scholarly journals Shape dependence of renormalized holographic entanglement entropy

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Giorgos Anastasiou ◽  
Javier Moreno ◽  
Rodrigo Olea ◽  
David Rivera-Betancour
Keyword(s):  
Lower Bound ◽  
Entanglement Entropy ◽  
Three Dimensional ◽  
Renormalization Scheme ◽  
Strong Subadditivity ◽  
Shape Dependence ◽  
Holographic Entanglement Entropy ◽  
Curvature Term ◽  
Topological Part ◽  
Willmore Energy

Abstract We study the holographic entanglement entropy of deformed entangling regions in three-dimensional CFTs dual to Einstein-AdS gravity, using a renormalization scheme based on the addition of extrinsic counterterms. In this prescription, when even- dimensional manifolds are considered, the universal contribution to the entanglement entropy is identified as the renormalized volume of the Ryu-Takayanagi hypersurface, which is written as the sum of a topological and a curvature term. It is shown that the change in the renormalized entanglement entropy due to the deformation of the entangling surface is encoded purely in the curvature contribution. In turn, as the topological part is given by the Euler characteristic of the Ryu-Takayanagi surface, it remains shape independent. Exploiting the covariant character of the extrinsic counterterms, we apply the renormalization scheme for the case of deformed entangling regions in AdS4/CFT3, recovering the results found in the literature. Finally, we provide a derivation of the relation between renormalized entanglement entropy and Willmore energy. The presence of a lower bound of the latter makes manifest the relation between the AdS curvature of the Ryu-Takayanagi surface and the strong subadditivity property.

scholarly journals Entanglement entropy in strongly correlated systems with confinement/deconfinement phase transition and anisotropy

2019 ◽  
Vol 222 ◽  
pp. 03024 ◽  
Author(s):  
Pavel Slepov
Keyword(s):  
Heavy Ions ◽  
Chemical Potential ◽  
Entanglement Entropy ◽  
Three Dimensional ◽  
Entropy Density ◽  
Strongly Correlated ◽  
Holographic Model ◽  
Holographic Entanglement Entropy ◽  
Maxwell Fields ◽  
Deconfinement Phase Transition

Five-dimensional anisotropic gravity with nontrivial dilaton field and two Maxwell fields is chosen for the holographic model, which allows to reproduce the multiplicity dependence on energy obtained from heavy-ions collisions [1, 2]. Holographic entanglement entropy and its density are calculated for three-dimensional subsystems in this anisotropic background. These elongated subsystems have arbitrary spatial orientation in relation to the line of heavy-ions collisions. The divergences of holographic entanglement entropy are discussed. The entanglement entropy density has sharp spikes around the critical temperature for given chemical potential and anisotropy.

scholarly journals Holographic entanglement entropy in cutoff AdS

2018 ◽  
Vol 33 (36) ◽  
pp. 1850226 ◽  
Author(s):  
Chanyong Park
Keyword(s):  
Fixed Point ◽  
Entanglement Entropy ◽  
Three Dimensional ◽  
Energy Scale ◽  
Field Theories ◽  
Dimensional Sphere ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
Holographic Entanglement Entropy ◽  
Length Contraction

We investigate the holographic entanglement entropy of deformed conformal field theories which are dual to a cutoff AdS space. The holographic entanglement entropy evaluated on a three-dimensional Poincaré AdS space with a finite cutoff can be reinterpreted as that of the dual field theory deformed by either a boost or [Formula: see text] deformation. For the boost case, we show that, although it trivially acts on the underlying theory, it nontrivially affects the entanglement entropy due to the length contraction. For a three-dimensional AdS, we show that the effect of the boost transformation can be reinterpreted as the rescaling of the energy scale, similar to the [Formula: see text] deformation. Under the boost and [Formula: see text] deformation, the [Formula: see text]-function of the entanglement entropy exactly shows the features expected by the Zamolodchikov’s [Formula: see text]-theorem. The deformed theory is always stationary at a UV fixed point and monotonically flows to another CFT in the IR fixed point. We also show that the holographic entanglement entropy in a Poincaré cutoff AdS space can reproduce the exact same result of the [Formula: see text] deformed theory on a two-dimensional sphere.

scholarly journals Swing surfaces and holographic entanglement beyond AdS/CFT

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Luis Apolo ◽  
Hongliang Jiang ◽  
Wei Song ◽  
Yuan Zhong
Keyword(s):  
Black Holes ◽  
Lorentz Invariance ◽  
Entanglement Entropy ◽  
Three Dimensional ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Asymptotically Flat ◽  
Infinite Dimensional ◽  
Holographic Entanglement Entropy

