Trace anomaly for Weyl fermions using the Breitenlohner-Maison scheme for ${\gamma }_{\ast }$

Abstract

We revisit the computation of the trace anomaly for Weyl fermions using dimensional regularization. For a consistent treatment of the chiral gamma matrix ${\gamma }_{\ast }$ in dimensional regularization, we work in $n$ dimensions from the very beginning and use the Breitenlohner-Maison scheme to define ${\gamma }_{\ast }$. 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.

arXiv comment33 pages

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• The Weyl anomaly in interacting quantum field theory on curved spacetimes