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}.
Categories: hep-th