# Weyl fermions in a non-abelian gauge background and trace anomalies

## TL;DR

This paper investigates the trace and chiral anomalies of Weyl fermions in non-abelian gauge backgrounds, demonstrating gauge invariance of the trace anomaly and clarifying the absence of parity-odd contributions.

## Contribution

It provides a gauge-invariant formulation of the trace anomaly for Weyl fermions in non-abelian backgrounds and clarifies debates on topological contributions.

## Key findings

- Trace anomaly can be expressed in a gauge-invariant form.
- No parity-odd topological contribution in the trace anomaly.
- Reconfirmation of the chiral anomaly in non-abelian gauge theories.

## Abstract

We study the trace and chiral anomalies of Weyl fermions in a non-abelian gauge background in four dimensions. Using a Pauli-Villars regularization we identify the trace anomaly, proving that it can be cast in a gauge invariant form, even in the presence of the non-abelian chiral anomaly, that we rederive to check the consistency of our methods. In particular, we find that the trace anomaly does not contain any parity-odd topological contribution, whose presence has been debated in the recent literature.