On the Weyl anomaly for chiral fermions

TL;DR

This paper calculates the parity-odd component of the Weyl anomaly for chiral fermions in gravitational backgrounds, revealing that all parity-odd contributions cancel, resulting in a parity-even anomaly.

Contribution

It introduces a real Lagrangian formulation and uses Pauli-Villars regularization to analyze the parity properties of the Weyl anomaly for chiral fermions.

Findings

Parity-odd terms cancel in the anomaly integrand

The resulting Weyl anomaly is parity-even

Methodology ensures a real Lagrangian and consistent regularization

Abstract

We compute the parity-odd part of the Weyl anomaly for chiral fermions in a background gravitational field. We start from a manifestly real form of the Lagrangian (that is, not only real up to a total derivative), and we regularize it by means of Pauli-Villars fermions. All parity-odd terms in the anomaly cancel in the integrand, so that the result of the anomaly is necessarily parity-even.