Anomaly and Nonplanar Diagrams in Noncommutative Gauge Theories

TL;DR

This paper investigates anomalies in noncommutative gauge theories, showing vanishing anomalies in some cases and finite anomalies due to UV/IR mixing in others, with implications for gauge invariance.

Contribution

It provides a detailed analysis of anomalies in noncommutative gauge theories, highlighting conditions under which anomalies vanish or appear due to UV/IR mixing effects.

Findings

Local chiral gauge anomalies vanish for noncommutative U(1) and U(N) with adjoint matter

Finite anomalies arise in noncommutative QED with fundamental matter due to UV/IR mixing

Nonplanar diagrams involve a generalized star-product of gauge fields

Abstract

Anomalies arising from nonplanar triangle diagrams of noncommutative gauge theory are studied. Local chiral gauge anomalies for both noncommutative U(1) and U(N) gauge theories with adjoint matter fields are shown to vanish. For noncommutative QED with fundamental matters, due to UV/IR mixing a finite anomaly emerges from the nonplanar contributions. It involves a generalized $\star$-product of gauge fields.