Topological anomalies from the path integral measure in supe(14)

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

Herewewriteh¯explicitlytoindicatethat¯weareworkingattheone-looplevel.2θθ ¯Using1

µ andQβφ=ψβ+Fθβ θ2(DαD

βαφ)Qβφ QβV,and1

µ+1

2(γµJ µ)(x) T µµ(x)θ+1

2(ψγ¯ν

ψ)γνθ

δ(θ)µjµ(x)

=1

2π[ψ(x)+F(x)θ (γµθ) µ (x)+δ(θ) ψ(x)]

orincomponentnotation

(γµJ µ)(x)=(γjµ)(x) ¯hg

µ

2πF(x),

ζ µ(x) 1µσ

(ψγ¯2π σ (x),

5 ψ)(x)=0,

jµ(x)=h¯g

µ

2(γµjµ)(x) (Tµµ)(x)θ+(γµζµ)(x)γ5θ δ(θ) µ(Uγµψ)

≡=QV U((φ ()x,ψ θ))[FU( ) g ψψ¯]θ+ µ U( )γµθ δ(θ) µ(Uγµψ)

whereV= [1(4.6)(4.8)