Holographic Entanglement Entropy

Abstract

We review the developments in the past decade on holographic entanglement entropy, a subject that has garnered much attention owing to its potential to teach us about the emergence of spacetime in holography. We provide an introduction to the concept of entanglement entropy in quantum field theories, review the holographic proposals for computing the same, providing some justification for where these proposals arise from in the first two parts. The final part addresses recent developments linking entanglement and geometry. We provide an overview of the various arguments and technical developments that teach us how to use field theory entanglement to detect geometry. Our discussion is by design eclectic; we have chosen to focus on developments that appear to us most promising for further insights into the holographic map. This is a draft of a few chapters of a book which will appear sometime in the near future, to be published by Springer. The book in addition contains a discussion of application of holographic ideas to computation of entanglement entropy in strongly coupled field theories, and discussion of tensor networks and holography, which we have chosen to exclude from the current manuscript.

154 pages. many figures. preliminary version of book chapters. comments welcome. v2: typos fixed and references added

References in corpus (4)

• Entwinement and the emergence of spacetime
• Universality of Gravity from Entanglement
• Operator Dictionaries and Wave Functions in AdS/CFT and dS/CFT
• Covariant Residual Entropy

Cited by in corpus (202)

• Towards Complexity for Quantum Field Theory States
• Entanglement entropy: holography and renormalization group
• QCD thermalization: Ab initio approaches and interdisciplinary connections
• Complexity and entanglement for thermofield double states
• Entanglement negativity and minimal entanglement wedge cross sections in holographic theories
• Holographic Pseudo Entropy
• Quantum Computational Complexity -- From Quantum Information to Black Holes and Back
• Complexity as a novel probe of quantum quenches: universal scalings and purifications
• Quantum Extremal Islands Made Easy, PartIII: Complexity on the Brane
• Entanglement hamiltonian and entanglement contour in inhomogeneous 1D critical systems
• Holographic Complexity Equals Which Action?
• Information Flow in Black Hole Evaporation
• The First Law of Complexity
• Particle Number Fluctuations, Rényi and Symmetry-resolved Entanglement Entropy in Two-dimensional Fermi Gas from Multi-dimensional Bosonization
• Path integral optimization as circuit complexity
• A Holographic Derivation of the Weak Gravity Conjecture
• Topological Complexity in AdS3/CFT2
• Holographic Axion Model: a simple gravitational tool for quantum matter
• The boundary dual of the bulk symplectic form
• Twisted and untwisted negativity spectrum of free fermions
• Aspects of capacity of entanglement
• Symmetry-Resolved Entanglement in AdS${}_3$/CFT${}_2$ coupled to $U(1)$ Chern-Simons Theory
• Pseudo Entropy in Free Quantum Field Theories
• Symmetry-resolved entanglement for excited states and two entangling intervals in AdS${}_3$/CFT${}_2$
• De Sitter Space and Entanglement
• Entanglement hamiltonians in 1D free lattice models after a global quantum quench
• Holographic Complexity and de Sitter Space
• On entanglement hamiltonians of an interval in massless harmonic chains
• Colloquium: Hydrodynamics and holography of charge density wave phases
• An Exact Construction of Codimension two Holography
• On holographic time-like entanglement entropy
• Entanglement, quantum randomness, and complexity beyond scrambling
• Entangled de Sitter from Stringy Axionic Bell pair I: An analysis using Bunch Davies vacuum
• Entanglement entropy of two disjoint intervals and the recursion formula for conformal blocks
• Charged Moments in $W_3$ Higher Spin Holography
• Wormholes & Holography: An Introduction
• 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
• Symmetry-resolved entanglement in critical non-Hermitian systems
• Probing the entanglement of operator growth
• Holographic Complexity in dS${}_{d+1}$
• Entanglement and Complexity of Purification in (1+1)-dimensional free Conformal Field Theories
• Aspects of Hyperscaling Violating Geometries at Finite Cutoff
• Holographic Entanglement Entropy in the QCD Phase Diagram with a Critical Point
• Multipartite Purification, Multiboundary Wormholes and Islands in AdS${}_3$/CFT${}_2$
• Small Schwarzschild de Sitter black holes, quantum extremal surfaces and islands
• Islands for Entanglement Negativity
• Complexity of mixed Gaussian states from Fisher information geometry
• Quantum Information Scrambling: From Holography to Quantum Simulators
• Covariant bit threads
• Subsystem trace distance in low-lying states of $(1+1)$-dimensional conformal field theories
• Entanglement entropy from entanglement contour: higher dimensions
• Free fermion entanglement with a semitransparent interface: the effect of graybody factors on entanglement islands
• Constructible reality condition of pseudo entropy via pseudo-Hermiticity
