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Weyl anomaly for chiral fermions

Enrique Álvarez1,*, Luis Álvarez-Gaumé2,†, Jesús Anero1,‡, and Carmelo P. Martín3,§

  • *Contact author: enrique.alvarez@uam.es
  • †Contact author: lalvarezgaume@scgp.stonybrook.edu
  • ‡Contact author: jesusanero@gmail.com
  • §Contact author: carmelop@fis.ucm.es
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Phys. Rev. D 113, 105016 – Published 22 May, 2026

DOI: https://doi.org/10.1103/ry3t-xm88

Abstract

We compute the parity-odd part of the Weyl anomaly for chiral fermions in a background gravitational field. We start from a manifestly real form of the Lagrangian (that is, not only real up to a total derivative), and we regularize it by means of Pauli-Villars fermions. All parity-odd terms in the anomaly cancel in the integrand, so that the result of the anomaly is necessarily parity even.

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Phys. Rev. D 113, 105016– Published 22 May, 2026
  • Received 3 March 2026
  • Accepted 29 April 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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