On Entanglement Entropy of Maxwell fields in 3+1 dimensions with a slab geometry

TL;DR

This paper calculates the entanglement entropy of a finite-width slab in Maxwell theory, revealing that a nonlocal mode significantly contributes to entropy, which is predominantly localized near the boundary with exponential corrections.

Contribution

It provides a detailed calculation of entanglement entropy in Maxwell fields with a slab geometry, highlighting the role of nonlocal modes and boundary effects.

Findings

A large portion of entropy arises from a nonlocal mode.

Entropy is mainly localized at the boundary with exponential decay.

The entropy of the slab equals boundary entropy plus exponential correction.

Abstract

We calculate the entanglement entropy of a slab of finite width in the pure Maxwell theory. We find that a large part of entropy is contributed by the entanglement of a mode, nonlocal in terms of the transverse magnetic field degrees of freedom. Even though the entangled mode is nonlocal, its contribution to the entropy is local in the sense that the entropy of a slab of a finite thickness is equal to the entropy of the boundary plus a correction exponential in thickness of the slab.