Holographic description of entanglement entropy of free CFT on torus

TL;DR

This paper explores a holographic approach to entanglement entropy in free conformal field theories on a torus, proposing a new description involving extremal surfaces in BTZ spacetime that differs from the Ryu-Takayanagi conjecture.

Contribution

It introduces a novel holographic description of entanglement entropy for free CFTs on a torus using extremal surfaces in BTZ spacetime, extending beyond the Ryu-Takayanagi framework.

Findings

High-temperature expansion terms match extremal surface areas in BTZ spacetime.

The new extremal surface approach has preferable properties over the Ryu-Takayanagi conjecture.

Provides a consistent holographic description for free CFTs on a torus.

Abstract

The Ryu-Takayanagi conjecture provides a holographic description for the entanglement entropy for the strongly coupled holographic CFTs in the semi-classical limit. It proposes that the entanglement entropy is given by the area of the minimal homologous surface in the dual bulk. We show that the common terms of the entanglement entropy for the free massless fermions or bosons on a torus in the high-temperature expansion can be described by the sum of the signed area of extremal surfaces in the BTZ spacetime. The resulting EE and the corresponding bunch of the exgremal surfaces have preferable properties rather than those from the Ryu-Takayanagi conjecture.