Entanglement negativity in Galilean conformal field theories

Malvimat, Vinay; Parihar, Himanshu; Paul, Boudhayan; Sengupta, Gautam

doi:10.1103/physrevd.100.026001

Cited by 30 publications

(121 citation statements)

References 30 publications

(98 reference statements)

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“…The authors of [43,44] developed a replica technique for computing the entanglement entropy of such Galilean conformal field theories (GCFT 1+1 ). Following this a replica technique to compute the entanglement negativity of bipartite states in a class of such GCFT 1+1 was established in [55].…”

Section: Introductionmentioning

confidence: 99%

“…In this article we address this issue through the BMS 3 /GCA 2 correspondence [58][59][60]. In this context we establish holographic constructions to compute the entanglement negativity of bipartite states in GCFT 1+1 s dual to bulk asymptotically flat (2 + 1) dimensional Einstein Gravity and Topologically Massive Gravity (TMG) [59,60,[63][64][65][66], following the corresponding constructions for relativistic CFT 1+1 s described in [20,21,55]. Interestingly our results match exactly with the universal parts of the corresponding replica technique results obtained in [55].…”

Section: Introductionmentioning

confidence: 99%

“…In this context we establish holographic constructions to compute the entanglement negativity of bipartite states in GCFT 1+1 s dual to bulk asymptotically flat (2 + 1) dimensional Einstein Gravity and Topologically Massive Gravity (TMG) [59,60,[63][64][65][66], following the corresponding constructions for relativistic CFT 1+1 s described in [20,21,55]. Interestingly our results match exactly with the universal parts of the corresponding replica technique results obtained in [55]. For the mixed state of disjoint intervals in proximity we substantiate our results through a rigorous geometric monodromy analysis [67] to obtain the corresponding large central charge limit.…”

Section: Introductionmentioning

confidence: 99%

“…In section 2 we briefly recollect the salient features of GCFT 1+1 s and the BMS 3 /GCA 2 correspondence. The replica techniques developed in [43,44,55] for computing the entanglement entropy and negativity respectively in such GCFT 1+1 s are reviewed in section 3. In section 4 we describe the covariant construction for computing the entanglement entropy in [59,60].…”

Section: Introductionmentioning

confidence: 99%

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Entanglement Negativity in Flat Holography

et al. 2022

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We advance holographic constructions for the entanglement negativity of bipartite states in a class of (1+1)-dimensional Galilean conformal field theories dual to asymptotically flat three dimensional bulk geometries described by Einstein Gravity and Topologically Massive Gravity. The construction involves specific algebraic sums of the lengths of bulk extremal curves homologous to certain combinations of the intervals appropriate to such bipartite states. Our analysis exactly reproduces the corresponding replica technique results in the large central charge limit. We substantiate our construction through a semi classical analysis involving the geometric monodromy technique for the case of two disjoint intervals in such holographic Galilean conformal field theories.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Entanglement Negativity in Flat Holography

et al. 2022

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“…A replica technique was developed for this quantity in [72,73] and furthermore, it was utilized to compute the entanglement negativity for various mixed state configurations in two dimensional relativistic conformal field theories (CFT 2 ). A replica technique was also advanced to study the entanglement negativity in Galilean conformal field theories in [74]. The progress in [72,73], led to the interesting question of the holographic construction for the entanglement negativity, which for pure states was attempted in [75].…”

Section: Introductionmentioning

confidence: 99%

Islands for entanglement negativity

et al. 2022

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We advance two alternative proposals for the island contributions to the entanglement negativity of various pure and mixed state configurations in quantum field theories coupled to semiclassical gravity. The first construction involves the extremization of an algebraic sum of the generalized Renyi entropies of order half. The second proposal involves the extremization of the sum of the effective entanglement negativity of quantum matter fields and the backreacted area of a cosmic brane spanning the entanglement wedge cross section which also extremizes the generalized Renyi reflected entropy of order half. These proposals are utilized to obtain the island contributions to the entanglement negativity of various pure and mixed state configurations involving the bath systems coupled to extremal and non-extremal black holes in JT gravity demonstrating an exact match with each other. Furthermore, the results from both the proposals match precisely with the island contribution to half the Renyi reflected entropy of order half providing a strong consistency check. We then allude to a possible doubly holographic picture of our island proposals and provide a derivation of the first proposal by determining the corresponding replica wormhole contributions.

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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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Entanglement negativity in Galilean conformal field theories

Cited by 30 publications

References 30 publications

Entanglement Negativity in Flat Holography

Entanglement Negativity in Flat Holography

Islands for entanglement negativity

Entanglement wedge cross-section for noncommutative Yang-Mills theory

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