On the trace anomaly of a Weyl fermion

TL;DR

This paper calculates the trace anomaly of a Weyl fermion in curved spacetime, finding it to be half that of a Dirac fermion and showing no imaginary Pontryagin term, clarifying previous theoretical debates.

Contribution

It provides a detailed calculation of the Weyl fermion's trace anomaly using Fujikawa's method with Pauli-Villars regulators, resolving ambiguities about the Pontryagin density contribution.

Findings

Trace anomaly of Weyl fermion is half that of Dirac fermion.

No imaginary Pontryagin density term appears in the anomaly.

Clarifies the nature of chiral fermion anomalies in four dimensions.

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.