The Entanglement Renyi Entropies of Disjoint Intervals in AdS/CFT

By T. Faulkner. 2013

304 citations recorded by the source corpus.

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.

Subfields: Atomic and Molecular Physics, and Optics, Computational Mathematics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/4eb9e73388eae4d306f40d1f69ab5ef42fd1d827

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Citations in the corpus

Entanglement Entropy at Large Central Charge (2013, methodology): “In fact, exactly the same monodromy prescription for computing S (n) A that we will derive from CFT was derived independently from 3d gravity in a completely different way [12].”
Holographic entanglement beyond classical gravity (2013, methodology): “Following the results in [5], it seems to be the case that the dominant contributions are in fact given by quotients by Schottky groups.”
Shape dependence of entanglement entropy in conformal field theories (2015, unknown): “As a result, entanglement entropy has provided great insights in a wide class of systems such as relativistic field theories [1–3], conformal field theories (CFTs) [4–6], topologically ordered phases of matter [7–10], strongly-coupled theories with holographic duals [11–13], etc.”
Virasoro conformal blocks in closed form (2015, unknown): “Deriving the exponentiated vacuum block, fvac, would have far-reaching consequences, including the determination of the two-interval Rényi entropy, Sn, for arbitrary interval spacings in the vacuum of sparse, large c CFTs [27]; the Einstein action evaluated on handlebody geometries asymptotic to rep”
Semiclassical Virasoro blocks from AdS3 gravity (2015, background): “two-interval Rényi entropies [44,45] – would be very interesting.”
Quantum corrections to holographic entanglement entropy (2013, methodology): “In situations where we can apply the replica trick, this formula was proven for AdS3 in [3,4] and more generally in [5].”
Quantum extremal islands made easy. Part II. Black holes on the brane (2020, background): “As emphasized in [1], the transition between the phase without an island and that with the island is nothing more than the usual transition between different classes of RT surfaces [73–75] – see figure 2.”