Holographic Entanglement Entropy: An Overview

Abstract

In this article, we review recent progresses on the holographic understandings of the entanglement entropy in the AdS/CFT correspondence. After reviewing the general idea of holographic entanglement entropy, we will explain its applications to confinement/deconfinement phase transitions, black hole entropy and covariant formulation of holography.

52 pages, Invited review article for a special issue "Entanglement entropy in extended quantum systems" in Journal of Physics A, edited by P.Calabrese, J. Cardy and B. Doyon; (v2) references added

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• A short review on entanglement in quantum spin systems
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• Black hole entropy as entanglement entropy: a holographic derivation
• Entanglement Entropy and Twist Fields
• A c-theorem for the entanglement entropy
• Power-law corrections to entanglement entropy of horizons
• Universal entanglement entropy in 2D conformal quantum critical points
• Numerical study of entanglement entropy in SU(2) lattice gauge theory
• Entropy Function and AdS(2)/CFT(1) Correspondence
• Dynamical black holes and expanding plasmas
• Stationary black holes and attractor mechanism
• Topological Entanglement Entropy from the Holographic Partition Function
• Entanglement entropy of black holes and AdS/CFT correspondence
• Holographic entanglement entropy for disconnected regions
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• Entanglement entropy for a Dirac fermion in three dimensions: vertex contribution
• Bi-partite entanglement entropy in massive two-dimensional quantum field theory
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• Area law and vacuum reordering in harmonic networks
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• Holographic Entanglement Entropy at Finite Temperature
• Bi-partite entanglement entropy in integrable models with backscattering
• Entanglement entropy in d+1 SU(N) gauge theory
• Entanglement Entropy in Quantum Gravity and the Plateau Problem
• Holographic entanglement entropy of de Sitter braneworld
• String duals of two-dimensional (4,4) supersymmetric gauge theories
• Holographic flavor in N=4 gauge theories in 3d from wrapped branes
• Geometric Entropy and Hagedorn/Deconfinement Transition
• Black Hole Entropy and Gravity Cutoff
• Entanglement properties of topological color codes
• Numerical metric extraction in AdS/CFT
• Entanglement entropy of two-dimensional Anti-de Sitter black holes
• CP Violation in the SUSY Seesaw: Leptogenesis and Low Energy
• The Thermodynamics of Kaluza-Klein Black Hole/Bubble Chains
• Entanglement entropy and the simulation of Quantum Mechanics
• A Comment or two on Holographic Dark Energy
• Renormalized Thermal Entropy in Field Theory
• A new mechanism for non-locality from string theory: UV-IR quantum entanglement and its imprints on the CMB
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• Free Yang-Mills vs. Toric Sasaki-Einstein
• Entanglement Entropy and The Density Matrix Renormalization Group
• Entanglement entropy of two dimensional systems and holography
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• Correlator of Wilson and t'Hooft Loops at Strong Coupling in $\mathcal{N}=4$ SYM Theory
• Entanglement Entropy and Spatial Geometry

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• Holographic Entanglement Entropy in Lovelock Gravities
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• Entanglement Entropy from a Holographic Viewpoint
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• Thermalization with a chemical potential from AdS spaces
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• Entanglement Entropy of Cosmological Perturbations
• State Operator Correspondence and Entanglement in AdS_2/CFT_1
• A universal feature of CFT Renyi entropy
• Higher Spin Entanglement and W_N Conformal Blocks
• Entanglement between Two Interacting CFTs and Generalized Holographic Entanglement Entropy
• Corner contribution to the entanglement entropy of an O(3) quantum critical point in 2+1 dimensions
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• Holographic Quantum Entanglement Negativity
