasKounnas∗)TheoreticalPhysicsDivision,CERNGeneva,SwitzerlandABSTRACTWeproposetwonewrealizationsoftheN=4,ˆc=4superconformalsystembasedonthecompactandnon-compactv
2、ersionsofparafermionicalgebras.Thetargetspaceinterpretationofthesesystemsisgivenintermsoffour-dimensionaltargetspaceswithnon-trivialmetricandtopologydifferentfromthepreviouslyknownfour-dimensionalsemi-wormholerealization.Theproposedˆc=4systemscanbeusedasabu
3、ildingblocktoconstructperturbativelystablesuperstringsolutionswithcovariantizedtargetspacesupersymmetryaroundnon-trivialgravitationalanddilatonbackgrounds.arXiv:hep-th/9304102v122Apr1993∗)OnleavefromEcoleNormaleSup´erieure,24,rueLhomond,75231ParisCedex05,F
4、rance.CERN-TH.6799/93hep-th/9304102February19931.INTRODUCTIONThestudyofstablestringsolutionsaroundnon-trivialgravitationalbackgroundsprovidesabetterunderstandingofthequantumgravitationalphenomena;inprinciple,itmayalsoshedsomelightonsomephysicalprocessesint
5、hepresenceofahighlycurvedorevensingularspace-time(e.g.black-holes,wormholes,singularcosmologicalsolutionsorother)[1]–[19].Approximateclassicalorsemi-classicalsolutionscanbeobtainedviatheα′ex-pansionofthetwo-dimensionalσ-model[22].Thesesolutions(inlowestord
6、erofα′)areidenticaltothoseoftheclassicalEinsteinequationsinthepresenceofadilatonfield,antisymmetrictensorfieldandsomeminimallycoupledgaugematter.Theα′σ-modelapproachisveryusefulsinceitprovidesuswithawell-definedmethodtoobtainandstudy,inlowenergies,thestring-i
7、nducedeffectivefieldtheories.Theα′expansionhoweverbreaksdownanditfailstodescribetheinterestingphysicsofthequantumgravitationalphenomenainshortdistances,inparticularallstringyphenomenaaroundhighlycurvedorsingularbackgrounds.Itisthereforenecessarytogobeyondthe
8、α′expansionandtrytoextendthephysicallyinteresting(semi)-classicalsolutionstosomeexactstringvacua.Inourdayswedonotknowyetofanysystematicwaytoextendtheσ-modelclassicalsolutionstosomeexact(super)-conformaltheori