On the trace anomaly of a Weyl fermion in a gauge background

We study the trace anomaly of a Weyl fermion in an abelian gauge background. Although the presence of the chiral anomaly implies a breakdown of gauge invariance, we find that the trace anomaly can be cast in a gauge invariant form. In particular, we find that it does not contain any odd-parity contribution proportional to the Chern–Pontryagin density, which would be allowed by the consistency conditions. We perform our calculations using Pauli–Villars regularization and heat kernel methods. The issue is analogous to the one recently discussed in the literature about the trace anomaly of a Weyl fermion in curved backgrounds.