scholarly journals Strong subadditivity and the covariant holographic entanglement entropy formula

2012 ◽  
Vol 2012 (6) ◽  
Author(s):  
Robert Callan ◽  
Jianyang He ◽  
Matthew Headrick
Keyword(s):  
Entanglement Entropy ◽  
Strong Subadditivity ◽  
Entropy Formula ◽  
Holographic Entanglement Entropy

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 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.

scholarly journals Spread of Entanglement in Non-Relativistic Theories

2018 ◽  
Vol 2018 ◽  
pp. 1-27
Author(s):  
Sagar F. Lokhande
Keyword(s):  
Broad Class ◽  
Entanglement Entropy ◽  
Time Dependent ◽  
Quantum Field Theories ◽  
Strongly Coupled ◽  
Conformal Field ◽  
Instantaneous Power ◽  
Holographic Entanglement Entropy ◽  
Quantum Quenches ◽  
Good Order

We use a simple holographic toy model to study global quantum quenches in strongly coupled, hyperscaling-violating-Lifshitz quantum field theories using entanglement entropy as a probe. Generalizing our conformal field theory results, we show that the holographic entanglement entropy of small subsystems can be written as a simple linear response relation. We use this relation to derive a time-dependent first law of entanglement entropy. In general, this law has a time-dependent term resembling relative entropy which we propose as a good order parameter to characterize out-of-equilibrium states in the post-quench evolution. We use these tools to study a broad class of quantum quenches in detail: instantaneous, power law, and periodic.

scholarly journals Entanglement entropy of AdS5 × S5 with massive flavors

2018 ◽  
Vol 33 (03) ◽  
pp. 1850008
Author(s):  
Sen Hu ◽  
Guozhen Wu
Keyword(s):  
Phase Transition ◽  
Line Segment ◽  
Entanglement Entropy ◽  
Point Of View ◽  
Nucl Phys ◽  
Zero Temperature ◽  
Holographic Entanglement Entropy ◽  
Deconfinement Phase Transition

We consider backreacted [Formula: see text] coupled with [Formula: see text] massive flavors introduced by D7 branes. The backreacted geometry is in the Veneziano limit with fixed [Formula: see text]. By dividing one of the directions into a line segment with length l, we get two subspaces. Then we calculate the entanglement entropy between them. With the method of [I. R. Klebanov, D. Kutasov and A. Murugan, Nucl. Phys. B 796, 274 (2008)], we are able to find the cut-off independent part of the entanglement entropy and finally find that this geometry shows no confinement/deconfinement phase transition at zero temperature from the holographic entanglement entropy point of view similar to the case in pure [Formula: see text].

scholarly journals Linearity of holographic entanglement entropy

2017 ◽  
Vol 2017 (2) ◽  
Author(s):  
Ahmed Almheiri ◽  
Xi Dong ◽  
Brian Swingle
Keyword(s):  
Entanglement Entropy ◽  
Holographic Entanglement Entropy
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