scholarly journals Bulk entanglement entropy for photons and gravitons in AdS$_3$

2020 ◽  
Vol 8 (5) ◽  
Author(s):  
Alexandre Belin ◽  
Nabil Iqbal ◽  
Jorrit Kruthoff
Keyword(s):  
Hilbert Space ◽  
Excited States ◽  
Central Charge ◽  
Entanglement Entropy ◽  
Vacuum State ◽  
Gravitational Theory ◽  
Perfect Agreement ◽  
Holographic Entanglement Entropy ◽  
The Difference ◽  
Chern Simons

We study quantum corrections to holographic entanglement entropy in AdS_33/CFT_22; these are given by the bulk entanglement entropy across the Ryu-Takayanagi surface for all fields in the effective gravitational theory. We consider bulk U(1)U(1) gauge fields and gravitons, whose dynamics in AdS_33 are governed by Chern-Simons terms and are therefore topological. In this case the relevant Hilbert space is that of the edge excitations. A novelty of the holographic construction is that such modes live not only on the bulk entanglement cut but also on the AdS boundary. We describe the interplay of these excitations and provide an explicit map to the appropriate extended Hilbert space. We compute the bulk entanglement entropy for the CFT vacuum state and find that the effect of the bulk entanglement entropy is to renormalize the relation between the effective holographic central charge and Newton’s constant. We also consider excited states obtained by acting with the U(1)U(1) current on the vacuum, and compute the difference in bulk entanglement entropy between these states and the vacuum. We compute this UV-finite difference both in the bulk and in the CFT finding a perfect agreement.

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 Symmetry-resolved entanglement for excited states and two entangling intervals in AdS3/CFT2

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Konstantin Weisenberger ◽  
Suting Zhao ◽  
Christian Northe ◽  
René Meyer
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Excited States ◽  
Vertex Operator Algebra ◽  
Central Charge ◽  
Entanglement Entropy ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
Chern Simons ◽  
Twist Fields

Abstract We test the proposal of [1] for the holographic computation of the charged moments and the resulting symmetry-resolved entanglement entropy in different excited states, as well as for two entangling intervals. Our holographic computations are performed in U(1) Chern-Simons-Einstein-Hilbert gravity, and are confirmed by independent results in a conformal field theory at large central charge. In particular, we consider two classes of excited states, corresponding to charged and uncharged conical defects in AdS3. In the conformal field theory, these states are generated by the insertion of charged and uncharged heavy operators. We employ the monodromy method to calculate the ensuing four-point function between the heavy operators and the twist fields. For the two-interval case, we derive our results on the AdS and the conformal field theory side, respectively, from the generating function method of [1], as well as the vertex operator algebra. In all cases considered, we find equipartition of entanglement between the different charge sectors. We also clarify an aspect of conformal field theories with a large central charge and $$ \hat{\mathfrak{u}}{(1)}_k $$ u ̂ 1 k Kac-Moody symmetry used in our calculations, namely the factorization of the Hilbert space into a gravitational Virasoro sector with large central charge, and a $$ \hat{\mathfrak{u}}{(1)}_k $$ u ̂ 1 k Kac-Moody sector.

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 Holographic complexity of “black” non-susy D3-brane and the high temperature limit

2019 ◽  
Vol 34 (01) ◽  
pp. 1950003 ◽  
Author(s):  
Sourav Karar ◽  
Sunandan Gangopadhyay ◽  
A. S. Majumdar
Keyword(s):  
High Temperature ◽  
Entanglement Entropy ◽  
Temperature Limit ◽  
Yang Mills ◽  
High Temperature Limit ◽  
Holographic Entanglement Entropy ◽  
The Difference ◽  
Super Yang Mills Theory

The holographic complexity of a “black” non-susy D3-brane is computed. The difference in the holographic complexity between this geometry in the Fefferman–Graham coordinates and that of the AdS5 geometry is obtained for a strip-type subsystem. This is then related to the changes in the energy and the entanglement entropy of the system. We next take the high temperature limit of the change in complexity and observe that it scales with the temperature in the same way as the holographic entanglement entropy. The crossover of the holographic complexity to its corresponding thermal counterpart is similar to the corresponding crossover of the holographic entanglement entropy in the high temperature limit. We further repeat the analysis for [Formula: see text] super-Yang–Mills theory and observe a similar behavior.

scholarly journals Wilson surface central charge from holographic entanglement entropy

2019 ◽  
Vol 2019 (5) ◽  
Author(s):  
John Estes ◽  
Darya Krym ◽  
Andy O’Bannon ◽  
Brandon Robinson ◽  
Ronnie Rodgers
Keyword(s):  
Central Charge ◽  
Entanglement Entropy ◽  
Holographic Entanglement Entropy

scholarly journals Entanglement entropy of AdS5 × S5 with massless flavors at nonzero temperature

2018 ◽  
Vol 33 (07) ◽  
pp. 1850033
Author(s):  
Sen Hu ◽  
Guozhen Wu
Keyword(s):  
Phase Transition ◽  
Minimal Surface ◽  
Event Horizon ◽  
Line Segment ◽  
Entanglement Entropy ◽  
Nonzero Temperature ◽  
Transition Phenomenon ◽  
Holographic Entanglement Entropy ◽  
Deconfinement Phase Transition ◽  
The Difference

We consider backreacted [Formula: see text] coupled with [Formula: see text] massless flavors introduced by D7-branes at nonzero temperature. The backreacted geometry is in the Veneziano limit. The temperature of this system is related to the event horizon at [Formula: see text]. Dividing one of the spatial directions into a line segment with length [Formula: see text], we will calculate the holographic entanglement entropy (HEE) between the two subspaces. We study the behavior near the event horizon, and finally find that there exists confinement/deconfinement phase transition phenomenon near the horizon since the difference between the entanglement entropy of the connected minimal surface and the disconnected one changes sign.

scholarly journals Bulk entanglement entropy in perturbative excited states

2018 ◽  
Vol 5 (3) ◽  
Author(s):  
Alexandre Belin ◽  
Nabil Iqbal ◽  
Sagar F. Lokhande
Keyword(s):  
Scalar Field ◽  
Closed Form ◽  
Excited States ◽  
Entanglement Entropy ◽  
Quantum Corrections ◽  
Particle State ◽  
Small Interval ◽  
Spatial Spread ◽  
Holographic Entanglement Entropy ◽  
Minimal Area

We compute the bulk entanglement entropy across the Ryu-Takayanagi surface for a one-particle state in a scalar field theory in AdS_33. We work directly within the bulk Hilbert space and include the spatial spread of the scalar wavefunction. We give closed form expressions in the limit of small interval sizes and compare the result to a CFT computation of entanglement entropy in an excited primary state at large cc. Including the contribution from the backreacted minimal area, we find agreement between the CFT result and the FLM and JLMS formulas for quantum corrections to holographic entanglement entropy. This provides a non-trivial check in a state where the answer is not dictated by symmetry. Along the way, we provide closed-form expressions for the scalar field Bogoliubov coefficients that relate the global and Rindler slicings of AdS_33.

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