scholarly journals Holographic entanglement entropy of de Sitter braneworld

2006 ◽  
Vol 74 (6) ◽  
Author(s):  
Yukinori Iwashita ◽  
Tsutomu Kobayashi ◽  
Tetsuya Shiromizu ◽  
Hirotaka Yoshino
Keyword(s):  
Entanglement Entropy ◽  
De Sitter ◽  
Holographic Entanglement Entropy

scholarly journals fR Gravity Effects on Charged Accelerating AdS Black Holes Using Holographic Tools

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Adil Belhaj ◽  
Hasan El Moumni ◽  
Karima Masmar
Keyword(s):  
Black Holes ◽  
Correlation Functions ◽  
Entanglement Entropy ◽  
De Sitter ◽  
Four Dimensions ◽  
Holographic Entanglement Entropy ◽  
Ads Black Holes ◽  
Gravity Effects ◽  
Behavioral Situation ◽  
Point Correlation

We investigate numerically fR gravity effects on certain AdS/CFT tools including holographic entanglement entropy and two-point correlation functions for a charged single accelerated Anti-de Sitter black hole in four dimensions. We find that both holographic entanglement entropy and two-point correlation functions decrease by increasing the acceleration parameter A, matching perfectly with literature. Taking into account the fR gravity parameter η, the decreasing scheme of the holographic quantities persist. However, we observe a transition-like point where the behavior of the holographic tools changes. Two regions meeting at such a transit-like point are shown up. In such a nomination, the first one is associated with slow accelerating black holes while the second one corresponds to a fast accelerating solution. In the first region, the holographic entanglement entropy and two-point correlation functions decrease by increasing the η parameter. However, the behavioral situation is reversed in the second one. Moreover, a cross-comparison between the entropy and the holographic entanglement entropy is presented, providing another counterexample showing that such two quantities do not exhibit similar behaviors.

scholarly journals Holographic entanglement entropy for noncommutative anti-de Sitter space

2016 ◽  
Vol 31 (12) ◽  
pp. 1650073
Author(s):  
Davood Momeni ◽  
Muhammad Raza ◽  
Ratbay Myrzakulov
Keyword(s):  
Field Theory ◽  
Hilbert Space ◽  
Conformal Field Theory ◽  
Surface State ◽  
Central Charge ◽  
Entanglement Entropy ◽  
Quantum Effects ◽  
De Sitter ◽  
Conformal Field ◽  
Holographic Entanglement Entropy

A metric is proposed to explore the noncommutative form of the anti-de Sitter (AdS) space due to quantum effects. It has been proved that the noncommutativity in AdS space induces a single component gravitoelectric field. The holographic Ryu–Takayanagi (RT) algorithm is then applied to compute the entanglement entropy (EE) in dual CFT2. This calculation can be exploited to compute ultraviolet–infrared (UV–IR) cutoff dependent central charge of the certain noncommutative CFT2. This noncommutative computation of the EE can be interpreted in the form of the surface/state correspondence. We have shown that noncommutativity increases the dimension of the effective Hilbert space of the dual conformal field theory (CFT).

scholarly journals De Sitter entropy as holographic entanglement entropy

2021 ◽  
Author(s):  
Nikolaos Tetradis
Keyword(s):  
Effective Action ◽  
Degrees Of Freedom ◽  
Entanglement Entropy ◽  
De Sitter Space ◽  
Conformal Anomaly ◽  
Dual Theory ◽  
De Sitter ◽  
Logarithmic Corrections ◽  
Holographic Entanglement Entropy ◽  
Gravitational Entropy

We review the results of refs. [1,2], in which the entanglement entropy in spaces with horizons, such as Rindler or de Sitter space, is computed using holography. This is achieved through an appropriate slicing of anti-de Sitter space and the implementation of a UV cutoff. When the entangling surface coincides with the horizon of the boundary metric, the entanglement entropy can be identified with the standard gravitational entropy of the space. For this to hold, the effective Newton's constant must be defined appropriately by absorbing the UV cutoff. Conversely, the UV cutoff can be expressed in terms of the effective Planck mass and the number of degrees of freedom of the dual theory. For de Sitter space, the entropy is equal to the Wald entropy for an effective action that includes the higher-curvature terms associated with the conformal anomaly. The entanglement entropy takes the expected form of the de Sitter entropy, including logarithmic corrections.

scholarly journals Holographic Cavalieri principle as a universal relation between holographic complexity and holographic entanglement entropy

2018 ◽  
Vol 27 (09) ◽  
pp. 1850103 ◽  
Author(s):  
Davood Momeni ◽  
Mir Faizal ◽  
Ratbay Myrzakulov
Keyword(s):  
Black Holes ◽  
String Theory ◽  
Entanglement Entropy ◽  
Circular Disk ◽  
Universal Relation ◽  
De Sitter ◽  
Cavalieri Principle ◽  
Holographic Entanglement Entropy ◽  
Type Iib String Theory

In this paper, we will propose a universal relation between the holographic complexity (dual to a volume in AdS) and the holographic entanglement entropy (dual to an area in anti-de Sitter (AdS)). We will explicitly demonstrate that our conjuncture holds for all metrics asymptotic to [Formula: see text], and then argue that such a relation should hold in general due to the AdS version of the Cavalieri principle. We will demonstrate that it holds for Janus solution, which have been recently been obtained in type IIB string theory. We will also show that this conjecture holds for a circular disk. This conjecture will be used to show that the proposal that the complexity equals action and the proposal that the complexity equals volume can represent the same physics. Thus, using this conjecture, we will show that the black holes are fastest computers, using the proposal that complexity equals volume.

scholarly journals Quantum holographic entanglement entropy to all orders in 1/N expansion

2020 ◽  
Vol 2020 (4) ◽  
Author(s):  
Shinji Hirano
Keyword(s):  
Partition Function ◽  
Minimal Surface ◽  
Path Integrals ◽  
Entanglement Entropy ◽  
Saddle Points ◽  
De Sitter ◽  
Three Sphere ◽  
Holographic Entanglement Entropy ◽  
Bulk Volume ◽  
Minimal Surface Area

Abstract We study holographic entanglement entropy in four-dimensional quantum gravity with negative cosmological constant. By using the replica trick and evaluating path integrals in the minisuperspace approximation, in conjunction with the Wheeler–DeWitt equation, we compute quantum corrections to the holographic entanglement entropy for a circular entangling surface on the boundary three-sphere. Similarly to our previous work on the sphere partition function, the path integrals are dominated by a replica version of asymptotically anti-de Sitter conic geometries at saddle points. As expected from a general conformal field theory argument, the final result is minus the free energy on the three-sphere, which agrees with the logarithm of the Airy partition function for the Aharony–Bergman–Jafferis–Maldacena theory that sums up all perturbative $1/N$ corrections despite the absence of supersymmetries. The all-order holographic entanglement entropy cleanly splits into two parts, (1) the $1/N$-corrected Ryu–Takayanagi minimal surface area and (2) the bulk entanglement entropy across the minimal surface, as suggested in the earlier literature. It is explicitly shown that the former comes from the localized conical singularity of the replica geometries and the latter from the replication of the bulk volume.

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.

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