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1、TIT/HEP-578December2007IntroductiontoAdS-CFTlecturesbyHoratiuNastaseGlobalEdgeInstitute,TokyoInstituteofTechnologyOokayama2-12-1,Meguro,Tokyo152-8550,JapanAbstractTheselecturespresentanintroductiontoAdS-CFT,andarein-arXiv:0712.0689v2[hep-th]20Dec2007tendedbothf
2、orbeginingandmoreadvancedgraduatestudents,whicharefamiliarwithquantum?eldtheoryandhaveaworkingknowledgeoftheirbasicmethods.Familiaritywithsupersymmetry,generalrelativityandstringtheoryishelpful,butnotnecessary,asthecourseintendstobeasself-containedaspossible.Iw
3、illintro-ducetheneededelementsof?eldandgaugetheory,generalrelativ-ity,supersymmetry,supergravity,stringsandconformal?eldthe-ory.ThenIdescribethebasicAdS-CFTscenario,ofN=4SuperYang-Mills’srelationtostringtheoryinAdS5×S5,andapplicationsthatcanbederivedfromit:3-po
4、intfunctions,quark-antiquarkpo-tential,?nitetemperatureandscatteringprocesses,theppwavecorrespondenceandspinchains.Ialsodescribesomegeneralprop-ertiesofgravitydualsofgaugetheories.1IntroductionThesenotesarebasedonlecturesgivenattheTokyoInstituteofTechnologyanda
5、ttheTokyoMetropolitanUniversityin2007.Thefullmaterialisdesignedtobetaughtin12lecturesof1.5hourseach,eachlecturecorrespondingtoasection.IhaveaddedsomematerialattheenddealingwithcurrentresearchonobtainingmodelsthatbetterdescribeQCD.Otherwise,thecoursedealswiththe
6、basicAdS-CFTscenario,relatingstringtheoryinAdS×S5toN=4SupersymmetricYang-Millstheoryin4dimensions,sincethisisthe5bestunderstoodandthemostrigorouslyde?nedcase.SowhatistheAntideSitter-ConformalFieldtheorycorrespondence,orAdS-CFT?Itisarelationbetweenaquantum?eldth
7、eorywithconformalinvariance(ageneralizationofscalinginvariance),livinginour?at4dimensionalspace,andstringtheory,whichisaquantumtheoryofgravityandother?elds,livinginthebackgroundsolutionofAdS×S55(5dimensionalAntideSitterspacetimesa5-sphere),acurvedspacewiththepr
8、opertythatalightsignalsenttoin?nitycomesbackina?nitetime.The?at4dimensionalspacelivesattheboundary(atin?nity)oftheAdS×S5,thusthecorrespondence(orequivalence)is5saidtobeanexa
