Electromagnetic duality anomaly in curved spacetimes

TL;DR

This paper demonstrates that electromagnetic duality symmetry, conserved at the classical level, is broken at the quantum level in curved spacetimes with non-trivial gravitational backgrounds, leading to observable effects like polarization non-conservation.

Contribution

It reveals a quantum electromagnetic duality anomaly in curved spacetimes with non-trivial Chern-Pontryagin invariants, analogous to the chiral anomaly.

Findings

Duality symmetry is broken quantum mechanically in certain curved spacetimes.

Quantum electromagnetic fields exhibit non-conservation of net polarization.

The anomaly is related to the gravitational Chern-Pontryagin invariant.

Abstract

The source-free Maxwell action is invariant under electric-magnetic duality rotations in arbitrary spacetimes. This leads to a conserved classical Noether charge. We show that this conservation law is broken at the quantum level in presence of a background classical gravitational field with a non-trivial Chern-Pontryagin invariant, in a parallel way to the chiral anomaly for massless Dirac fermions. Among the physical consequences, the net polarization of the quantum electromagnetic field is not conserved.