Investigation of Pontryagin trace anomaly using Pauli-Villars regularization

TL;DR

This paper explores the Pontryagin trace anomaly in chiral fermions within curved spacetime, employing Pauli-Villars regularization and two calculation methods to confirm the anomaly's form.

Contribution

It provides a detailed calculation of the Pontryagin trace anomaly using Pauli-Villars regularization, confirming the anomaly's explicit form for chiral fermions.

Findings

Pontryagin term in trace anomaly derived

Results agree with previous theoretical predictions

Used both Feynman diagram and Fujikawa's methods

Abstract

In this paper, we investigate the Pontryagin trace anomaly for chiral fermions in a general curved background using Pauli-Villars regularization. We use both Feynman diagram method and Fujikawa's method to calculate the parity-odd contribution (Pontryagin term). Our result indicates that the trace anomaly of energy-momentum tensor for chiral fermions has Pontryagin term $P=\frac{i}{1536\pi^2}\epsilon_{\nu\sigma\kappa\lambda}R^{\nu\sigma}_{\ \ \rho\mu}R^{\rho\mu\kappa\lambda}$ which agrees with the work of Bonora et al \cite{Bonora:2014qla}.