Axial anomaly in nonlinear conformal electrodynamics

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