On the trace anomaly of a Weyl fermion

Abstract

We calculate the trace anomaly of a Weyl fermion coupled to gravity by using Fujikawa's method supplemented by the choice of a consistent regulator. The latter is constructed out of Pauli-Villars regulating fields. The motivation for presenting such a calculation stems from recent studies that suggest that the trace anomaly of chiral fermions in four dimensions might contain an imaginary part proportional to the Pontryagin density. We find that the trace anomaly of a Weyl fermion is given by half the trace anomaly of a Dirac fermion, so that no imaginary part proportional to the Pontryagin density is seen to arise.

25 pages, added references and acknowledgments

References in corpus (3)

• Trace anomalies in chiral theories revisited
• General solutions of the Wess-Zumino consistency condition for the Weyl anomalies
• Anomaly-induced effective action and Chern-Simons modification of general relativity

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• Gauge-invariant coefficients in perturbative quantum gravity
• Chiral fermions, dimensional regularization, and the trace anomaly
• Chiral current induced by torsional Weyl anomaly
• On the simplified path integral on spheres
• Trace anomaly of Weyl fermions in the Breitenlohner--Maison scheme for ${\gamma }_{\ast }$
• The Weyl anomaly in interacting quantum field theory on curved spacetimes