• Codimension-n Holography for Cones
• Influence of inhomogeneities on holographic mutual information and butterfly effect
• Non-local observables at finite temperature in AdS/CFT
• Entanglement and geometry from subalgebras of the Virasoro algebra
• Negativity Spectra in Random Tensor Networks and Holography
• Complex geodesics in de Sitter space
• Einstein-AdS action, renormalized volume/area and holographic Renyi entropies
• On the foundations and extremal structure of the holographic entropy cone
• Cosmological spectrum of two-point correlation function from vacuum fluctuation of Stringy Axion field in De Sitter space: A study of the role of Quantum Entanglement
• On de Sitter future-past extremal surfaces and the "entanglement wedge"
• Long-distance entanglement of purification and reflected entropy in conformal field theory
• Holographic complexity: A tool to probe the property of reduced fidelity susceptibility
• Relative entropy for coherent states in chiral CFT
• Subsystem complexity after a global quantum quench
• String Stars in Anti de Sitter Space
• Holographic Mutual Information and Critical Exponents of the Strongly Coupled Plasma
• Holographic Study of Reflected Entropy in Anisotropic Theories
• A Holographic Argument for the Penrose Inequality in AdS
• Holographic reconstruction of black hole spacetime: machine learning and entanglement entropy
• Fix the dual geometries of $T\bar{T}$ deformed CFT${}_2$ and highly excited states of CFT${}_2$
• Topological terms, AdS_2n gravity and renormalized Entanglement Entropy of holographic CFTs
• Complexity of warped conformal field theory
• Entanglement Entropy in Generalised Quantum Lifshitz Models
• Bounds on gravitational brane couplings and tomography in AdS3 black hole microstates
• Entanglement Wedge Cross Section in Holographic Excited States
• Entanglement and negativity Hamiltonians for the massless Dirac field on the half line
• Reflected Entropy in AdS${}_3$/WCFT
• Universal Thermal Corrections to Symmetry-Resolved Entanglement Entropy and Full Counting Statistics
• IR dynamics and entanglement entropy
• Liouville description of conical defects in dS${}_4$, Gibbons-Hawking entropy as modular entropy, and dS${}_3$ holography
• Entanglement, Soft Modes, and Celestial Holography
• Holographic Studies of The Generic Massless Cubic Gravities
• Bulk reconstruction using timelike entanglement in (A)dS
• Holographic Entanglement Entropy on Generic Time Slices
• Geometry of small causal diamonds
• Renormalization of Entanglement Entropy from topological terms
• News vs Information
• AdS Vacuum Bubbles, Holography and Dual RG Flows
• Entanglement, Replicas, and Thetas
• Shape dependence of renormalized holographic entanglement entropy
• $T\bar{T}$ deformed YM${}_2$ on general backgrounds from an integral transformation
• Jackiw-Teitelboim quantum gravity with defects and the Aharonov-Bohm effect
• Conformal Properties of Hyperinvariant Tensor Networks
• Entanglement entropy and Fisher information metric for closed bosonic strings in homogeneous plane wave background
• Entanglement Entropy for $T\bar{T}$, $J\bar{T}$, $T\bar{J}$ deformed holographic CFT
• De Finetti theorems and entanglement in large-N theories and gravity
• Complexity = Anything Can Grow Forever in de Sitter
• Entanglement Hamiltonians and the quasiparticle picture
• Holographic Reconstruction of Bubbles
• Circuit Complexity for Carrollian Conformal (BMS) Field Theories
• Entanglement Wedge Cross Section Growth During Thermalization
• The $\hslash \to 0$ Limit of the Entanglement Entropy
• Entanglement entropies of an interval for the massless scalar field in the presence of a boundary
• Primordial Gravitational Wave Circuit Complexity
• The refined quantum extremal surface prescription from the asymptotic equipartition property
• Entanglement Entropy in Scalar Quantum Electrodynamics
• Duality transformations and the entanglement entropy of gauge theories
• Symmetry Resolution in non-Lorentzian Field Theories
• Traversable AdS Wormhole via Non-local Double Trace or Janus Deformation
• Minimal surfaces in AdS C-metric
• Holographic Timelike Entanglement Entropy from Rindler Method
• Circuit Complexity in ${\mathcal{Z}}_2$ $\mathcal{EEF}\mathcal{T}$
• On shape dependence of holographic entanglement entropy in AdS4/CFT3 with Lifshitz scaling and hyperscaling violation
• Quantum computational complexity, Einstein's equations and accelerated expansion of the Universe
• Large-$d$ phase transitions in holographic mutual information
• What's the Point? Hole-ography in Poincare AdS
• NoRA: A Tensor Network Ansatz for Volume-Law Entangled Equilibrium States of Highly Connected Hamiltonians
• Holographic Entanglement Entropy in Boundary Quantum Field Theory
• Subsystem complexity after a local quantum quench
• Relation between time- and spacelike entanglement entropy
• Non-geometric States in a Holographic Conformal Field Theory
• A note on holographic subregion complexity and QCD phase transition
• Positive gravitational subsystem energies from CFT cone relative entropies
• The Aharonov-Bohm Effect on Entanglement Entropy in Conformal Field Theory