• Entanglement entropies in free fermion gases for arbitrary dimension
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• Complexity Growth Rate in Lovelock Gravity
• The Holographic Entropy Cone for Five Regions
• Holographic Phases of Renyi Entropies
• Finite Temperature Critical Behavior of Mutual Information
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• Holographic Entanglement Entropy in P-wave Superconductor Phase Transition
• Entropic Counterpart of Perturbative Einstein Equation
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• Quantum noise and entanglement generated by a local quantum quench
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• Entanglement in De Sitter Space
• Bound states and entanglement in the excited states of quantum spin chains
• Spin structures and entanglement of two disjoint intervals in conformal field theories
• Nonlocal probes of thermalization in holographic quenches with spectral methods
• Entanglement Entropy and Wilson Loop in Stückelberg Holographic Insulator/Superconductor Model
• On the Time Evolution of Holographic n-partite Information
• Holographic thermalization in Gauss-Bonnet gravity
• Gravitational effective action and entanglement entropy in UV modified theories with and without Lorentz symmetry
• On entanglement hamiltonians of an interval in massless harmonic chains
• Wilson Lines and Holographic Entanglement Entropy in Galilean Conformal Field Theories
• Schrödinger Holography with and without Hyperscaling Violation
• Scaling of entanglement entropy in the (branching) multi-scale entanglement renormalization ansatz
• The holographic entropy increases in quadratic curvature gravity
• Charged Entanglement Entropy of Local Operators
• Entropy Creation in Relativistic Heavy Ion Collisions
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• Hidden conformal symmetry of rotating charged black holes
• Deconfinement as an entropic self-destruction: a solution for the quarkonium suppression puzzle?
• Growth of mutual information in a quenched one-dimensional open quantum many body system
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• Complexity of Holographic Superconductors
• Holographic entanglement negativity conjecture for adjacent intervals in $Ad{S}_3/CF{T}_2$
• Numerical determination of entanglement entropy for a sphere
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• Quantum entanglement in de Sitter space from Stringy Axion: An analysis using $\alpha$ vacua
• Holographic spacetime, black holes and quantum error correcting codes: A review
• Pedagogical introduction to SYK model and 2D Dilaton Gravity
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• Renyi entropy, stationarity, and entanglement of the conformal scalar
• Charged Renyi entropies and holographic superconductors
• Double Local Quenches in 2D CFTs and Gravitational Force
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• Holographic entanglement entropy in metal/superconductor phase transition with Born-Infeld electrodynamics
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• Covariant Holographic Entanglement Negativity for Adjacent Subsystems in $\mathrm{Ad}{\mathrm{S}}_3/CF{\mathrm{T}}_2$
• An equal area law for holographic entanglement entropy of the AdS-RN black hole
• Quantum complexity in gravity, quantum field theory, and quantum information science
• Non-equilibrium condensation process in holographic superconductor with nonlinear electrodynamics
• Holographic entanglement entropy in general holographic superconductor models
• Topological pseudo entropy
• Holographic Entanglement Entropy in the QCD Phase Diagram with a Critical Point
• Simulating quantum field theory in curved spacetime with quantum many-body systems
• Generalized Gravitational Entropy for Warped Anti-de Sitter Space
• Balanced Partial Entanglement and Mixed State Correlations
• Multipartite Purification, Multiboundary Wormholes and Islands in AdS${}_3$/CFT${}_2$
• Understanding the entanglement entropy and spectra of 2D quantum systems through arrays of coupled 1D chains
• Entanglement in Four-Dimensional SU(3) Gauge Theory
• Notes on Entanglement in Abelian Gauge Theories
• Genus Two Partition Functions and Renyi Entropies of Large c CFTs
