Holographic entanglement entropy of two disjoint intervals in AdS$_3$/CFT$_2$

TL;DR

This paper investigates the holographic entanglement entropy for two disjoint intervals in AdS3/CFT2, challenging the minimal surface assumption and proposing a sum over all extremal surfaces as a more complete dual description.

Contribution

It introduces a new candidate for the holographic entanglement entropy involving a sum over all extremal surfaces, addressing cases with multiple saddle points.

Findings

Multiple extremal surfaces can contribute equally to entanglement entropy.

A new holographic dual candidate is proposed as a sum of signed areas of extremal surfaces.

Derived from CFT calculations and proposed a corresponding gravity action.

Abstract

The Ryu-Takayanagi conjecture predicts a holographic dual of the entanglement entropy of a CFT. It proposes that the entanglement entropy is given by the area of the minimal surface in the dual spacetime. In the semi-classical limit, this conjecture is supported by the saddle point approximation. If there are multiple classical solutions, it is assumed that only the minimal action contributes to the entanglement entropy. However, we will point out that these saddles equally contribute to the entanglement entropy in some cases. Therefore, the derivation of the conjecture is incomplete if there are multiple extremal surfaces that extend from a sub-system on the AdS boundary. We will consider two disjoint intervals in CFT$_{1+1}$ as the simplest but non-trivial example, and propose another candidate for a holographic dual of the entanglement entropy of this system, which is the sum of all the signed areas of extremal surfaces in the dual spacetime. After that, we will derive it from the CFT calculations and propose the corresponding gravity side action.