Holographic Entanglement Entropy: A Topical Review

In this topic review, we introduce recent developments on holographic entanglement entropy. After briefly reviewing the basic notions of entanglement in quantum information and quantum field theory, we introduce the Ryu-Takayanagi’s prescription of computing the entanglement entropy holographically. We review the inequalities on the holographic entanglement entropy, and its derivation from Euclidean gravity. In particular, we discuss its implications in semi-classical AdS ₃/CFT ₂ correspondence, and furthermore review the recent studies on the emergence of geometry and gravity from entanglement. (topical review)