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.
Highlights
In [9,10,11,12] the authors advanced a comprehensive procedure to compute the entanglement entropy in (1 + 1) dimensional conformal field theories (C F T1+1) employing a replica technique
To summarize we have established a holographic entanglement negativity conjecture involving the bulk geometry for bipartite mixed states of disjoint intervals in a dual C F T1+1 through the Ad S3/C F T2 correspondence
Using the large central charge result we have established a holographic construction for the entanglement negativity of the above mixed state configurations, which involves a specific algebraic sum of the lengths of bulk space like geodesics anchored on appropriate intervals
Summary
In [9,10,11,12] the authors advanced a comprehensive procedure to compute the entanglement entropy in (1 + 1) dimensional conformal field theories (C F T1+1) employing a replica technique. In [32,33] two of the present authors (VM and GS) proposed a holographic entanglement negativity conjecture and its covariant generalization for bipartite states in the Ad S3/C F T2 scenario This was substantiated by a large central charge analysis of the entanglement negativity of the C F T1+1 utilizing the monodromy technique in [34]. In this article we address this interesting issue and propose a holographic entanglement negativity conjecture for such mixed state configuration of two disjoint intervals in the Ad S3/C F T2 scenario To this end we utilize the large central charge analysis presented in [18] to extract the universal part of the entanglement negativity for the mixed state in question both at zero and finite temperatures and for a finite size system in C F T1+1.
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