Trace anomaly for chiral fermions via Hadamard subtraction

Abstract

We calculate the trace (conformal) anomaly for chiral fermions in a general curved background using Hadamard subtraction. While in intermediate steps of the calculation imaginary terms proportional to the Pontryagin density appear, imposing a vanishing divergence of the stress tensor these terms completely cancel, and we recover the well-known result equal to half the trace anomaly of a Dirac fermion. We elaborate in detail on the advantages of the Hadamard method for the general definition of composite operators in general curved spacetimes, and speculate on possible causes for the appearance of the Pontryagin density in other calculations.

40 pages, additional references and new appendix on two-component fermions

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• CP-violating super Weyl anomaly
• Conformal Contact Terms and Semi-Local Terms
• Hadamard states on spherically symmetric characteristic surfaces, the semi-classical Einstein equations and the Hawking effect
• Chiral fermions, dimensional regularization, and the trace anomaly
• CP-violating supersymmetry anomaly
• Path integral calculation of heat kernel traces with first order operator insertions
• The Weyl anomaly in interacting quantum field theory on curved spacetimes
• Møller maps for Dirac fields in external backgrounds