Generalized entanglement entropy

TL;DR

This paper introduces new measures of entanglement in quantum field theories, including a global symmetry entanglement entropy and a field space entanglement entropy, and explores their holographic duals and geometric realizations.

Contribution

It proposes a global symmetry entanglement entropy and analyzes the holographic realization of field space entanglement entropy, especially in geometries with interior decoupling regions.

Findings

Global symmetry entanglement entropy relates to internal space partitioning.

Field space entanglement entropy cannot be exactly realized holographically.

Differential entropy in throat regions approximates field space entanglement entropy.

Abstract

We discuss two measures of entanglement in quantum field theory and their holographic realizations. For field theories admitting a global symmetry, we introduce a global symmetry entanglement entropy, associated with the partitioning of the symmetry group. This quantity is proposed to be related to the generalized holographic entanglement entropy defined via the partitioning of the internal space of the bulk geometry. The second measure of quantum field theory entanglement is the field space entanglement entropy, obtained by integrating out a subset of the quantum fields. We argue that field space entanglement entropy cannot be precisely realised geometrically in a holographic dual. However, for holographic geometries with interior decoupling regions, the differential entropy provides a close analogue to the field space entanglement entropy. We derive generic descriptions of such inner throat regions in terms of gravity coupled to massive scalars and show how the differential entropy in the throat captures features of the field space entanglement entropy.