Chiral anomalies in noncommutative gauge theories

TL;DR

This paper investigates chiral anomalies in noncommutative gauge theories, establishing uniqueness of solutions, absence of reducible and mixed anomalies, and clarifying anomalies for adjoint fermions using cohomological methods.

Contribution

It provides a comprehensive cohomological analysis of chiral anomalies in noncommutative U(N) gauge theories across all even dimensions, revealing the structure and constraints of anomalies.

Findings

Only one solution to the WZ consistency condition per dimension

No reducible or mixed anomalies in product gauge groups

Clarification of anomalies for chiral fermions in the adjoint representation

Abstract

Using cohomological methods we discuss several issues related to chiral anomalies in noncommutative U(N) YM theories in any even dimension. We show that for each dimension there is only one solution of the WZ consistency condition and that there cannot be any reducible anomaly, nor any mixed anomaly when the gauge group is a product group. We also clarify some puzzling aspects of the issue of the anomaly when chiral fermions are in the adjoint representation.