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

Trace anomaly for chiral fermions via Hadamard subtraction