Electromagnetic Duality and Entanglement Anomalies

TL;DR

This paper investigates electromagnetic duality in abelian p-forms, revealing anomalies in effective actions and entanglement entropy that depend on the dimensionality of the manifold, and clarifies previous conflicting results.

Contribution

It provides a detailed calculation of duality anomalies in arbitrary dimensions and relates entanglement entropy changes to edge modes, resolving prior discrepancies in the field.

Findings

Effective actions agree in odd dimensions

In even dimensions, actions differ by Euler number terms

Entanglement entropy exhibits an anomaly related to edge modes

Abstract

Duality is an indispensable tool for describing the strong-coupling dynamics of gauge theories. However, its actual realization is often quite subtle: quantities such as the partition function can transform covariantly, with degrees of freedom rearranged in a nonlocal fashion. We study this phenomenon in the context of the electromagnetic duality of abelian $p$-forms. A careful calculation of the duality anomaly on an arbitrary $D$-dimensional manifold shows that the effective actions agree exactly in odd $D$, while in even $D$ they differ by a term proportional to the Euler number. Despite this anomaly, the trace of the stress tensor agrees between the dual theories. We also compute the change in the vacuum entanglement entropy under duality, relating this entanglement anomaly to the duality of an "edge mode" theory in two fewer dimensions. Previous work on this subject has led to conflicting results; we explain and resolve these discrepancies.