arXiv subjects
Publications and source records attributed to S. Abdallah.
We review recent discussions regarding the parity-odd contribution to the trace anomaly of a chiral fermion. We pay special attention to the perturbative approach in terms of Feynman diagrams, comparing in detail the results obtained using dimensional regularization and the Breitenlohner--Maison prescription with other approaches.
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.
We revisit the computation of the trace anomaly for Weyl fermions using dimensional regularization. For a consistent treatment of the chiral gamma matrix $γ_*$ in dimensional regularization, we work in $n$ dimensions from the very beginning and use the Breitenlohner-Maison scheme to define $γ_*$. 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.