Axial anomaly in nonlinear conformal electrodynamics

TL;DR

This paper investigates the axial anomaly of Dirac fermions in nonlinear conformal electrodynamics on gravitational instanton backgrounds, revealing an imbalance in chiral fermions caused by nonlinearity and duality symmetry.

Contribution

It introduces a study of axial anomalies in nonlinear conformal electrodynamics coupled with gravity, extending known instanton solutions while preserving duality symmetry.

Findings

Identifies an excess of positive chiral fermions causing the anomaly.

Generalizes Eguchi-Hanson and Taub-NUT configurations with nonlinear electrodynamics.

Shows the impact of nonlinearity on fermionic anomalies in gravitational backgrounds.

Abstract

We study the axial anomaly of Dirac spinors on gravitational instanton backgrounds in the context of nonlinear electrodynamics. In order to do so, we consider Einstein gravity minimally coupled to a recently proposed conformal electrodynamics that enjoys duality transformation invariance. These symmetries allow us to generalize the Eguchi-Hanson configuration while preserving its geometry. We then compute the Dirac index of the nonlinearly charged Eguchi-Hanson and Taub-NUT configurations. We find that there is an excess of positive chiral Dirac fermions over the negative ones which triggers the anomaly.