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International Journal of Modern Physics A

Holographic entanglement negativity for disjoint subsystems in AdSd+1/CFTd

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

Published Oct 17, 2024• 1 citation
Publisher

Abstract

In this paper, we propose a construction to compute the holographic entanglement negativity (HEN) for bipartite mixed state configurations of two disjoint subsystems in higher-dimensional conformal field theories (CFTds) dual to bulk AdS[Formula: see text] geometries. Our proposal follows from the corresponding AdS3/CFT2 scenario and involves an algebraic sum of the areas of bulk RT surfaces for certain combinations of subsystems. By utilizing our construction, we compute the HEN at the leading order through a perturbative expansion, for such bipartite mixed states of two disjoint subsystems with long rectangular strip geometries in CFTds dual to bulk pure AdS[Formula: see text] geometries and AdS[Formula: see text]-Schwarzschild black holes.

DOI
10.1142/s0217751x24501409

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Holographic entanglement negativity for disjoint subsystems in AdSd+1/CFTd\mathrm{AdS_{d+1}/CFT_d}AdSd+1​/CFTd​
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Holographic entanglement negativity for disjoint intervals in AdS3/CFT2AdS_3/CFT_2AdS3​/CFT2​ 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)(1+1)(1+1) dimensional conformal field theories ( CFT1+1CFT_{1+1}CFT1+1​ ) through the AdS3/CFT2AdS_3/CFT_2AdS3​/CFT2​ 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 CFT1+1CFT_{1+1}CFT1+1​ . The construction is utilized to compute the holographic entanglement negativity for such mixed states in CFT1+1CFT_{1+1}CFT1+1​ s dual to bulk pure AdS3AdS_3AdS3​ 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.
Abstract We utilize a holographic construction to compute the entanglement negativity for bipartite mixed state configurations of a single subsystem in CFTd s with a conserved charge dual to bulk A d S d + 1 geometries. In this context, we obtain the holographic entanglement negativity for single subsystems with long rectangular strip geometries in CFTd s with a conserved charge dual to bulk non extremal and extremal Reissner–Nordström (RN)- A d S d + 1 black holes at the leading order in a perturbation theory. We demonstrate that the holographic entanglement negativity computed involves the elimination of thermal contributions at the leading order confirming earlier results in the literature. This also conforms to quantum information theory expectations and constitutes further consistency checks for the holographic construction.
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.
We propose a covariant holographic entanglement negativity construction for time dependent mixed states of adjacent intervals in (1+1)-dimensional conformal field theories dual to non-static bulk AdS3 configurations. Our prescription applied to (1+1)-dimensional conformal field theories with a conserved charge dual to non-extremal and extremal rotating BTZ black holes exactly reproduces the corresponding replica technique results, in the large central charge limit. We also utilize our construction to obtain the time dependent holographic entanglement negativity for the mixed state in question for the (1+1)-dimensional CFT dual to a bulk Vaidya-AdS3 configuration.