Trace anomaly for chiral fermions via Hadamard subtraction

TL;DR

This paper computes the trace anomaly for chiral fermions in curved spacetime using Hadamard subtraction, revealing the cancellation of Pontryagin density terms and confirming the anomaly as half that of a Dirac fermion.

Contribution

It demonstrates the application of Hadamard subtraction to derive the trace anomaly for chiral fermions and discusses the cancellation of Pontryagin density terms in this context.

Findings

Pontryagin density terms cancel when stress tensor divergence vanishes.

Trace anomaly for chiral fermions is half that of Dirac fermions.

Hadamard method effectively defines composite operators in curved spacetime.

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.