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On the trace anomaly of a Weyl fermion in a gauge background
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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. The latter 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 a conjectured contribution of an odd-parity term to the trace anomaly of a Weyl fermion in curved backgrounds.
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Weyl fermions in a non-abelian gauge background and trace anomalies
The trace anomaly of four-dimensional Weyl fermions in a non-abelian gauge background is (1/48 pi^2) tr F^2 with no parity-odd Chern-Pontryagin contribution, derived via Pauli-Villars regularization.
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