The effective gravitational action of a massless chiral fermion and the absence of parity-odd contributions
Abstract
We consider the field theory of a quantum massless left handed fermion coupled to a background graviton field, hμν, on four-dimensional Minkowski spacetime. By using the BPHZL renormalization scheme, we prove that, up to order four in the number of graviton fields, there are no parity-odd contributions to the renormalized gravitational effective action. As a side result, we show that, modulo arbitrary UV finite diffeomorphism invariant parity-even counterterms, the gravitational effective action in question is equal, up to order four in the number of graviton fields, to half the corresponding gravitational action for a Dirac fermion non-chirally coupled to gravity. Also as a side result, we conclude the the Weyl anomaly is purely parity-even and that its value is half the value of the Weyl anomaly for a Dirac fermion non-chirally coupled to gravity.
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BibTeX
@misc{anero2026effective,
title = {{The effective gravitational action of a massless chiral fermion and the absence of parity-odd contributions}},
author = {J. Anero and Carmelo P. Martin},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.28045},
eprint = {2605.28045},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.28045},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The effective gravitational action of a massless chiral fermion and the absence of parity-odd contributions
AU - J. Anero
AU - Carmelo P. Martin
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2605.28045
UR - https://arxiv.org/abs/2605.28045
AB - We consider the field theory of a quantum massless left handed fermion coupled to a background graviton field, h_μν, on four-dimensional Minkowski spacetime. By using the BPHZL renormalization scheme, we prove that, up to order four in the number of graviton fields, there are no parity-odd contributions to the renormalized gravitational effective action. As a side result, we show that, modulo arbitrary UV finite diffeomorphism invariant parity-even counterterms, the gravitational effective action in question is equal, up to order four in the number of graviton fields, to half the corresponding gravitational action for a Dirac fermion non-chirally coupled to gravity. Also as a side result, we conclude the the Weyl anomaly is purely parity-even and that its value is half the value of the Weyl anomaly for a Dirac fermion non-chirally coupled to gravity.
ER -