Topological anomalies from the path integral measure in supe

A fully quantum version of the Witten-Olive analysis of the central charge in the N=1 Wess-Zumino model in $d=2$ with a kink solution is presented by using path integrals in superspace. We regulate the Jacobians with heat kernels in superspace, and obtain

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aUT-03-07YITP-SB-03-11TopologicalmeasureanomaliesinfromsuperspacethepathintegralKazuoFujikawa1DepartmentofPhysics,UniversityofTokyoBunkyo-ku,Tokyo113,JapanPetervanNieuwenhuizen2C.N.YangInstituteforTheoreticalPhysicsStateUniversityofNewYork,StonyBrook,NY11794-3840,USAAbstractAfullyquantumversionoftheWitten-OliveanalysisofthecentralchargeintheN=1Wess-Zuminomodelind=2withakinksolutionispresentedbyusingpathintegralsinsuperspace.WeregulatetheJacobianswithheatkernelsinsuperspace,andobtainallsuperconformalanomaliesasoneJacobianfactor.Theconservedquantumcurrentsdi erfromtheNoethercurrentsbytermsproportionalto eldequations,andthesetermscontributetotheanomalies.Weidentifytheparticularvariationofthesuper eldwhichproducesthecentralchargecurrentanditsanomaly;itisthevariationoftheauxiliary eld.ThequantumsupersymmetryalgebrawhichincludesthecontributionsofsuperconformalanomaliesisderivedbyusingtheBjorken-Johnson-Lowmethodinsteadofsemi-classicalDiracbrackets.Wecon rmearlierresultsthattheBPSboundremainssaturatedatthequantumlevelduetoequalanomaliesintheenergyandcentralcharge.1Introductionandbriefsummary

Supersymmetryandtopologyareintimatelylinked.Forexample,instantonsplayanimportantroleinthee ectiveactionforrigidlysupersymmetric(susy)models[1].TheDonaldsoninvariants,whichcharacterizetopologicalpropertiesofcompactmanifolds,canbecomputedbyusingaparticulartopological eldtheorywhichisobtainedbytwistingaEuclideansupersymmetricN=(2,2)model[2].Weshallconsiderherethesurfacetermsinthesupersymmetryalgebra[3]whichformthecentralcharges.

Thesupersymmetryalgebraofthekink,anN=(1,1)rigidlysupersymmetricmodelin1+1dimensionswithasolitonsolution,readsasfollowsattheclassicallevel[3]

{Qcl,Qcl}=2Hcl 2Zcl(1.1)