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1、IntroductiontoMTheoryMiaoLiEnricoFermiInst.andDept.ofPhysicsUniversityofChicago5640S.EllisAve.,ChicagoIL60637,USAThisisanintroductiontosomerecentdevelopmentsinstringtheoryandMtheory.Wetrytoconcentrateonthemainphysicalaspects,andoftenleavemoretechnicaldetailstot
2、heoriginalliterature.1arXiv:hep-th/9811019v210Dec1998Nov.19981LecturesdeliveredatthedualityworkshopatCCAST,China,Sept.1998.`1.IntroductionInthepastfouryears,aseriesofexcitingdevelopmentsintheareaofsupersymmetric eldtheoriesandstringtheoryhascompletelychangedthe
3、landscapeofthesesubjects.Dualityhasbeenthecentralthemeofthesedevelopments.Bynow,itisacommonbeliefthatdi erentstringtheoriesallhavethesameorigin,althoughthisuniquetheorystillremainssomewhatmysterious.ThistheoryisdubbedMtheory[1].Itappearsthatallde-greesoffreedom
4、,givenenoughsupersymmetries,areinourpossession,andthefuturee ortwillbedirectedtoward ndingoutanonperturbativeformulationofMtheory.Thoughabstractandseeminglyremotefromtherealworld,Mtheoryalreadyhasfoundmanyusefulapplications,inparticulartosupersymmetricgaugetheo
5、riesinvariousdimensions[2],andtoquantumpropertiesofblackholes[3].Stringtheoryisthemostpromisingapproachtoquantumgravity[4].Theprimarymotivationformanystringtheoristsistounderstandhowtheuniversallyacceptedtheoryinparticlephysics,calledthestandardmodel,comesabout
6、fromsomedeeperprinciples,andhowoneeventuallyunderstandssomegenuinequantumgravityphenomena.Ontheonehand,toresolvetheso-calledhierarchyprobleminscales,supersymmetryisahelpfultoolprovideditisbrokendynamically.Thiscertainlydemandssomenonperturbativetreatmentofquant
7、um eldtheoryorstringtheory.Ontheotherhand,anyvisiblequantumgravitye ectsmustinvolvenonperturbativeprocesses,thisisbecausethee ectivecouplingconstantGm2becomesoforder1inthequantumgravityregime.StringtheorywasNformulated,priortothesecondstringrevolution,onlypertu
8、rbatively.Thus,wehadlittlehopetoachieveeithergoalinthepast.Amongvariousdualitiesinstringtheory,T-dualitywas rstdiscovered[5].Itcanberealizedorderbyorderintheperturbationtheo
