The UV and IR Origin of Nonabelian Chiral Gauge Anomalies on Noncommutative Minkowski Space-time

TL;DR

This paper investigates the origins of gauge anomalies in noncommutative nonabelian chiral gauge theories, showing that anomalies arise solely from planar diagrams and depend on the matter representation.

Contribution

It provides a detailed analysis of UV and IR contributions to gauge anomalies, highlighting the role of diagram topology and matter content in noncommutative gauge theories.

Findings

Anomalies originate only from planar triangle diagrams.

Non-planar diagrams do not contribute to gauge anomalies.

The matter representation determines anomaly presence, with adjoint fermions being anomaly-free.

Abstract

We discuss both the UV and IR origin of the one-loop triangle gauge anomalies for noncommutative nonabelian chiral gauge theories with fundamental, adjoint and bi-fundamental fermions for U(N) groups. We find that gauge anomalies only come from planar triangle diagrams, the non-planar triangle contributions giving rise to no breaking of the Ward identies. Generally speaking, theories with fundamental and bi-fundamental chiral matter are anomalous. Theories with only adjoint chiral fermions are anomaly free.