Holographic entanglement negativity conjecture for adjacent intervals in AdS3/CFT2

Jain, Prem C.; Malvimat, Vinay; Mondal, Sayid; Sengupta, Gautam

doi:10.1016/j.physletb.2019.04.037

Cited by 51 publications

(109 citation statements)

References 21 publications

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“…Interestingly, the area law for entanglement negativity has also been reported for condensed matter system such as the finite temperature quantum spin model and the two dimensional harmonic lattice [34,35]. Subsequently, a covariant version of the holographic entanglement negativity conjecture described in [29], was proposed in [36] for time dependent mixed state configurations of adjacent intervals in a dual CF T 1+1 .…”

Section: Introductionmentioning

confidence: 86%

“…Recently, in a subsequent communication [29] the present authors proposed an independent holographic entanglement negativity conjecture for a bipartite mixed state configuration of adjacent intervals in a dual CF T 1+1 . The conjecture involved a specific algebraic sum of the lengths of space like geodesics in the dual bulk AdS 3 configuration which are anchored on appropriate intervals.…”

Section: Introductionmentioning

confidence: 88%

“…In this section we briefly review the holographic entanglement negativity conjecture for a bipartite mixed state configuration of adjacent subsystems in dual CF T s. To this end we first describe the holographic entanglement negativity conjecture for the mixed state configuration above in the context of the AdS 3 /CF T 2 scenario [29]. Following this we briefly discuss the extension of our conjecture to a generic higher dimensional AdS d+1 /CF T d scenario [32].…”

Section: Holographic Entanglement Negativity Conjecturementioning

confidence: 98%

“…In the large central charge limit this three point twist correlator eq. (2.2) may be expressed in terms of the lengths of bulk space like geodesics anchored on the appropriate intervals, through the standard AdS/CF T dictionary as follows [29]…”

Section: Holographic Entanglement Negativity Conjecturementioning

confidence: 99%

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Holographic entanglement negativity for conformal field theories with a conserved charge

et al. 2018

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We study the application of our recent holographic entanglement negativity conjecture for mixed states of adjacent subsystems in conformal field theories with a conserved charge. In this context we obtain the holographic entanglement negativity for zero and finite temperature mixed state configurations in d-dimensional conformal field theories dual to bulk extremal and non extremal charged AdS d+1 black holes. Our results conform to quantum information theory expectations and constitute significant consistency checks for our conjec-

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Section: Introductionmentioning

confidence: 86%

Section: Introductionmentioning

confidence: 88%

Section: Holographic Entanglement Negativity Conjecturementioning

confidence: 98%

Section: Holographic Entanglement Negativity Conjecturementioning

confidence: 99%

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Holographic entanglement negativity for conformal field theories with a conserved charge

et al. 2018

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“…We plan to return to these interesting questions in the future. Let us remark that in [9][10][11] it was suggested that in holographic framework the mutual information, multiplied by a constant, could be a dual to the entanglement negativity E. This was revised by a suggestion [14] that the entanglement wedge cross section E W , supplemented by the backreaction of the hanging minimal (cosmological) surfaces to the geometry, is actually a gravity dual of entanglement negativity. While lots of important work [4,6,7, has been carried out and most obvious inequalities tested, we feel that it is premature to identify E W one way or the other.…”

Section: Introductionmentioning

confidence: 99%

Notes on entanglement wedge cross sections

Jokela

Pönni

2019

J. High Energ. Phys.

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We consider the holographic candidate for the entanglement of purification E P , given by the minimal cross sectional area of an entanglement wedge E W . The E P is generally very complicated quantity to obtain in field theories, thus to establish the conjectured relationship one needs to test if E W and E P share common features. In this paper the entangling regions we consider are slabs, concentric spheres, and creases in field theories in Minkowski space. The latter two can be mapped to regions in field theories defined on spheres, thus corresponding to entangled caps and orange slices, respectively. We work in general dimensions and for slabs we also consider field theories at finite temperature and confining theories. We find that E W is neither a monotonic nor continuous function of a scale. We also study a full ten-dimensional string theory geometry dual to a non-trivial RG flow of a three-dimensional Chern-Simons matter theory coupled to fundamentals. We show that also in this case E W behaves non-trivially, which if connected to E P , lends further support that the system can undergo purification simply by expansion or reduction in scale. * niko.jokela@helsinki.fi † arttu.ponni@helsinki.fi

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Entanglement wedge cross-section for noncommutative Yang-Mills theory

Chowdhury

Saha

Gangopadhyay

2022

J. High Energ. Phys.

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The signature of noncommutativity on various measures of entanglement has been observed by considering the holographic dual of noncommutative super Yang-Mills theory. We have followed a systematic analytical approach in order to compute the holographic entanglement entropy corresponding to a strip like subsystem of length l. The relationship between the subsystem size (in dimensionless form) $$ \frac{l}{a} $$ l a and the turning point (in dimensionless form) introduces a critical length scale $$ \frac{l_c}{a} $$ l c a which leads to three domains in the theory, namely, the deep UV domain (l < lc; aut » 1, aut ∼ aub), deep noncommutative domain (l > lc, aub> aut » 1) and deep IR domain (l > lc, aut « 1). This in turn means that the length scale lc distinctly points out the UV/IR mixing property of the non-local theory under consideration. We have carried out the holographic study of entanglement entropy for each of these domains by employing both analytical and numerical techniques. The broken Lorentz symmetry induced by noncommutativity has motivated us to redefine the entropic c-function. We have obtained the noncommutative correction to the c-function upto leading order in the noncommutative parameter. We have also looked at the behaviour of this quantity over all the domains of the theory. We then move on to compute the minimal cross-section area of the entanglement wedge by considering two dis- joint subsystems A and B. On the basis of EP = EW duality, this leads to the holographic computation of the entanglement of purification. The correlation between two subsystems, namely, the holographic mutual information I(A : B) has also been computed. Moreover, the computations of EW and I(A : B) has been done for each of the domains in the theory. We have then briefly discussed the effect of the UV cut-off on the IR behaviours of these quantities. Finally, we consider a black hole geometry with a noncommutative parameter and study the influence of both noncommutativity and finite temperature on the various measures of quantum entanglement.

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Holographic entanglement negativity conjecture for adjacent intervals in AdS3/CFT2

Cited by 51 publications

References 21 publications

Holographic entanglement negativity for conformal field theories with a conserved charge

Holographic entanglement negativity for conformal field theories with a conserved charge

Notes on entanglement wedge cross sections

Entanglement wedge cross-section for noncommutative Yang-Mills theory

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