Entanglement entropy of a superflow

TL;DR

This paper investigates the entanglement entropy of a two-dimensional free Dirac fermion system with a winding mass, comparing field theory and gravity dual calculations, and finds agreement to order m^2.

Contribution

It demonstrates that classical general relativity accurately captures the entanglement entropy of a winding mass Dirac fermion system to order m^2, supporting the duality conjecture.

Findings

GR correctly reproduces EE to order m^2

Agreement holds for all orders in winding q

Supports the duality between the fermion theory and higher-spin gravity

Abstract

We consider the theory of $N$ free Dirac fermions with a uniformly winding mass, $m e^{iqx}$, in two spacetime dimensions. This theory (which describes for instance a superconducting current in an $N$-channel wire) has been proposed to have a higher-spin gravity with scalar matter as the large-$N$ dual. To order $m^2$, however, thermodynamic quantities in it can be computed using standard general relativity instead. Here, we consider the question if the same is true for the entanglement entropy (EE). By comparing results obtained on two sides of the duality, we find that general relativity indeed accounts correctly for the EE of an interval to order $m^2$ (and all orders in $q$).