Anomaly cancellation in three-dimensional noncommutative gauge theories

TL;DR

This paper demonstrates anomaly cancellation in a three-dimensional noncommutative gauge theory with domain wall fermions, extending understanding of anomalies in noncommutative spaces and their dependence on fermion representations.

Contribution

It shows anomaly cancellation in 3D noncommutative gauge theories with domain wall fermions, specifically for fundamental and adjoint representations, in the small noncommutativity limit.

Findings

Anomaly cancels in the considered noncommutative gauge theory.

Cancellation holds for fermions in fundamental and adjoint representations.

Results are valid in the small noncommutativity limit.

Abstract

The anomaly found by Callan and Harvey is shown to be cancelled in a three-dimensional noncommutative gauge theory coupled to a fermion with a mass function depending on one spatial coordinate (domain wall mass). This evaluation has been done for the fermion in the fundamental and adjoint representations of the gauge group in the limit of small noncommutativity $\theta$ parameter.