UV/IR Mixing and Anomalies in Noncommutative Gauge Theories

TL;DR

This paper investigates anomalies in noncommutative gauge theories, revealing that UV/IR mixing influences non-planar anomalies and that adjoint fermions are anomaly-free in certain dimensions.

Contribution

It applies Fujikawa's path integral method to compute anomalies in noncommutative gauge theories, highlighting the role of UV/IR mixing in non-planar sectors.

Findings

Non-planar anomalies arise from UV/IR mixing.

Adjoint fermions have no anomalies in certain dimensions.

Anomalies vanish in the low noncommutative momentum limit.

Abstract

Using path integral method (Fujikawa's method) we calculate anomalies in noncommutative gauge theories with fermions in the bi-fundamental and adjoint representations. We find that axial and chiral gauge anomalies coming from non-planar contributions are derived in the low noncommutative momentum limit $\widetilde{p}^{\mu}(\equiv \theta^{\mu\nu}p_{\nu}) \to 0$. The adjoint chiral fermion carries no anomaly in the non-planar sector in $D=4k (k=1,2,...,)$ dimensions. It is naturally shown from the path integral method that anomalies in non-planar sector originate in UV/IR mixing.