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• Charged Rényi negativity of massless free bosons
• Two dimensional quantum quenches and holography
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• Renyi Entropy and Geometry
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• Multi-charged moments of two intervals in conformal field theory
• On the Architecture of Spacetime Geometry
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• On shape dependence of holographic entanglement entropy in AdS4/CFT3
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• Entanglement thermodynamics for charged black holes
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• Boomerang RG flows with intermediate conformal invariance
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• Holographic Rényi Entropy of Single Interval on Torus: with W symmetry
• Black holes as gases of punctures with a chemical potential: Bose-Einstein condensation and logarithmic corrections to the entropy
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• Entanglement and negativity Hamiltonians for the massless Dirac field on the half line
• Holographic entanglement entropy in metal/superconductor phase transition with exponential nonlinear electrodynamics
• On the Monogamy of Holographic $n$-partite Information
• Charged Rényi Entropies in CFTs with Einstein-Gauss-Bonnet Holographic Duals
• Thermodynamic law from the entanglement entropy bound
• Holographic Weyl Anomalies for 4d Defects in 6d SCFTs
• Remarks on effective action and entanglement entropy of Maxwell field in generic gauge
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• Simple counterterms for asymptotically AdS spacetimes in Lovelock gravity
• Holographic Studies of The Generic Massless Cubic Gravities
• Holographic entanglement entropy, deformed black branes, and deconfinement in AdS/QCD
• Non-conformal brane plane waves and entanglement entropy
• Rényi Entropy of Free Compact Boson on Torus
• The imaginary part of the gravitational action at asymptotic boundaries and horizons
• Entanglement entropy for non-coplanar regions in quantum field theory
• Entanglement, Tensor Networks and Black Hole Horizons
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• Holographic Entanglement Entropy on Generic Time Slices
• Logarithmic Corrections to the Entanglement Entropy
• Symmetry-protected topological order in magnetization plateau states of quantum spin chains
• Gravitational decoupling for hairy black holes in asymptotically AdS spacetimes
• Time Evolution of Entanglement Negativity from Black Hole Interiors
• Introduction to the AdS/CFT correspondence
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• Disentangling the gravity dual of Yang-Mills theory
• Complexity of operators generated by quantum mechanical Hamiltonians
• Superhorizon entanglement from inflationary particle production
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• Generalized Volume-Complexity For Two-Sided Hyperscaling Violating Black Branes
• A note on the AdS/CFT correspondence and the nature of spacetime in quantum gravity
• Holographic Dual to Conical Defects: I. Moving Massive Particle
• Entanglement Entropy Renormalization for the NC scalar field coupled to classical BTZ geometry
• Jackiw-Teitelboim quantum gravity with defects and the Aharonov-Bohm effect
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• Vacuum densities for a brane intersecting the AdS boundary
• Entanglement Entropy for $T\bar{T}$, $J\bar{T}$, $T\bar{J}$ deformed holographic CFT
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• Horizon entanglement area law from regular black hole thermodynamics
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• Holographic torus entanglement and its RG flow
• Holographic QCD and magnetic fields
• On the Shape Dependence of Entanglement Entropy
• Generalized Volume-Complexity for RN-AdS Black Hole
• Dynamics of charge imbalance resolved negativity after a global quench in free scalar field theory
• Holographic entanglement entropy in two-order insulator/superconductor transitions
• Reissner-Nordstrom Black Holes in Quartic Quasi-Topological Gravity Theory
• Entanglement and Majorana edge states in the Kitaev model
