Electric-magnetic duality in the quantum theory

TL;DR

This paper investigates the limitations of electric-magnetic duality symmetry in quantum Maxwell theory within dynamic gravitational backgrounds, revealing an anomaly similar to the chiral anomaly in fermions.

Contribution

It demonstrates that the classical duality symmetry does not extend to the quantum level in curved spacetimes with non-trivial gravitational fields, introducing a new anomaly concept.

Findings

Duality symmetry breaks down quantum mechanically in certain gravitational backgrounds.

Identifies a gravitationally induced anomaly analogous to the chiral anomaly.

Highlights limitations of classical symmetries in quantum gravitational contexts.

Abstract

It is known that an electric-magnetic duality transformation is a symmetry of the classical source-free Maxwell theory in generic spacetimes. This provides a conserved Noether charge, physically related to the polarization state of the electromagnetic field. We argue that this conservation law fails to hold at the quantum level in presence of a background classical gravitational field with non-trivial dynamics, as determined by the Chern-Pontryagin scalar. This is the spin 1 analog of the chiral anomaly for massless Dirac fermions.