Entanglement, Soft Modes, and Celestial Holography

TL;DR

This paper computes the vacuum entanglement entropy in 4D Maxwell theory, revealing that soft modes and asymptotic charges contribute significantly, with implications for celestial holography and edge mode dynamics.

Contribution

It demonstrates how soft modes and asymptotic charge correlations account for entanglement entropy in Maxwell theory using conformal embedding techniques.

Findings

Soft mode contributions are linked to asymptotic charge correlations.

Embedding Minkowski space in Einstein universe simplifies entropy calculations.

Edge modes play a crucial role in the entanglement structure.

Abstract

We evaluate the vacuum entanglement entropy across a cut of future null infinity for free Maxwell theory in four-dimensional Minkowski spacetime. The Weyl invariance of 4D Maxwell theory allows us to embed the Minkowski spacetime inside the Einstein static universe. The Minkowski vacuum can then be described as a thermofield double state on the (future) Milne wedges of the original and inverted Minkowski patches. We show that the soft mode contribution to entanglement entropy is due to correlations between asymptotic charges of these Milne wedges or, equivalently, nontrivial conformally soft (or edge) mode configurations at the entangling surface.