Anomalies in noncommutative gauge theories, Seiberg-Witten transformation and Ramond-Ramond couplings

TL;DR

This paper derives an exact expression for axial anomalies in noncommutative gauge theories using the inverse Seiberg-Witten map, linking noncommutative and ordinary anomalies and ensuring consistency with known results.

Contribution

It introduces a novel exact formula for unintegrated axial anomalies in noncommutative gauge theories based on the inverse Seiberg-Witten map and related identities.

Findings

Derived an exact unintegrated axial anomaly expression using the inverse Seiberg-Witten map.

Showed that anomalies reduce to ordinary axial anomalies under Seiberg-Witten transformation.

Established compatibility with existing anomaly results in noncommutative theories.

Abstract

We propose an exact expression for the unintegrated form of the star gauge invariant axial anomaly in an arbitrary even dimensional gauge theory. The proposal is based on the inverse Seiberg-Witten map and identities related to it, obtained earlier by comparing Ramond-Ramond couplings in different decsriptions. The integrated anomalies are expressed in terms of a simplified version of the Elliott formula involving the noncommutative Chern character. These anomalies, under the Seiberg-Witten transformation, reduce to the ordinary axial anomalies. Compatibility with existing results of anomalies in noncommutative theories is established.