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Trace anomaly for chiral fermions via Hadamard subtraction. (English) Zbl 1427.83100
Summary: 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.

MSC:
83E30 String and superstring theories in gravitational theory
81T50 Anomalies in quantum field theory
83C47 Methods of quantum field theory in general relativity and gravitational theory
Software:
xAct
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