Investigation of Pontryagin trace anomaly using Pauli-Villars regularization

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=i1536π2ϵνσκλRρμνσRρμκλ which agrees with the work of Bonora et al. [1].