Area terms and entanglement entropy in the $c=1$ string theory

TL;DR

This paper investigates entanglement entropy in two-dimensional string theory and its dual matrix model, proposing a generalized form that includes a dilaton-dependent gravitational term and analyzing its potential origins.

Contribution

It introduces a framework for understanding entanglement entropy in 2D string theory, highlighting the absence of an area term in previous models and exploring mechanisms for its emergence.

Findings

The gravitational area-like term is absent in previous $c=1$ model analyses.

The leg-pole transformation cannot generate the area term.

Possible origin of the area term in non-singlet sectors is discussed.

Abstract

We study entanglement entropy in the low-energy effective field theory of two-dimensional string theory as well as in the singlet sector of the dual $c=1$ matrix quantum mechanics. From the target space perspective, we argue that a generic bulk subregion is expected to have an associated generalized entanglement entropy combining a dilaton-dependent gravitational term and a matter contribution coming from the tachyon. Given that the gravitational area-like term is absent in previous analyses of entanglement entropy in the $c=1$ model, we examine several possible mechanisms for its emergence. We show that the nonlocal transformation induced by the leg-pole factor that relates the target space tachyon and the matrix model collective excitations cannot account for the area-like term, and we comment on its possible origin in the non-singlet sectors of the theory.