On entanglement entropy in non-Abelian lattice gauge theory and 3D quantum gravity

TL;DR

This paper introduces a new, excitation-based definition of entanglement entropy for gauge theories, including non-Abelian cases, which is background-independent and applicable to quantum gravity, unifying previous approaches.

Contribution

It proposes a relational entanglement entropy framework for gauge theories, extending to non-Abelian and 3D quantum gravity, and connects various existing definitions.

Findings

Provides a background-independent entanglement entropy definition.

Relates the new approach to existing proposals and the magnetic centre choice.

Applies the framework to 3D lattice gauge theories and quantum gravity.

Abstract

Entanglement entropy is a valuable tool for characterizing the correlation structure of quantum field theories. When applied to gauge theories, subtleties arise which prevent the factorization of the Hilbert space underlying the notion of entanglement entropy. Borrowing techniques from extended topological field theories, we introduce a new definition of entanglement entropy for both Abelian and non-Abelian gauge theories. Being based on the notion of excitations, it provides a completely relational way of defining regions. Therefore, it naturally applies to background independent theories, e.g. gravity, by circumventing the difficulty of specifying the position of the entangling surface. We relate our construction to earlier proposals and argue that it brings these closer to each other. In particular, it yields the non-Abelian analogue of the "magnetic centre choice", as obtained through an extended-Hilbert-space method, but applied to the recently introduced fusion basis for 3D lattice gauge theories. We point out that the different definitions of entanglement theory can be related to a choice of (squeezed) vacuum state.