Entanglement entropy in two dimensional string theory

TL;DR

This paper calculates the entanglement entropy in two-dimensional string theory's dual matrix model, revealing a finite, logarithmic contribution linked to the emergent spacetime's short-distance entanglement.

Contribution

It provides the first explicit computation of entanglement entropy in 2D string theory's dual matrix quantum mechanics, highlighting the role of nonperturbative effects in spacetime emergence.

Findings

Identifies a logarithmically large, finite entanglement contribution.

Links entanglement entropy to the nonperturbative 'graininess' of space.

Demonstrates the role of short-distance entanglement in emergent spacetime.

Abstract

To understand an emergent spacetime is to understand the emergence of locality. Entanglement entropy is a powerful diagnostic of locality, because locality leads to a large amount of short distance entanglement. Two dimensional string theory is among the very simplest instances of an emergent spatial dimension. We compute the entanglement entropy in the large $N$ matrix quantum mechanics dual to two dimensional string theory, in the semiclassical limit of weak string coupling. We isolate a logarithmically large, but finite, contribution that corresponds to the short distance entanglement of the tachyon field in the emergent spacetime. From the spacetime point of view, the entanglement is regulated by a nonperturbative `graininess' of space.