An introduction to AdSCFT equivalence 9903007v1

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1、NORDITA-99/14HEFebruary1999AnintroductiontoAdS/CFTequivalencePaoloDiVecchiaNORDITABlegdamsvej17,DK-2100CopenhagenØ,DenmarkTalkgivenatthe32ndInternationalSymposiumontheTheoryofElementaryParticles,Buckow,Germany(September1998)AbstractThisisanintroductiontotheMaldacenaconjectureontheequiv

2、alencebetweenN=4superYang-MillsinMinkowskispace-timeandtypeIIBstringtheorycompactifiedonAdS5⊗S5.1IntroductionGravitationalinteractionsaredescribedbytheEinstein’stheoryofgeneralrelativityormoreingeneralbysupergravitythatisitssupersymmetricextension,whiletheotherinteractionsaredescribedby

3、gaugefieldtheories.Actuallyalsothetheoryofgeneralrelativityisagaugetheorycorrespondingtothegaugingofthespace-timePoincar´egroup,whilethosethataremoreusuallycalledgaugetheoriescorrespondarXiv:hep-th/9903007v128Feb1999tothegaugingofaninternalsymmetrygroup.Butapartfromthefactthattheyarebot

4、hgaugetheoriesdoesitexistanydeeperrelationbetweenthem?Dotheyimplyeachotherinaconsistentquantumtheoryofgravity?Intheframeworkoffieldthe-orythereisnoconnection;theycanbothexistindependentlyfromeachother,butanyfieldtheoryinvolvinggravitysuffersfromtheproblemofnon-renormalizability.However,wh

5、enwetrytolookatthisquestionintheframeworkofstringtheory,weseethattheyoccurnaturallytogetherinthesametheoryandactuallyithasnotbeenpossibletoconstructastringtheorywithoutbothofthem.Stringtheorieswerebornfromtheattemptofdescribingthepropertiesofthestronginteractionsthroughtheconstructiono

6、fthedualresonancemodel.Itbecamesoonclear,however,thatthismodelinitsconsistentform,thatlateronwasrec-ognizedtocorrespondtothequantizationofarelativisticstring,containedallsortofmasslessparticlesasgluons,gravitonsandothersexceptamasslesspseudoscalar1particlecorrespondingtothepionthatinth

7、echirallimitistheonlymasslesspar-ticlethatweexpectinstronginteractions.Becauseofthisandotherunphysicalfeaturesitbecameclearsincethemiddleoftheseventiesthatstringtheoriescouldnotprovideatheoryforstronginteractions,thatinthemeantimeweresuccessfullydescribedintheframeworkofQCD,butcouldi