# Axial gravity, massless fermions and trace anomalies

## TL;DR

This paper investigates odd parity trace anomalies in Weyl fermion theories within curved 4d backgrounds, introduces axial gravity, and confirms previous results through a more thorough and alternative derivation involving axial tensors and dimensional regularization.

## Contribution

It introduces axial gravity and provides a new derivation of trace anomalies using axial tensors, clarifying the role of tadpole and seagull terms in the anomaly calculation.

## Key findings

- Confirmation of earlier trace anomaly results with dimensional regularization
- Introduction of axial gravity as a new framework for fermion coupling
- Alternative derivation using Dirac fermions and axial tensors

## 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.