Deriving covariant holographic entanglement

Abstract

We provide a gravitational argument in favour of the covariant holographic entanglement entropy proposal. In general time-dependent states, the proposal asserts that the entanglement entropy of a region in the boundary field theory is given by a quarter of the area of a bulk extremal surface in Planck units. The main element of our discussion is an implementation of an appropriate Schwinger-Keldysh contour to obtain the reduced density matrix (and its powers) of a given region, as is relevant for the replica construction. We map this contour into the bulk gravitational theory, and argue that the saddle point solutions of these replica geometries lead to a consistent prescription for computing the field theory Renyi entropies. In the limiting case where the replica index is taken to unity, a local analysis suffices to show that these saddles lead to the extremal surfaces of interest. We also comment on various properties of holographic entanglement that follow from this construction.

39 pages. 9 figures

References in corpus (10)

• Towards a derivation of holographic entanglement entropy
• Minkowski-space correlators in AdS/CFT correspondence: recipe and applications
• Schwinger-Keldysh Propagators from AdS/CFT Correspondence
• Causality & holographic entanglement entropy
• Remarks on the entanglement entropy for disconnected regions
• Entanglement entropy in three dimensional gravity
• Generalized gravitational entropy without replica symmetry
• Covariant Residual Entropy
• Topological aspects of generalized gravitational entropy
• Complex Entangling Surfaces for AdS and Lifshitz Black Holes?

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