Topological anomalies from the path integral measure in superspace

TL;DR

This paper presents a fully quantum analysis of the central charge and anomalies in the N=1 Wess-Zumino model with a kink, using superspace path integrals and heat kernel regularization, confirming the BPS bound saturation at the quantum level.

Contribution

It introduces a novel quantum superspace path integral approach to analyze superconformal anomalies and the central charge in the Wess-Zumino model, extending previous semi-classical results.

Findings

All superconformal anomalies are derived as a single Jacobian factor.

The quantum supersymmetry algebra includes superconformal anomalies.

The BPS bound remains saturated at the quantum level due to equal energy and central charge anomalies.

Abstract

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 all superconformal anomalies as one Jacobian factor. The conserved quantum currents differ from the Noether currents by terms proportional to field equations, and these terms contribute to the anomalies. We identify the particular variation of the superfield which produces the central charge current and its anomaly; it is the variation of the auxiliary field. The quantum supersymmetry algebra which includes the contributions of superconformal anomalies is derived by using the Bjorken-Johnson-Low method instead of semi-classical Dirac brackets. We confirm earlier results that the BPS bound remains saturated at the quantum level due to equal anomalies in the energy and central charge.