• A Flat Space Analogue for the Quantum Origin of Structure
• Operational islands and black hole dissipation in JT gravity
• Holographic Entanglement Entropy and Van der Waals transitions in Einstein-Maxwell-dilaton theory
• Determination of the entanglement entropy in elastic scattering using model-independent method for hadron femtoscopy
• Sum rule for the pseudo-Rényi entropy
• Complexity and uncomplexity during energy injection
• Holographic thermal entropy from geodesic bit threads
• Entropy Linear Response Theory with Non-Markovian Bath
• Extracting Hawking Radiation Near the Horizon of AdS Black Holes
• Holographic entropy production in a Bjorken expanding hot and dense strongly coupled quantum fluid
• $dS$ extremal surfaces, replicas, boundary Renyi entropies in $dS/CFT$ and time entanglement
• AdS/CFT Correspondence with a 3D Black Hole Simulator
• Topological invariants of the Ryu-Takayanagi ($RT$) surface used to observe holographic superconductor phase transition
• Horizon thermodynamics and cosmological equations: A holographic-like connection between thermostatistical quantities on a cosmological horizon and in the bulk
• Minimal Areas from Entangled Matrices
• Holographic networks for (1+1)-dimensional de Sitter spacetime
• Entanglement and non-locality in quantum protocols with identical particles
• Geometric quantum complexity of bosonic oscillator systems
• Subsystem entropy in 2d CFT and KdV ETH
• Pacman geometries and the Hayward term in JT gravity
• Entanglement structures from modified IR geometry
• Holographic Interpretation of Shannon Entropy of Coherence of Quantum Pure States
• Field Space Entanglement Entropy, Zero Modes and Lifshitz Models
• The multiple realizability of general relativity in quantum gravity
• From Quantum Relative Entropy to the Semiclassical Einstein Equations
• Holographic entanglement properties in the QCD phase diagram from EMD models
• Holographic n-partite Information in Hyperscaling Violating Geometry
• Holographic entanglement entropy of the double Wick rotated BTZ black hole
• Inverted c-functions in thermal states
• A falling magnetic monopole as a holographic local quench
• Complexity for link complement States in Chern Simons Theory
• Entanglement entropy on finitely ramified graphs
• N-level ghost-spins and entanglement
• Quantum Scalar Field Theory Based on the Extended Least Action Principle
• Outer entropy = Bartnik-Bray inner mass, and the gravitational ant conjecture
• More on Holographic Volumes, Entanglement, and Complexity
• Entanglement Entropy Inequalities in BCFT by Holography
• The Holographic Entanglement Entropy of Schwarzschild Black Holes
• Field equations and particle motion in covariant emergent gravity
• Holographic Mutual Information of Two Disjoint Spheres
• The Dynamics of Entropies at the Onset of Interactions
• Revisit the entanglement entropy with gravitational anomaly
• Squashed Entanglement from Generalized Rindler Wedge
• Upper bounds of holographic entanglement entropy growth rate for thermofield double states
• The Fermionic Entanglement Entropy of the Vacuum State of a Schwarzschild Black Hole Horizon
• Relative entropy close to the edge
• Left-Right Entanglement Entropy for a Dp-brane with Dynamics and Background Fields
• Entanglement entropy evolution during gravitational collapse
• Quantum Mechanics from Relational Properties, Part III: Path Integral Implementation
• Entanglement Entropy of $(2+1)$D Quantum Critical Points with Quenched Disorder: Dimensional Reduction Approach
• Schwarzschild Black Holes and Asymptotic $Ad{S}_2$
• Flavors of entanglement
• Holographic derivation of a class of short range correlation functions
• Holographic multipartite entanglement structures in IR modified geometries
• Finite complexity of the de Sitter vacuum
• Exploring uberholography
• Symmetry Resolved Entanglement Entropy in a Non-Abelian Fractional Quantum Hall State
• Spread of Entanglement in Non-Relativistic Theories
• Local geometry from entanglement entropy
• Entanglement entropies of an interval in the free Schrödinger field theory at finite density
• Cluster algebraic description of entanglement patterns for the BTZ black hole
• Entanglement entropy of two disjoint intervals and spin structures in interacting chains in and out of equilibrium
• The Area Term of the Entanglement Entropy of a Supersymmetric $O(N)$ Vector Model in Three Dimensions
• Holographic entanglement entropy for relativistic hydrodynamic flows
• Entanglement entropy, the Einstein equation and the Sparling construction
• Mutual information and holographic entanglement entropy for strongly-coupled R-charged plasmas
• Critical spin models from holographic disorder
• Lecture notes on strings in AdS${}_3$ from the worldsheet and the AdS${}_3$/CFT${}_2$ duality
• Volume-law entanglement fragmentation of quasiparticles
• QFT Entanglement Entropy, 2D Fermion and Gauge Fields
• Alternative Framework to Quantize Fermionic Fields
• Position dependence of the holographic entanglement entropy for an accelerating quark-antiquark pair
• String Scattering and Evolution of Ryu-Takayanagi Surface
• Entanglement Suppression Due to Black Hole Scattering