Holographic Derivation of Entanglement Entropy from AdS/CFT

TL;DR

This paper proposes a holographic method to derive entanglement entropy in conformal field theories using the AdS/CFT correspondence, linking minimal surface areas in AdS space to entropy calculations.

Contribution

It introduces a new holographic approach to compute entanglement entropy from minimal surfaces in AdS space, extending the Bekenstein-Hawking analogy.

Findings

Accurately reproduces 2D CFT entanglement entropy from AdS_3.

Shows consistency with free N=4 super Yang-Mills calculations.

Establishes a geometric interpretation of entanglement entropy in holography.

Abstract

A holographic derivation of the entanglement entropy in quantum (conformal) field theories is proposed from AdS/CFT correspondence. We argue that the entanglement entropy in d+1 dimensional conformal field theories can be obtained from the area of d dimensional minimal surfaces in AdS_{d+2}, analogous to the Bekenstein-Hawking formula for black hole entropy. We show that our proposal perfectly reproduces the correct entanglement entropy in 2D CFT when applied to AdS_3. We also compare the entropy computed in AdS_5 \times S^5 with that of the free N=4 super Yang-Mills.