On the trace anomaly of a Weyl fermion in a gauge background

TL;DR

This paper investigates the trace anomaly of a Weyl fermion in an abelian gauge background, demonstrating it can be expressed in a gauge-invariant way without odd-parity terms, using Pauli-Villars and heat kernel methods.

Contribution

It shows that the trace anomaly for a Weyl fermion can be written in a gauge-invariant form without odd-parity contributions, clarifying a debated issue.

Findings

Trace anomaly can be gauge invariant

No odd-parity Chern-Pontryagin term in the anomaly

Uses Pauli-Villars and heat kernel regularization methods

Abstract

We study the trace anomaly of a Weyl fermion in an abelian gauge background. Although the presence of the chiral anomaly implies a breakdown of gauge invariance, we find that the trace anomaly can be cast in a gauge invariant form. In particular, we find that it does not contain any odd-parity contribution proportional to the Chern-Pontryagin density. The latter would be allowed by the consistency conditions. We perform our calculations using Pauli-Villars regularization and heat kernel methods. The issue is analogous to the one recently discussed in the literature about a conjectured contribution of an odd-parity term to the trace anomaly of a Weyl fermion in curved backgrounds.