Holographic Entanglement Negativity for Disjoint Subsystems in Conformal Field Theories with a Conserved Charge

Afrasiar, Mir; Basak, Jaydeep Kumar; Raj, Vinayak; Sengupta, Gautam

doi:10.48550/arxiv.2106.14918

Cited by 5 publications

(6 citation statements)

References 52 publications

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“…Note that, these proposals have further been extended to various other holographic frameworks including flat holography [134], anomalous AdS/CFT [149] as well as higher dimensional scenarios [140,[146][147][148].…”

Section: Entanglement Negativitymentioning

confidence: 99%

“…The entanglement negativity has been explored in conformal field theories [130][131][132] through appropriate replica techniques 2 . Subsequently several holographic constructions for computing the entanglement negativity in the context of the AdS/CFT correspondence was advanced in a series of interesting works 3 in [136][137][138][139][140][141][142][143][144][145][146][147][148][149] which reproduced the field theoretic results in the large central charge limit [134,150,151]. Interestingly, in [152][153][154][155][156], an alternative holographic proposal based on the bulk entanglement wedge cross-section (EWCS) was also investigated.…”

Section: Introductionmentioning

confidence: 99%

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Defect extremal surfaces for entanglement negativity

Basu¹,

Parihar²,

Raj³

et al. 2022

Preprint

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We propose a doubly holographic version of the semi-classical island formula for the entanglement negativity in the framework of the defect AdS/BCFT correspondence where the AdS bulk contains a defect conformal matter theory. In this context, we propose a defect extremal surface (DES) formula for computing the entanglement negativity modified by the contribution from the defect matter theory on the end-of-the-world brane. The equivalence of the DES proposal and the semi-classical island formula for the entanglement negativity is demonstrated in AdS 3 /BCFT 2 framework. Furthermore, in the time-dependent AdS 3 /BCFT 2 scenarios involving eternal black holes in the lower dimensional effective description, we investigate the time evolution of the entanglement negativity through the DES and the island formulae and obtain the analogues of the Page curves.

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Section: Entanglement Negativitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Defect extremal surfaces for entanglement negativity

Basu¹,

Parihar²,

Raj³

et al. 2022

Preprint

Self Cite

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“…In this paper, we follow the second proposal where entanglement negativity is given by certain combination of the static minimal surfaces in the bulk. Some recent works in this directions can be found in [83][84][85][86][87][88][89][90][91][92][93].…”

Section: Holograhic Computation Of the Entanglement Negativitymentioning

confidence: 99%

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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“…However a general holographic prescription for mixed states in CFT d s remained an open issue. Subsequently, in a series of communications an elegant holographic characterization of entanglement negativity for various bipartite states in CFTs were proposed in [23][24][25][26][27][28][29][30][31][32][33][34][35]. These proposals involved specific algebraic sums of bulk codimension two (H)RT surfaces homologous to appropriate combinations of subsystems in the dual CFT d s 1 .…”

Section: Introductionmentioning

confidence: 99%

Entanglement negativity, reflected entropy, and anomalous gravitation

Basu,

Parihar,

Raj

et al. 2022

Preprint

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We investigate mixed state entanglement measures of entanglement negativity and reflected entropy for bipartite states in two dimensional conformal field theories with an anomaly through appropriate replica techniques. Furthermore we propose holographic constructions for these measures from the corresponding bulk dual geometries involving topologically massive gravity in AdS 3 and find exact agreement with the field theory results. In this connection we extend an earlier holographic proposal for the entanglement negativity to the bulk action with a gravitational Chern-Simons term and compute its contribution to the entanglement wedge cross section dual to the reflected entropy.

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Holographic Entanglement Negativity for Disjoint Subsystems in Conformal Field Theories with a Conserved Charge

Cited by 5 publications

References 52 publications

Defect extremal surfaces for entanglement negativity

Defect extremal surfaces for entanglement negativity

Entanglement wedge cross-section for noncommutative Yang-Mills theory

Entanglement negativity, reflected entropy, and anomalous gravitation

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