Entanglement entropy of electromagnetic edge modes

TL;DR

This paper clarifies the nature of the vacuum entanglement entropy in Maxwell theory by identifying an overlooked contribution from edge modes, resolving longstanding puzzles about its interpretation and divergence structure.

Contribution

It demonstrates that the unexpected entropy term is due to electromagnetic edge modes and explains the divergence behavior using heat kernel regularization.

Findings

Edge modes account for the mysterious entropy term.

Heat kernel regularization explains negative divergences.

Resolves puzzles about gauge field divergences in 3+1 dimensions.

Abstract

The vacuum entanglement entropy of Maxwell theory, when evaluated by standard methods, contains an unexpected term with no known statistical interpretation. We resolve this two-decades old puzzle by showing that this term is the entanglement entropy of edge modes: classical solutions determined by the electric field normal to the entangling surface. We explain how the heat kernel regularization applied to this term leads to the negative divergent expression found by Kabat. This calculation also resolves a recent puzzle concerning the logarithmic divergences of gauge fields in 3+1 dimensions.