Trace anomaly for Weyl fermions using the Breitenlohner-Maison scheme for $\gamma_*$

TL;DR

This paper recalculates the trace anomaly for Weyl fermions using the Breitenlohner-Maison scheme in dimensional regularization, showing the parity-odd part vanishes and the parity-even part is half that of a Dirac fermion, with a detailed stress tensor analysis.

Contribution

It provides a consistent dimensional regularization approach for Weyl fermions and clarifies the structure of their trace anomaly, including the vanishing parity-odd contribution.

Findings

Parity-odd trace anomaly contribution vanishes.

Parity-even trace anomaly is half that of a Dirac fermion.

Stress tensor remains conserved at second order in perturbations.

Abstract

We revisit the computation of the trace anomaly for Weyl fermions using dimensional regularization. For a consistent treatment of the chiral gamma matrix $\gamma_*$ in dimensional regularization, we work in $n$ dimensions from the very beginning and use the Breitenlohner-Maison scheme to define $\gamma_*$. We show that the parity-odd contribution to the trace anomaly vanishes (for which the use of dimension-dependent identities is crucial), and that the parity-even contribution is half the one of a Dirac fermion. To arrive at this result, we compute the full renormalized expectation value of the fermion stress tensor to second order in perturbations around Minkowski spacetime, and also show that it is conserved.