Minimal surfaces and entanglement entropy in anti-de Sitter space

TL;DR

This paper explores the geometric calculation of entanglement entropy in holographic duals of conformal field theories by explicitly analyzing minimal surfaces in anti-de Sitter space for various boundary domain configurations.

Contribution

It provides explicit formulas for minimal surfaces in AdS for different boundary domain arrangements and models a dynamic 'tearing' process of these surfaces.

Findings

Explicit minimal surface expressions for various boundary configurations

Renormalized area calculations for these surfaces

Modeling of dynamical tearing of minimal surfaces

Abstract

According to Ryu and Takayanagi, the entanglement entropy in conformal field theory (CFT) is related through the AdS/CFT correspondence to the area of a minimal surface in the bulk. We study this holographic geometrical method of calculating the entanglement entropy in the vacuum case of a CFT which is holographically dual to empty anti-de Sitter (AdS) spacetime. Namely, we investigate the minimal surfaces spanned on boundaries of spherical domains at infinity of hyperbolic space, which represents a time-slice of AdS spacetime. We consider a generic position of two spherical domains: two disjoint domains, overlapping domains, and touching domains. In all these cases we find the explicit expressions for the minimal surfaces and the renormalized expression for the area. We study also the embedding of the minimal surfaces into full AdS spacetime and we find that for a proper choice of the static Killing vector we can model a dynamical situation of "tearing" of the minimal surface when the domains on which it is spanned are moved away from each other.