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Minimal surfaces and entanglement entropy in anti-de Sitter space

  • Pavel KrtoušEmail author
  • Andrei Zelnikov
Open Access
Article

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. All these cases are treated in a unified way. We find exact expressions in a closed form 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.

Keywords

AdS-CFT Correspondence Holography and condensed matter physics (AdS/CMT) Space-Time Symmetries 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2014

Authors and Affiliations

  1. 1.Institute of Theoretical Physics, Faculty of Mathematics and PhysicsCharles University in PraguePragueCzech Republic
  2. 2.Theoretical Physics Institute, Department of PhysicsUniversity of AlbertaEdmontonCanada

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