arXiv:2102.05676 · Physics Letters B

Covariant holographic negativity from the entanglement wedge in AdS3/CFT2

Jaydeep Kumar Basak, Himanshu Parihar, Boudhayan Paul, Gautam Sengupta

Published Sep 13, 2022• 9 citations

Abstract

We propose a covariant holographic construction based on the extremal entanglement wedge cross section, for the entanglement negativity of bipartite states in CFT1+1s dual to non static bulk AdS3 geometries. Utilizing our proposal we obtain the holographic entanglement negativity for bipartite mixed states in CFT1+1s dual to bulk extremal and non extremal rotating BTZ black holes and the time dependent Vaidya-AdS3 geometries. Our results correctly reproduce the replica technique results modulo certain constants for the corresponding dual CFT1+1s in the large central charge limit for the bulk black hole geometries. Furthermore for all the cases our results also match upto such constants with the corresponding results from an earlier alternate covariant holographic construction in the literature. This demonstrates the equivalence modulo constants of the two constructions for the AdS3/CFT2 scenario.

DOI: 10.1016/j.physletb.2022.137451

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arXiv:2102.05676 · Physics Letters B

Covariant holographic negativity from the entanglement wedge in AdS3/CFT2

Jaydeep Kumar Basak, Himanshu Parihar, Boudhayan Paul, Gautam Sengupta

Published Sep 13, 2022• 9 citations

arXiv HTML PDF

Abstract

DOI: 10.1016/j.physletb.2022.137451

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Covariant holographic entanglement negativity for disjoint intervals in

AdS_3/CFT_2

We advance a construction for the covariant holographic entanglement negativity for time dependent mixed states of disjoint intervals in

(1+1)

dimensional conformal field theories (

CFT_{1+1}

) dual to bulk non static

AdS_3

geometries. Application of our proposal to such mixed states in a

CFT_{1+1}

dual to bulk non extremal and extremal rotating BTZ black holes exactly reproduces the replica technique results in the large central charge limit. We also investigate the time dependent holographic entanglement negativity for such mixed states in a

CFT_{1+1}

dual to a bulk Vaidya-

AdS_3

geometry in the context of their thermalization involving bulk black hole formation.

We propose a covariant holographic conjecture for the entanglement negativity of bipartite mixed states in

(1+1)

-dimensional conformal field theories dual to bulk non static

AdS_{3}

configurations. Application of our conjecture to

(1+1)

-dimensional conformal field theories dual to bulk non extremal and extremal rotating BTZ black holes exactly reproduce the corresponding entanglement negativity obtained through the replica technique, in the large central charge limit. We briefly discuss the issue of the generalization of our conjecture to higher dimensions.

Holographic entanglement negativity for disjoint intervals in

AdS_3/CFT_2

A d S 3 / C F T 2

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.