Holographic Derivation of Entanglement Entropy from the anti–de Sitter Space/Conformal Field Theory Correspondence

Abstract

A holographic derivation of the entanglement entropy in quantum (conformal) field theories is proposed from anti–de Sitter/conformal field theory (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 ${\mathrm{AdS}}_{d+2}$, analogous to the Bekenstein-Hawking formula for black hole entropy. We show that our proposal agrees perfectly with the entanglement entropy in 2D CFT when applied to ${\mathrm{AdS}}_3$. We also compare the entropy computed in ${\mathrm{AdS}}_5\times {\mathrm{S}}^5$ with that of the free $\mathcal{N}=4$ super Yang-Mills theory.