Topological anomalies from the path integral measure in supe(10)

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

wherethesecondrelationisderivedbyperformingtheintegral

1(θ1 θ3)pθ2] d2θ2in

2¯D(θ1)δ(θ1 θ2)= exp[ iθ1pθ2],

D2(θ1)δ(θ1 θ2)= p2δ(θ1 θ2).

Usingtheseresults,weobtainthefollowingequations

Γ(x,θ)= 1

D2 1

12gΦD+(gΦ)2,

2gDΦ 1¯DD,(2.28)4

Γ2(x,θ)δ(θ θ1)=[

4p2 1

2gΦD+(gΦ)2]2δ(θ θ1).(2.29)

Weusetheheatkernelexp[(Γ/M)2]ing(2.29)we nd

(exp[1

[ 212gDΦ 1

M

M

2Γ(x,θ)}|θ,x 2