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

Abstract

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.

26 pages, minor changes and reference added

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• Weyl Anomalies of Four Dimensional Conformal Boundaries and Defects
• Axial gravity and anomalies of fermions
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• Trace anomaly for Weyl fermions using the Breitenlohner-Maison scheme for ${\gamma }_{\ast }$
• CP-violating super Weyl anomaly
• Weyl fermions in a non-abelian gauge background and trace anomalies
• Conformal Contact Terms and Semi-Local Terms
• Nonlinear chiral kinetic theory
• Chiral fermions, dimensional regularization, and the trace anomaly
• On the trace anomaly for Weyl fermions
• CP-violating supersymmetry anomaly
• Path integral calculation of heat kernel traces with first order operator insertions