Classical and quantum aspects of electric-magnetic duality rotations in curved spacetimes

TL;DR

This paper explores the classical and quantum properties of electric-magnetic duality in curved spacetimes, revealing that quantum effects can break polarization conservation due to a spin-one anomaly.

Contribution

It demonstrates that electric-magnetic duality symmetry is preserved classically in curved spacetimes but can be broken quantum mechanically, extending the concept of chiral anomalies to spin-one fields.

Findings

Classical duality symmetry persists in curved backgrounds.

Quantum effects can violate polarization conservation.

Analogous to fermion chiral anomaly for electromagnetic fields.

Abstract

It is well known that the source-free Maxwell equations are invariant under electric-magnetic duality rotations, F --> F cos {\theta} + *F sin {\theta}. These transformations are indeed a symmetry of the theory in Noether sense. The associated constant of motion is the difference in the intensity between self- and anti-self dual components of the electromagnetic field or, equivalently, the difference between the right and left circularly polarized components. This conservation law holds even if the electromagnetic field interacts with an arbitrary classical gravitational background. After re-examining these results, we discuss whether this symmetry is maintained when the electromagnetic field is quantized. The answer is in the affirmative in the absence of gravity, but not necessarily otherwise. As a consequence, the net polarization of the quantum electromagnetic field fails to be conserved in curved spacetimes. This is a quantum effect, and it can be understood as the generalization of the fermion chiral anomaly to fields of spin one.