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1、FERMILAB-PUB-96/445-TINTRODUCTIONTOSUPERSYMMETRYJOSEPHD.LYKKENFermiNationalAcceleratorLaboratoryP.O.Box500Batavia,IL60510Theselecturesgiveaself-containedintroductiontosupersymmetryfromamodernperspective.Emphasisisplacedonmaterialessentialtounderstandingduali
2、ty.Topicsinclude:centralchargesandBPS-saturatedstates,supersymmetricnonlin-earsigmamodels,N=2Yang-Millstheory,holomorphyandtheN=2Yang-Millsβfunction,supersymmetryin2,6,10,and11spacetimedimensions.1Introduction“Nevermind,lads.Sametimetomorrow.Wemustgetawinner
3、oneday.”–PeterCook,asthedoomsdayprophetin“TheEndoftheWorld”.Supersymmetry,alongwithitsmonozygoticsiblingsuperstringtheory,hasbecomethedominantframeworkforformulatingphysicsbeyondthestandardmodel.Thisdespitethefactthat,asofthismorning,thereisnounambiguousexpe
4、rimentalevidenceforeitheridea.Theoristsfindsupersymmetryappealingforreasonswhicharebothphenomenologicalandtechnical.IntheselecturesIwillfocusexclusivelyonthetechnicalappeal.Therearemanygoodrecentre-viewsofthephenomenologyofsupersymmetry.1Somegoodtechnicalrevi
5、ewsareWessandBagger,2West,3andSohnius.4Thegoaloftheselecturesistoprovidethestudentwiththetechnicalback-arXiv:hep-th/9612114v111Dec1996groundrequisitefortherecentapplicationsofdualityideastosupersymmetricgaugetheoriesandsuperstrings.Morespecifically,ifyouabsor
6、bthematerialintheselectures,youwillunderstandSection2ofSeibergandWitten,5andyouwillhaveavaguenotionofwhytheremightbesuchathingasM-theory.Beyondthat,you’reonyourown.2RepresentationsofSupersymmetry2.1Thegeneral4-dimensionalsupersymmetryalgebraAsymmetryoftheS-m
7、atrixmeansthatthesymmetrytransformationshavetheeffectofmerelyreshufflingtheasymptoticsingleandmultiparticlestates.TheknownsymmetriesoftheS-matrixinparticlephysicsare:1•Poincar´einvariance,thesemi-directproductoftranslationsandLorentzrotations,withgeneratorsPm,M
8、mn.•So-called“internal”globalsymmetries,relatedtoconservedquantumnumberssuchaselectricchargeandisospin.ThesymmetrygeneratorsareLorentzscalarsandgenerateaLiealgebra,j[Bℓ,Bk]=iCℓkBj,(1)jwheretheCa
