Reflected entropy in Galilean conformal field theories and flat holography

Basak, Jaydeep Kumar; Chourasiya, Himanshu; Raj, Vinayak; Sengupta, Gautam

doi:10.48550/arxiv.2202.01201

Cited by 6 publications

(20 citation statements)

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“…The PEE in this case is given by which matches exactly with the EWCS for the mixed state configuration under consideration as obtained in [49]. We may also compare this result with the reflected entropy computed in [41,52] through field theoretic replica techniques and find agreement upto a constant stemming from the undetermined OPE coefficient for the CGA 2 three-point function. This further substantiates the claim for a holographic duality between the EWCS and the BPE.…”

Section: Topologically Massive Gravitysupporting

confidence: 72%

“…Subsequently, a covariant geometric picture of the entanglement wedge cross-section for bipartite mixed states in holographic GCFT 2 s was developed in [49] in order to investigate a relation between the EWCS and the holographic entanglement negativity in such non-relativistic theories 1 . Remarkably, recent field theoretic replica calculations for the reflected entropy for various bipartite states in such GCFT 2 s [41,52] match exactly with the EWCS obtained in [49] in the large central charge limit.…”

Section: Introductionsupporting

confidence: 73%

“…In the following we will compute the BPE in such flat holographic settings for adjacent and non-adjacent intervals in the dual GCFT 2 s and observe that our results match exactly with the minimal EWCS computed in [49]. We will also compare our results with the reflected entropy computed through suitable replica techniques devised in [41,52] and find agreement upto some constant, owing to the undetermined OPE coefficients.…”

Section: Entanglement In Galilean Conformal Field Theory and Flat Hol...supporting

confidence: 53%

“…Inspired by the above developments, a geometric construction for the entanglement wedge and subsequently a prescription to compute the minimal EWCS for the connected wedge configuration was put forward in [49]. Recently, the authors in [41,52] computed the reflected entropy in dual GCFT 2 s and found agreements with the results of [49].…”

Section: Entanglement In Galilean Conformal Field Theory and Flat Hol...mentioning

confidence: 95%

“…In a separate context, a class of (1+1)-dimensional non-relativistic field theories with Galilean conformal symmetry (GCFT 2 ) [23][24][25][26][27][28][29][30][31][32][33][34][35][36][37] have been proposed to have (2+1)-dimensional asymptotically flat geometries as their gravitational duals [38,39]. The entanglement structure of bipartite pure and mixed states in such GCFT 2 s were investigated utilizing suitable replica techniques in a series of communications [26,27,[40][41][42]. In the framework of flat space holography [38,39], the bulk dual spacetimes for such GCFT 2 s may involve pure Einstein gravity or topologically massive gravity [43][44][45][46][47][48] and the asymptotic symmetries of these 3d geometries are described by the Galilean conformal algebra (GCA 2 ).…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Balanced Partial Entanglement in Flat Holography

Basu¹

2022

Preprint

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We advance a construction for the balanced partial entanglement entropy (BPE) for bipartite mixed states in a class of (1+1)-dimensional Galilean conformal field theories dual to Einstein gravity and topologically massive gravity in asymptotically flat spacetimes. We compare our results with the entanglement wedge cross section (EWCS) in the dual geometries and find exact agreement. Furthermore, utilizing a geometric picture, we demonstrate the holographic duality between the EWCS and the BPE in the context of flat holography.

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Section: Topologically Massive Gravitysupporting

confidence: 72%

Section: Introductionsupporting

confidence: 73%

Section: Entanglement In Galilean Conformal Field Theory and Flat Hol...supporting

confidence: 53%

Section: Entanglement In Galilean Conformal Field Theory and Flat Hol...mentioning

confidence: 95%

Section: Introductionmentioning

confidence: 99%

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Balanced Partial Entanglement in Flat Holography

Basu¹

2022

Preprint

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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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Reflected entropy in AdS3/WCFT

Chen

Liu

2022

J. High Energ. Phys.

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Reflected entropy is a newly proposed notion in quantum information. It has important implications in holography. In this work, we study the reflected entropy in the framework of the AdS3/WCFT correspondence. We determine the scaling dimensions and charges of various twist operators in non-Abelian orbifold WCFT by generalizing the uniformization map and taking into account of the charge conservation. This allows us to compute the reflected entropy, logarithmic negativity and odd entropy for two disjoint intervals in holographic WCFT. We find that the reflected entropy can be related holographically to the pre-entanglement wedge cross-section, which is given by the minimal distance between the benches in two swing surfaces.

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Reflected entropy in Galilean conformal field theories and flat holography

Cited by 6 publications

References 0 publications

Balanced Partial Entanglement in Flat Holography

Balanced Partial Entanglement in Flat Holography

Entanglement wedge cross-section for noncommutative Yang-Mills theory

Reflected entropy in AdS3/WCFT

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