Axial gravity and anomalies of fermions

TL;DR

This paper investigates the anomaly structure of Dirac fermions in a metric-axial-tensor background, recovering known anomalies in specific limits and providing new insights into chiral fermion trace anomalies.

Contribution

It introduces a framework to analyze fermion anomalies in a metric-axial-tensor background, extending previous results to include the trace anomaly of chiral fermions.

Findings

Computed the full anomaly structure of fermions in MAT background

Recovered Dirac and Weyl fermion anomalies in specific limits

Derived the trace anomaly for chiral fermions

Abstract

We consider a Dirac fermion in a metric-axial-tensor (MAT) background. By regulating it with Pauli-Villars fields we analyze and compute its full anomaly structure. Appropriate limits of the MAT background allows to recover the anomalies of Dirac and Weyl fermions in the usual curved spacetime, obtaining in particular the trace anomaly of a chiral fermion, which has been the object of recent analyses.