Topological anomalies from the path integral measure in supe(19)

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

Ifoneconsiderstherigidconformalsupersymmetytransformationgeneratedbytheparameter

¯(x)=a¯(x)x(5.6)

theactiontransformsasfollows

δS=

andoneobtainstheidentity

¯g µ(x))=γµjµ(x) h µ(xJ d2x[( µa¯(x))xjµ(x)+a¯(x)γµjµ(x)],(5.7)

π µ(x)ψ(x)=γµJ(5.9)

where(γµjµ(x))ingγµγνγµ=0instrictlyd=2oneobtains

µ(x))exp=(γµjµ)exp=γµjµ= 2U( )ψ(x)(γµJ

and

µ(x))anomaly= (γµJh¯g(5.10)