Noncommutative Supersymmetric Gauge Anomaly

TL;DR

This paper develops a method to compute gauge anomalies in noncommutative supersymmetric Yang-Mills theories with chiral matter, resulting in a simplified expression that includes known bosonic anomalies.

Contribution

It extends existing techniques to noncommutative supersymmetric gauge theories, providing a compact and explicit formula for the gauge anomaly.

Findings

Derived a simple, compact expression for the gauge anomaly.

Confirmed the lowest component matches known bosonic anomalies.

Validated the method through component reduction in WZ gauge.

Abstract

We extend the general method of hep-th/0009192 to compute the consistent gauge anomaly for noncommutative 4d SSYM coupled to chiral matter. The choice of the minimal homotopy path allows us to obtain a simple and compact result. We perform the reduction to components in the WZ gauge proving that our result contains, as lowest component, the bosonic chiral anomaly for noncommutative YM theories recently obtained in literature.