AdS from Entanglement Entropy

TL;DR

This paper demonstrates how anti-de Sitter space naturally arises from conformal field theories through entanglement entropy, establishing a link between divergence behavior and AdS geometry, especially in two dimensions.

Contribution

It provides a detailed analysis of the connection between entanglement entropy divergences and AdS geometry, confirming the relationship explicitly for 2D CFTs and discussing extensions to higher dimensions.

Findings

Leading divergence in entanglement entropy relates to AdS radius.

Confirmed the AdS emergence from 2D CFTs.

Comments on higher-dimensional CFTs included.

Abstract

We show that the anti-de Sitter(AdS) space naturally emerges from the conformal field theory(CFT). The behavior of the leading divergent term in the entanglement entropy implies the underlying AdS geometry. The coefficient of the leading divergent term is related to the radius of the AdS space. All these are confirmed fully for the two dimensional CFTs. We also give comments for the higher dimensional CFTs.