The Entanglement Renyi Entropies of Disjoint Intervals in AdS/CFT

Abstract

We study entanglement Renyi entropies (EREs) of 1+1 dimensional CFTs with classical gravity duals. Using the replica trick the EREs can be related to a partition function of n copies of the CFT glued together in a particular way along the intervals. In the case of two intervals this procedure defines a genus n-1 surface and our goal is to find smooth three dimensional gravitational solutions with this surface living at the boundary. We find two families of handlebody solutions labelled by the replica index n. These particular bulk solutions are distinguished by the fact that they do not spontaneously break the replica symmetries of the boundary surface. We show that the regularized classical action of these solutions is given in terms of a simple numerical prescription. If we assume that they give the dominant contribution to the gravity partition function we can relate this classical action to the EREs at leading order in G_N. We argue that the prescription can be formulated for non-integer n. Upon taking the limit n -> 1 the classical action reproduces the predictions of the Ryu-Takayanagi formula for the entanglement entropy.

arXiv comment49 pages, 13 figures

References in corpus (21)

• Holographic Derivation of Entanglement Entropy from AdS/CFT
• The Black Hole in Three Dimensional Space Time
• Entanglement Entropy and Quantum Field Theory
• Topological entanglement entropy
• Detecting topological order in a ground state wave function
• Entanglement entropy and conformal field theory
• Towards a derivation of holographic entanglement entropy
• AdS3 Black Holes and a Stringy Exclusion Principle
• Holographic Entanglement Entropy: An Overview
• Entanglement Renyi entropies in holographic theories
• Quantum Gravity Partition Functions in Three Dimensions
• Three-Dimensional Gravity Revisited
• On the RG running of the entanglement entropy of a circle
• Entanglement entropy of two disjoint intervals in conformal field theory II
• A refinement of entanglement entropy and the number of degrees of freedom
• Quantum effective action from the AdS/CFT correspondence
• Holographic Calculations of Renyi Entropy
• Bose-Fermi duality and entanglement entropies
• Mutual information and the structure of entanglement in quantum field theory
• Proof of Polyakov conjecture for general elliptic singularities
• Polyakov conjecture for hyperbolic singularities

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