Matrix Entanglement

TL;DR

This paper introduces 'matrix entanglement' as a novel way to describe entanglement in gauge/gravity duality, linking matrix degrees of freedom to geometric and black hole phenomena.

Contribution

It proposes a new framework for understanding entanglement in gauge theories via matrix degrees of freedom, distinct from target-space entanglement, with applications to fuzzy spheres and black hole evaporation.

Findings

Matrix entanglement defines spatial entanglement nonperturbatively.

Application to fuzzy sphere links to brane world-volume theories.

Suggests gauge theory origin of the Page curve for black hole evaporation.

Abstract

In gauge/gravity duality, matrix degrees of freedom on the gauge theory side play important roles for the emergent geometry. In this paper, we discuss how the entanglement on the gravity side can be described as the entanglement between matrix degrees of freedom. Our approach, which we call 'matrix entanglement', is different from 'target-space entanglement' proposed and discussed recently by several groups. We consider several classes of quantum states to which our approach can play important roles. When applied to fuzzy sphere, matrix entanglement can be used to define the usual spatial entanglement in two-brane or five-brane world-volume theory nonperturbatively in a regularized setup. Another application is to a small black hole in AdS5*S5 that can evaporate without being attached to a heat bath, for which our approach suggests a gauge theory origin of the Page curve. The confined degrees of freedom in the partially-deconfined states play the important roles.