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

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 γ matrix. We obtain a vanishing odd-parity contribution for Weyl fermions in four dimensions, while the evenparity contribution is exactly half the one for a Dirac fermion.

Trace anomalies for Weyl fermions: too odd to be true?

“…The nuisance is that other groups have failed to derive this non-vanishing f . A variety of approaches have all obtained a vanishing f , including a Pauli-Villars regularization [28,29], a Hadamard approach [30], as well as another Feynman diagrammatic method [31,32]. The first independent support to Bonora's group arrived last year, when a theory of massive fermions (in the massless limit) was considered [33].…”

Trace anomaly for Weyl fermions using the Breitenlohner-Maison scheme for γ*

“…The nuisance is that other groups have failed to derive this non-vanishing f . A variety of approaches have all obtained a vanishing f , including a Pauli-Villars regularization [32,33], a Hadamard approach [34], as well as another Feynman diagrammatic method [35,36]. The first independent support to Bonora's group arrived last year, when a theory of massive fermions (in the massless limit) was considered [37].…”