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• Quantum information probes of charge fractionalization in large-$N$ gauge theories
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• Holographic entanglement entropy of the near horizon 1/4 BPS F-D$p$ bound states
• Probing Critical Surfaces in Momentum Space Using Real-Space Entanglement Entropy: Bose versus Fermi
• Quantum decoherence in the entanglement entropy of a composite particle and its relationship to coarse graining in the Husimi function
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• Complexity Growth Following Multiple Shocks
• Towards an Entanglement Measure for Mixed States in CFTs Based on Relative Entropy
• The BTZ black hole with a time-dependent boundary
• Quantum Correction of the Wilson Line and Entanglement Entropy in the Pure AdS${}_3$ Einstein Gravity Theory
• Thermodynamical property of entanglement entropy and deconfinement phase transition
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• Area Law Violations and Quantum Phase Transitions in Modified Motzkin Walk Spin Chains
• Entanglement of scales as a possible mechanism for decoherence and thermalization in relativistic heavy ion collisions
• Holographic Approach to Entanglement Entropy in Disordered Systems
• Entanglement Entropy: Non-Gaussian States and Strong Coupling
• Finite temperature negativity Hamiltonians of the massless Dirac fermion
• A note on holographic subregion complexity and QCD phase transition
• AdS to dS phase transition mediated by thermalon in Einstein-Gauss-Bonnet gravity from Renyi statistics
• Entanglement Entropy of Local Operators in Quantum Lifshitz Theory
• Holographic subregion complexity of a 1+1 dimensional $p$-wave superconductor
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• On minimal entanglement wedge cross section for holographic entanglement negativity
• Holographic entropy production in a Bjorken expanding hot and dense strongly coupled quantum fluid
• Replica Trick Calculation for Entanglement Entropy of Static Black Hole Spacetimes
• Complexity and uncomplexity during energy injection
• Time-dependent quantum correlations in two-dimensional expanding spacetime
• Entanglement and Topology in RG Flows Across Dimensions: Caps, Bridges and Corners
• Probes of holographic thermalization in a simple model with momentum relaxation
• New Torsional Deformations of Locally AdS${}_3$ Space
• Entanglement Entropy and Thermal Phase Transitions from Curvature Singularities
• Holographic Rényi Entropy and Generalized Entropy method
• Entanglement entropy from the holographic stress tensor
• Multipartite Entanglement and Firewalls
• Probing AdS Wormholes by Entanglement Entropy
• Holographic entanglement entropy and mutual information in deformed field theories at finite temperature
• Static Elliptic Minimal Surfaces in AdS(4)
• Inverse problem of correlation functions in holography
• AdS/CFT Correspondence with a 3D Black Hole Simulator
• Entanglement in Theory Space
• Holographic complexity of hyperbolic black holes
• Entanglement entropy for pure gauge theories in 1+1 dimensions using the lattice regularization
• Entanglement Entropy and Duality in AdS(4)
• Corrections to de Sitter entropy through holography
• Topological invariants of the Ryu-Takayanagi ($RT$) surface used to observe holographic superconductor phase transition
• Holographic time-dependent entanglement entropy in $p$-brane gas geometries
• Holographic entanglement entropy and entanglement thermodynamics of `black' non-susy D3 brane
• Mixed state information theoretic measures in boosted black brane
• A New Paradigm for Topological or Rotational Non-Abelian Gauge Fields from Einstein-Skyrme Holography
• Relative entropy in higher spin holography
• The mixed-state entanglement in holographic p-wave superconductor model
• On universal terms of holographic entanglement entropy in theories with hyperscaling violation
• Geometric quantum complexity of bosonic oscillator systems
• Quantum discord and entropic measures of two relativistic fermions
• Non-equilibrium dynamics in Holography
• Entanglement entropy and Schmidt number as measures of delocalization of $\alpha$ clusters in one-dimensional nuclear systems
• Entanglement entropy in a four-dimensional cosmological background
