Eur. Phys. J. C (2017) 77: 511
https://doi.org/10.1140/epjc/s10052-017-5071-7

Regular Article - Theoretical Physics

Axial gravity, massless fermions and trace anomalies

¹ International School for Advanced Studies (SISSA), Via Bonomea 265, 34136, Trieste, Italy
² INFN, Sezione di Trieste and KEK Theory Center, KEK, Tsukuba, Japan
³ Department of Physics, Faculty of Science, University of Zagreb, Bijenička cesta 32, 10000, Zagreb, Croatia
⁴ Department of Physics, University of Rijeka, Radmile Matejčić 2, 51000, Rijeka, Croatia
⁵ Departamento de Física Teórica, UERJ-Universidade Estadual do Rio de Janeiro, Rua São Francisco Xavier 524, Maracanã, Rio de Janeiro, RJ, 20550-013, Brazil
⁶ UFF-Universidade Federal Fluminense, Instituto de Física, Campus da Praia Vermelha, Avenida General Milton Tavares de Souza s/n, Niterói, RJ, 24210-346, Brazil

^* e-mail: bonora@sissa.it

Received: 4 April 2017
Accepted: 13 July 2017
Published online: 1 August 2017

Abstract

This article deals with two main topics. One is odd parity trace anomalies in Weyl fermion theories in a 4d curved background, the second is the introduction of axial gravity. The motivation for reconsidering the former is to clarify the theoretical background underlying the approach and complete the calculation of the anomaly. The reference is in particular to the difference between Weyl and massless Majorana fermions and to the possible contributions from tadpole and seagull terms in the Feynman diagram approach. A first, basic, result of this paper is that a more thorough treatment, taking account of such additional terms and using dimensional regularization, confirms the earlier result. The introduction of an axial symmetric tensor besides the usual gravitational metric is instrumental to a different derivation of the same result using Dirac fermions, which are coupled not only to the usual metric but also to the additional axial tensor. The action of Majorana and Weyl fermions can be obtained in two different limits of such a general configuration. The results obtained in this way confirm the previously obtained ones.