Abstract We propose a holographic entanglement entropy prescription for general states and regions in two models of holography beyond AdS/CFT known as flat3/BMSFT and (W)AdS3/WCFT. Flat3/BMSFT is a candidate of holography for asymptotically flat three- dimensional spacetimes, while (W)AdS3/WCFT is relevant in the study of black holes in the real world. In particular, the boundary theories are examples of quantum field theories that feature an infinite dimensional symmetry group but break Lorentz invariance. Our holographic entanglement entropy proposal is given by the area of a swing surface that consists of ropes, which are null geodesics emanating from the entangling surface at the boundary, and a bench, which is a spacelike geodesic connecting the ropes. The proposal is supported by an extension of the Lewkowycz-Maldacena argument, reproduces previous results based on the Rindler method, and satisfies the first law of entanglement entropy.

scholarly journals On shape dependence of holographic entanglement entropy in AdS4/CFT3

2015 ◽  
Vol 2015 (12) ◽  
pp. 1-58 ◽  
Author(s):  
Piermarco Fonda ◽  
Domenico Seminara ◽  
Erik Tonni
Keyword(s):  
Entanglement Entropy ◽  
Shape Dependence ◽  
Holographic Entanglement Entropy

scholarly journals Chern-Simons gravity dual of BCFT

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Tadashi Takayanagi ◽  
Takahiro Uetoko
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Entanglement Entropy ◽  
Einstein Gravity ◽  
Conformal Field ◽  
Holographic Entanglement Entropy ◽  
The World ◽  
Higher Spin ◽  
End Of The World ◽  
Chern Simons

Abstract In this paper we provide a Chern-Simons gravity dual of a two dimensional conformal field theory on a manifold with boundaries, so called boundary conformal field theory (BCFT). We determine the correct boundary action on the end of the world brane in the Chern-Simons gauge theory. This reproduces known results of the AdS/BCFT for the Einstein gravity. We also give a prescription of calculating holographic entanglement entropy by employing Wilson lines which extend from the AdS boundary to the end of the world brane. We also discuss a higher spin extension of our formulation.

scholarly journals Entanglement entropy in cubic gravitational theories

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Elena Cáceres ◽  
Rodrigo Castillo Vásquez ◽  
Alejandro Vilar López
Keyword(s):  
Entanglement Entropy ◽  
Gravitational Theory ◽  
Riemann Tensor ◽  
Holographic Entanglement Entropy ◽  
Gravitational Theories ◽  
Entropy Functional ◽  
Wide Range ◽  
Splitting Problem ◽  
Range Of Values

Abstract We derive the holographic entanglement entropy functional for a generic gravitational theory whose action contains terms up to cubic order in the Riemann tensor, and in any dimension. This is the simplest case for which the so-called splitting problem manifests itself, and we explicitly show that the two common splittings present in the literature — minimal and non-minimal — produce different functionals. We apply our results to the particular examples of a boundary disk and a boundary strip in a state dual to 4- dimensional Poincaré AdS in Einsteinian Cubic Gravity, obtaining the bulk entanglement surface for both functionals and finding that causal wedge inclusion is respected for both splittings and a wide range of values of the cubic coupling.

scholarly journals Probing phase transitions of holographic entanglement entropy with fixed area states

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Donald Marolf ◽  
Shannon Wang ◽  
Zhencheng Wang
Keyword(s):  
Phase Transitions ◽  
Entanglement Entropy ◽  
Many Body ◽  
Btz Black Hole ◽  
Holographic Entanglement Entropy ◽  
Volume Limit ◽  
Cutoff Dependence ◽  
Diagonal Approximation ◽  
Fixed Area ◽  
Many Body Systems

Abstract Recent results suggest that new corrections to holographic entanglement entropy should arise near phase transitions of the associated Ryu-Takayanagi (RT) surface. We study such corrections by decomposing the bulk state into fixed-area states and conjecturing that a certain ‘diagonal approximation’ will hold. In terms of the bulk Newton constant G, this yields a correction of order O(G−1/2) near such transitions, which is in particular larger than generic corrections from the entanglement of bulk quantum fields. However, the correction becomes exponentially suppressed away from the transition. The net effect is to make the entanglement a smooth function of all parameters, turning the RT ‘phase transition’ into a crossover already at this level of analysis.We illustrate this effect with explicit calculations (again assuming our diagonal approximation) for boundary regions given by a pair of disconnected intervals on the boundary of the AdS3 vacuum and for a single interval on the boundary of the BTZ black hole. In a natural large-volume limit where our diagonal approximation clearly holds, this second example verifies that our results agree with general predictions made by Murthy and Srednicki in the context of chaotic many-body systems. As a further check on our conjectured diagonal approximation, we show that it also reproduces the O(G−1/2) correction found Penington et al. for an analogous quantum RT transition. Our explicit computations also illustrate the cutoff-dependence of fluctuations in RT-areas.

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