• The entanglement entropy of typical pure states and replica wormholes
• Generalized Entanglement, Charges and Intertwiners
• Entanglement of higher-derivative oscillators in holographic systems
• Mixed state entanglement in deformed field theory at finite temperature
• Holographic Superconductors in a Cohesive Phase
• High temperature behavior of non-local observables in boosted strongly coupled plasma: A holographic study
• Subsystem entropy in 2d CFT and KdV ETH
• Entropic relations for indistinguishable quantum particles
• Entanglement Entropy and Decoupling in the Universe
• Entanglement Entropy with Background Gauge Fields
• Towards self dual Loop Quantum Gravity
• An Operator Product Expansion for the Mutual Information in AdS/CFT
• Entanglement structures from modified IR geometry
• Extracting Many-Body Quantum Resources within One-Body Reduced Density Matrix Functional Theory
• Entanglement entropy of spherical domains in anti-de Sitter space
• A Holographic Approach to Spacetime Entanglement
• Symmetric Orbifolds and Entanglement Entropy for Primary Excitations in Two Dimensional CFT
• Holographic entanglement properties in the QCD phase diagram from EMD models
• Generalized holographic complexity of rotating black holes
• Inflation as a Solution to the Early Universe Entropy Problem
• Holographic entanglement entropy of the double Wick rotated BTZ black hole
• On Classical Equivalence Between Noncritical and Einstein Gravity : The AdS/CFT Perspectives
• Field Space Entanglement Entropy, Zero Modes and Lifshitz Models
• Entanglement entropy between real and virtual particles in ${\varphi }^4$ quantum field theory
• Entangled spins and ghost-spins
• Quantum Local Quench, AdS/BCFT and Yo-Yo String
• Entropy of Thermal CFTs on Curved Backgrounds
• Holographic thermalization from non relativistic branes
• Entanglement Entropy of the Gross-Neveu Model
• A note on electromagnetic edge modes
• Vacuum densities and the Casimir forces for branes orthogonal to the AdS boundary
• The Holographic Entanglement Entropy of Schwarzschild Black Holes
• More on Holographic Volumes, Entanglement, and Complexity
• Linguistic Matrix Theory
• The entanglement entropy of the quantum Hall edge and its geometric contribution
• Comments on the T-dual of the gravity dual of D5-branes on $S^3$
• Entanglement entropy between virtual and real excitations in quantum electrodynamics
• Holographic Mutual Information of Two Disjoint Spheres
• On the foundations of quantum theory
• On the Holographic Entanglement Entropy for Non-smooth Entangling Curves in AdS(4)
• On a new relation between entanglement and geometry from M(atrix) theory
• Holographic entanglement entropy and complexity of microstate geometries
• On the Complexity of a Charged Quantum Oscillator
• Quantum Holographic Entanglement Entropy to All Orders in $1/N$ Expansion
• Smooth Entropy Transfer of Quantum Gravity Information Processing
• The operator algebra of cyclic orbifolds
• Hamilton-Jacobi formulation of holographic Entanglement Entropy
• Holographic RG flow triggered by a classically marginal operator
• Convexity of the entanglement energy of SU($2N$)-symmetric fermions with attractive interactions
• Properties of gapped systems in AdS/BCFT
• Detecting many-body entanglements in noninteracting ultracold atomic fermi gases
• Renyi information from entropic effects in one higher dimension
• Compressible forced viscous fluid from product Einstein manifolds
• D3 branes in a Melvin universe: a new realm for gravitational holography
• Holographic entanglement entropy beyond coherent states
• Entanglement entropy in a holographic p-wave superconductor model
• Emergent gauge fields and their nonperturbative effects in correlated electrons
• Entanglement Entropy for D3-, M2- and M5-brane backgrounds
• Entanglement Entropy and Thermodynamics of Dynamical Black Holes
• On the AdS/CFT correspondence and quantum entanglement
• Flavors of entanglement
• Inflation from entropy
• Holographic approach to thermalization in general anisotropic theories
• Entanglement entropy evolution during gravitational collapse
• Schwarzschild Black Holes and Asymptotic $Ad{S}_2$
• Entanglement entropy and Wilson loop
• Projective approach to the entanglement entropy of 1-$d$ fermions
