Entanglement branes in a two-dimensional string theory

TL;DR

This paper explores the concept of entanglement in string theory by analyzing the Gross-Taylor model, revealing that entanglement entropy involves open strings ending on an E-brane at the entangling surface.

Contribution

It develops a canonical framework for open strings in the Gross-Taylor model and introduces the concept of E-branes as the entangling surface in string theory.

Findings

Open strings with endpoints on E-branes describe entanglement.

The modular Hamiltonian corresponds to a thermal ensemble of open strings.

Closed strings are decomposed into open strings at the Hilbert space level.

Abstract

What is the meaning of entanglement in a theory of extended objects such as strings? To address this question we consider the spatial entanglement between two intervals in the Gross-Taylor model, the string theory dual to two-dimensional Yang-Mills theory at large $N$. The string diagrams that contribute to the entanglement entropy describe open strings with endpoints anchored to the entangling surface, as first argued by Susskind. We develop a canonical theory of these open strings, and describe how closed strings are divided into open strings at the level of the Hilbert space. We derive the Modular hamiltonian for the Hartle-Hawking state and show that the corresponding reduced density matrix describes a thermal ensemble of open strings ending on an object at the entangling surface that we call an E-brane.