Chiral fermions, dimensional regularization, and the trace anomaly

TL;DR

This paper examines the trace anomaly of chiral fermions in dimensional regularization, confirming no parity-odd terms arise when coupling to an abelian gauge field, and clarifies subtle issues in regularization methods.

Contribution

It provides a detailed analysis of the trace anomaly for chiral fermions using a specific regularization scheme, clarifying the absence of parity-odd terms and simplifying the background for better understanding.

Findings

No parity-odd term in the trace anomaly was found.

The Breitenlohner-Maison/'t Hooft-Veltman prescription effectively handles $ ext{γ}^5$.

Simplified background reduces algebraic complexity.

Abstract

We investigate the trace anomaly of a chiral fermion in dimensional regularization, considering in detail the simplest case of coupling to an abelian gauge field. We apply the Breitenlohner-Maison/'t Hooft-Veltman prescription for dealing with the chiral matrix $\gamma^5$ and verify that no parity-odd term arises in the trace anomaly. The issue treated here is analogous to that of a chiral fermion in curved spacetime, discussed in recent literature. The advantage of having a simplified background minimizes the amount of algebraic calculations and allows pinpointing better the subtle points carried by dimensional regularization.