• Resource and stability near a critical point from the quantum information perspective
• Geometric Flow Description of Minimal Surfaces
• HEE and HSC for flavors: perturbative structure in open string geometries
• Entanglement at the Soft-Hair Horizon
• Ratio of critical quantities related to Hawking temperature-entanglement entropy criticality
• Entanglement entropy of cosmological perturbations for S-brane Ekpyrosis
• Topological Classification of a 4D AdS Black Hole with Non-Minimal Maxwell Coupling
• Scalar filed evolution and area spectrum for Lovelock-AdS black holes
• Towards Entanglement Entropy of Random Large-N Theories
• Holographic entanglement negativity for a single subsystem in conformal field theories with a conserved charge
• A Holographic Two-Impurity Kondo Model
• Spherically symmetric black holes in Gravity from Entropy and spontaneous emission
• Second Rényi entropy and annulus partition function for one-dimensional quantum critical systems with boundaries
• Game Theory in Cosmology
• Thermal Correction to Entanglement Spectrum for Conformal Field Theories
• Holographic entanglement negativity for disjoint subsystems in $\mathrm{Ad}{\mathrm{S}}_{\mathrm{d}+1}/CF{\mathrm{T}}_{\mathrm{d}}$
• Non-local Probes in Holographic Theories with Momentum Relaxation
• Holographic Entanglement Entropy for noncommutative Anti-de Sitter space
• Holographic entanglement entropy for relativistic hydrodynamic flows
• Mutual information and holographic entanglement entropy for strongly-coupled R-charged plasmas
• Total and Symmetry resolved Entanglement spectra in some Fermionic CFTs from the BCFT approach
• Holographic Entanglement Entropy for Excited States in Two Dimensional CFT
• Exact Solvability Of Entanglement For Arbitrary Initial State in an Infinite-Range Floquet System
• Non-relativistic entanglement entropy from Horava gravity
• How is the Presence of Horizons and Localized Matter Encoded in the Entanglement Entropy?
• Intrinsic Entropy of Squeezed Quantum Fields and Nonequilibrium Quantum Dynamics of Cosmological Perturbations
• Non-equilibrium phase and entanglement entropy in 2D holographic superconductors via Gauge-String duality
• Replica wormhole and AMPS firewall
• Is monogamy of entanglement geometrical?
• A Information-Theoretic View on Spacetime
• $2$-Rényi CCNR Negativity of Compact Boson for multiple disjoint intervals
• Electromagnetic Wightman functions and vacuum densities for a brane intersecting the AdS boundary
• Entanglement entropy of a simple quantum system
• A universal approach to Renyi entropy of multiple disjoint intervals
• Quantum information measures and their applications in quantum field theory
• Entanglement Suppression Due to Black Hole Scattering
• Higher-curvature Corrections to Holographic Entanglement with Momentum Dissipation
• Holographic Subregion Complexity and Fidelity Susceptibility in Noncommutative Yang--Mills Theory
• Entanglement Temperature With Gauss-Bonnet Term
• Lecture notes on strings in AdS${}_3$ from the worldsheet and the AdS${}_3$/CFT${}_2$ duality
• Entanglement Entropy and Complexity of Multicomponent Universe from Holography
• Bulk entanglement and its shape dependence
• Emergent geometry through quantum entanglement in Matrix theories
• Black Hole Entropy from Entropy of Hawking Radiation
• Cosmological Implications of Thermodynamic Split Conjecture
• Conformal defects in supergravity - backreacted Dirac delta sources
• AdS/CFT without holography: A hidden dimension on the CFT side and implications for black-hole entropy
• The Influence of Angular Momentum and Chemical Potential on Holographic Entanglement Entropy
• Emergent gravity from patterns in natural numbers
• Quantum Information Approaches to Quantum Gravity
• Entanglement and Excitations in Gauge/Gravity Duality
• De Sitter entropy as holographic entanglement entropy
• Thermodynamic Split Conjecture and an Observational Test for Cosmological Entropy
• Non-perturbative Aspects of Quantum Field Theories from Holography
• Computing Black Hole Entropy at Infinity
• On Emergent Geometry from Entanglement Entropy in Matrix theory
• Emergence of cosmological Friedmann equations from quantum entanglement
• Rényi negativities in non-equilibrium open free-boson chains