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arXiv:1810.08015 · The European Physical Journal C

Holographic entanglement negativity for disjoint intervals in $$AdS_3/CFT_2$$ A d S 3 / C F T 2

Vinay Malvimat, Sayid Mondal, Boudhayan Paul, Gautam Sengupta

Published Mar 1, 2019• 45 citations
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Abstract

We advance a holographic construction for the entanglement negativity of bipartite mixed state configurations of two disjoint intervals in $$(1+1)$$ dimensional conformal field theories ( $$CFT_{1+1}$$ ) through the $$AdS_3/CFT_2$$ correspondence. Our construction constitutes the large central charge analysis of the entanglement negativity for mixed states under consideration and involves a specific algebraic sum of bulk space like geodesics anchored on appropriate intervals in the dual $$CFT_{1+1}$$ . The construction is utilized to compute the holographic entanglement negativity for such mixed states in $$CFT_{1+1}$$ s dual to bulk pure $$AdS_3$$ geometries and BTZ black holes respectively. Our analysis exactly reproduces the universal features of corresponding replica technique results in the large central charge limit which serves as a consistency check.

DOI
10.1140/epjc/s10052-019-6693-8

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Abstract We advance a holographic conjecture for the entanglement negativity of bipartite quantum states in (1 + 1)-dimensional conformal field theories in the AdS 3 /CF T 2 framework. Our conjecture exactly reproduces the replica technique results in the large central charge limit, for both the pure state described by the CF T 1+1 vacuum dual to bulk the pure AdS 3 geometry and the finite temperature mixed state dual to a Euclidean BTZ black hole respectively. The holographic entanglement negativity characterizes the distillable entanglement and reduces to a specific sum of holographic mutual informations. We briefly allude to a possible higher dimensional generalization of our conjecture in a generic AdS d+1 /CF T d scenario.
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