Holographic Entanglement Entropy: An Overview

TL;DR

The paper surveys the holographic understanding of entanglement entropy in AdS/CFT, presenting the Ryu–Takayanagi prescription that equates EE to the area of a minimal bulk surface. It verifies the framework through exact AdS$_3$/CFT$_2$ results, explores higher-dimensional generalizations, and demonstrates EE as a diagnostic for confinement, topological order, and black hole entropy. Covariant extensions are developed to handle time-dependent backgrounds, linking EE to the Bousso bound and horizon dynamics. Together, these results position holographic EE as a universal, geometry-driven tool for probing quantum information in strongly coupled field theories and gravity.

Abstract

In this article, we review recent progresses on the holographic understandings of the entanglement entropy in the AdS/CFT correspondence. After reviewing the general idea of holographic entanglement entropy, we will explain its applications to confinement/deconfinement phase transitions, black hole entropy and covariant formulation of holography.

Figures (11)

• Figure 1: Examples of bipartitioning for the entanglement entropy. A choice of the subsystems $A$ and $B$ is shown for each of the two examples: $(a)$ a spin chain, $(b)$ a quantum field theory.
• Figure 2: (a) The path integral representation of the reduced density matrix $[\rho_A]_{\phi_+\phi_-}$. (b) The $n$-sheeted Riemann surface $\mathcal{R}_n$. (Here we take $n=3$ for simplicity.)
• Figure 3: The holographic calculation of entanglement entropy via AdS/CFT.
• Figure 4: A holographic proof of the strong subadditivity of the entanglement entropy. To make the figures simple, we project the time slice of a $(d+2)$-dimensional AdS space onto a two-dimensional plane. This simplification does not change our result.
• Figure 5: (a) Minimal surfaces $\gamma_A$ in the BTZ black hole for various sizes of $A$. (b) $\gamma_A$ and $\gamma_B$ wrap the different parts of the horizon. (c) When $\partial A$ gets larger, $\gamma_A$ is separated into two parts: one is wrapped on the horizon and the other localized near the boundary.