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1、IntroductiontoMTheoryMiaoLiEnricoFermiInst.andDept.ofPhysicsUniversityofChicago5640S.EllisAve.,ChicagoIL60637,USAThisisanintroductiontosomerecentdevelopmentsinstringtheoryandMtheory.Wetrytoconcentrateonthemainphysicalaspects,andoftenleavemoretechnicaldetailstotheoriginallitera
2、ture.1arXiv:hep-th/9811019v210Dec1998Nov.19981LecturesdeliveredatthedualityworkshopatCCAST,China,Sept.1998.`1.IntroductionInthepastfouryears,aseriesofexcitingdevelopmentsintheareaofsupersymmetric eldtheoriesandstringtheoryhascompletelychangedthelandscapeofthesesubjects.Duality
3、hasbeenthecentralthemeofthesedevelopments.Bynow,itisacommonbeliefthatdi erentstringtheoriesallhavethesameorigin,althoughthisuniquetheorystillremainssomewhatmysterious.ThistheoryisdubbedMtheory[1].Itappearsthatallde-greesoffreedom,givenenoughsupersymmetries,areinourpossession,a
4、ndthefuturee ortwillbedirectedtoward ndingoutanonperturbativeformulationofMtheory.Thoughabstractandseeminglyremotefromtherealworld,Mtheoryalreadyhasfoundmanyusefulapplications,inparticulartosupersymmetricgaugetheoriesinvariousdimensions[2],andtoquantumpropertiesofblackholes[3]
5、.Stringtheoryisthemostpromisingapproachtoquantumgravity[4].Theprimarymotivationformanystringtheoristsistounderstandhowtheuniversallyacceptedtheoryinparticlephysics,calledthestandardmodel,comesaboutfromsomedeeperprinciples,andhowoneeventuallyunderstandssomegenuinequantumgravity
6、phenomena.Ontheonehand,toresolvetheso-calledhierarchyprobleminscales,supersymmetryisahelpfultoolprovideditisbrokendynamically.Thiscertainlydemandssomenonperturbativetreatmentofquantum eldtheoryorstringtheory.Ontheotherhand,anyvisiblequantumgravitye ectsmustinvolvenonperturbati
7、veprocesses,thisisbecausethee ectivecouplingconstantGm2becomesoforder1inthequantumgravityregime.StringtheorywasNformulated,priortothesecondstringrevolution,onlyperturbatively.Thus,wehadlittlehopetoachieveeithergoalinthepast.Amongvariousdualitiesinstringtheory,T-dualitywas rstd
8、iscovered[5].Itcanberealizedorderbyorderintheperturbationtheo
