Supersymmetry anomalies and the Wess-Zumino Model in a supergravity background

TL;DR

This paper investigates supersymmetry anomalies in the Wess-Zumino model within a supergravity background, demonstrating that potential anomalies can be canceled with counterterms, thus preserving supersymmetry.

Contribution

It provides a detailed calculation of supersymmetry Ward identities in a supergravity background and shows that anomalies can be eliminated with finite counterterms.

Findings

No supersymmetry anomaly is found after counterterm adjustment

Dimensional regularisation effectively computes Ward identity corrections

Supersymmetry is preserved in the studied model

Abstract

We briefly recall the procedure for computing the Ward Identities in the presence of a regulator which violates the symmetry being considered. We compute the first non-trivial correction to the supersymmetry Ward Identity of the Wess-Zumino model in the presence of background supergravity using dimensional regularisation. We find that the result can be removed using a finite local counter term and so there is no supersymmetry anomaly.