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- Title
Trace anomaly of weyl fermions via the path integral.
- Authors
Larue, Rémy; Quevillon, Jérémie; Zwicky, Roman
- Abstract
We compute the trace, diffeomorphism and Lorentz anomalies of a free Weyl fermion in a gravitational background field by path integral methods. This is achieved by regularising the variation of the determinant of the Weyl operator building on earlier work by Leutwyler. The trace anomaly is found to be one half of the one of a Dirac fermion. Most importantly we establish that the potential parity-odd curvature term R R ~ , corresponding to the Pontryagin density, vanishes. This is to the contrary of some recent findings in the literature which gave rise to a controversy. We verify, that the regularisation does not lead to (spurious) anomalies in the Lorentz and diffeomorphism symmetries. We argue that in d = 2 (mod 4) P- and CP-odd terms cannot appear and that for d = 4 (mod 4) they are absent at least at leading order.
- Subjects
WEYL fermions; PATH integrals; GRAVITATIONAL fields; SPACE-time symmetries; FERMIONS
- Publication
Journal of High Energy Physics, 2023, Vol 2023, Issue 12, p1
- ISSN
1126-6708
- Publication type
Article
- DOI
10.1007/JHEP12(2023)064