Sphere partition functions &amp; cut-off AdS

Caputa, Paweł; Datta, Shouvik; Shyam, Vasudev

doi:10.1007/jhep05(2019)112

Cited by 81 publications

(91 citation statements)

References 61 publications

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“…Based on the observation that the Bekenstein-Hawking entropy is proportional to the area of the black hole, Ryu and Takayanagi [40] derived that the entanglement entropy of a subsystem may be computed holographically by computing the area of minimal surface in the bulk enclosing the subsystem.The authors of [12] were able to give further evidence in favor of the conjecture of [4] by showing that the entanglement entropy for antipodal points in a two-dimensional CFT deformed by a TT deformation matches the entanglement entropy computed in AdS 3 in presence of a hard radial cutoff. This analysis has been extended to higher dimensions [13,14,34,35], and to dS 3 [36] in the context of the DS/dS duality which we will review shortly. This leads to the question -what happens to the entanglement entropy for intervals different from antipodal points?…”

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Entanglement entropy and $$ T\overline{T} $$ deformations beyond antipodal points from holography

Grieninger

2019

J. High Energ. Phys.

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We consider the entanglement entropies in dS d sliced (A)dS d+1 in the presence of a hard radial cutoff. By considering a one parameter family of analytic solutions, parametrized by their turning point in the bulk r , we are able to compute the entanglement entropy for generic intervals on the cutoff slice. It has been proposed that the field theory dual of this scenario is a strongly coupled CFT, deformed by a certain irrelevant deformation -the socalled TT deformation. Surprisingly, we find that we may write the entanglement entropies formally in the same way as the entanglement entropy for antipodal points on the sphere by introducing an effective radius R eff = R cos(β ), where R is the radius of the sphere and β related to the length of the interval. Geometrically, this is equivalent to following the TT trajectory until the generic interval corresponds to antipodal points on the sphere. Finally, we check our results by comparing the asymptotic behavior (no Dirichlet wall present) with the results of Casini, Huerta and Myers. In the second part of this work, we extend the field theory calculation of the entanglement entropy for antipodal points for a d-dimensional field theory in context of DS/dS holography.One remarkable development in the recent years has been a novel access to irrelevant (nonrenormalizable) deformations in two dimensional quantum field theories (QFTs). Unlike the usual irrelevant deformations, the so-called TT deformation [1-3] has the intriguing feature that it is -unlike the usual irrelevant deformations -exactly solvable. Starting from a generic seed QFT, we are able to define a trajectory from the IR to the UV in the field theory space triggered by deforming the QFT with a TT deformation in each step. Even through the theory flows towards the UV, we are still able to derive a lot of interesting quantities in exact form simply from possessing an understanding of undeformed theory. These quantities include the finite volume spectrum, the S-matrix and the deformed classical Lagrangian -all of which have been extensively discussed in the literature (see [38] for lecture notes).An interesting approach to TT deformations is the proposal of a holographic dual by McGough, Mezei, and Verlinde [4] in order to use the powerful toolkit provided by holographic dualities for studying problems in strongly coupled field theories. From a bulk perspective, deforming a field theory by an irrelevant deformation has drastic effects on the UV behavior. McGough, Mezei, and Verlinde conjectured to simply chop off the asymptotic region of the spacetime. In other words, deforming the conformal field theory (CFT) by the TT operator is dual to introducing a hard radial cutoff (Dirichlet wall) at a finite radial position r = r c in the bulk. The hard radial cutoff removes the UV region of the spacetime and the dual field theory which lives on the cutoff surface is no longer conformal. For Anti-de Sitter (AdS) this was more extensively studied in [11].One interesting aspect of quantum theories -especially with re...

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Entanglement entropy and $$ T\overline{T} $$ deformations beyond antipodal points from holography

Grieninger

2019

J. High Energ. Phys.

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“…In the context of AdS/CFT correspondence the partition function at a finite cutoff has been also studied in[21,22] .…”

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An infalling observer and behind the horizon cutoff

Akhavan

Alishahiha

2019

SciPost Phys.

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Using Papadodimas and Raju construction of operators describing the interior of a black hole, we present a general relation between partition functions of operators describing inside and outside the black hole horizon. In particular for an eternal black hole the partition function of the interior modes may be given in terms those partition functions associated with the modes of left and right exteriors. By making use of this relation we observe that setting a finite UV cutoff will enforce us to have a cutoff behind the horizon whose value is fixed by the UV cutoff. The resultant cutoff is in agreement with what obtained in the context of holographic complexity.

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“…Evidence for this non-CFT/non-AdS kind of duality including matching of the energy spectrum, holographic entanglement entropies, exact holographic renormalization and so on. For recent progress on holographic aspects of TT deformation see also [44][45][46][47][48][49][50][51][52][53][54][55].…”

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confidence: 99%

The correlation function of (1, 1) and (2, 2) supersymmetric theories with $$ T\overline{T} $$ deformation

Sun

2020

J. High Energ. Phys.

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In the paper, based on recent studies on TT deformation of 2D field theory with supersymmetry, we investigate the deformed correlation functions in N = (1, 1) and N = (2, 2) 2D superconformal field theories. Up to the leading order in perturbation theory, we compute the correlation functions under TT deformation. The correlation functions in these undeformed theories are almost known, and together with the help of superconformal Ward identity in N = (1, 1) and N = (2, 2) theories respectively we can obtain the correlation functions with operator TT inserted. Finally, by employing dimensional regularization, we can work out the integrals in the first order perturbation. The study in this paper extends previous works on the correlation functions of TT deformed bosonic CFT to the supersymmetric case. 1

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Sphere partition functions & cut-off AdS

Cited by 81 publications

References 61 publications

Entanglement entropy and $$ T\overline{T} $$ deformations beyond antipodal points from holography

Entanglement entropy and $$ T\overline{T} $$ deformations beyond antipodal points from holography

An infalling observer and behind the horizon cutoff

The correlation function of (1, 1) and (2, 2) supersymmetric theories with $$ T\overline{T} $$ deformation

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