Electric-magnetic duality and renormalization in curved spacetimes

TL;DR

This paper investigates how electric-magnetic duality symmetry in electromagnetism is broken by quantum effects in curved spacetime, revealing a duality anomaly similar to conformal symmetry breaking, with parallels in scalar field theory.

Contribution

It demonstrates that duality symmetry is broken during renormalization in curved backgrounds and draws parallels with scalar field anomalies in 1+1 dimensions.

Findings

Duality symmetry does not hold in quantum electromagnetism in curved spacetime.

A duality anomaly appears during the renormalization process.

Similar anomalies are observed in massless scalar fields in 1+1 dimensions.

Abstract

We point out that the duality symmetry of free electromagnetism does not hold in the quantum theory if an arbitrary classical gravitational background is present. The symmetry breaks in the process of renormalization, as also happens with conformal invariance. We show that a similar duality-anomaly appears for a massless scalar field in $1+1$ dimensions.