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

TL;DR

This paper investigates the conformal anomaly of Weyl fermions in four dimensions using a perturbative approach with dimensional regularization and the Breitenlohner--Maison scheme, finding specific parity contributions.

Contribution

It provides a detailed calculation of the conformal anomaly for Weyl fermions employing the Breitenlohner--Maison scheme, clarifying parity contributions and their relation to Dirac fermions.

Findings

Odd-parity contribution vanishes for Weyl fermions.

Even-parity contribution is half that of a Dirac fermion.

Results clarify the structure of conformal anomalies in chiral fermions.

Abstract

We revisit the conformal anomaly for a Weyl fermion in four dimensions that has generated some debate recently. We employ a perturbative expansion for the metric around Minkowski space, dimensional regularization and a Breitenlohner--Maison prescription for the chiral $\gamma$ matrix. We obtain a vanishing odd-parity contribution for Weyl fermions in four dimensions, while the even-parity contribution is exactly half the one for a Dirac fermion.