Three-dimensional quantum geometry and black holes

Abstract

We review some aspects of three-dimensional quantum gravity with emphasis in the `CFT -> Geometry' map that follows from the Brown-Henneaux conformal algebra. The general solution to the classical equations of motion with anti-de Sitter boundary conditions is displayed. This solution is parametrized by two functions which become Virasoro operators after quantisation. A map from the space of states to the space of classical solutions is exhibited. Some recent proposals to understand the Bekenstein-Hawking entropy are reviewed in this context. The origin of the boundary degrees of freedom arising in 2+1 gravity is analysed in detail using a Hamiltonian Chern-Simons formalism.

39 pages, Latex, no figures. Invited talk at the Second Meeting "Trends in Theoretical Physics", held in Buenos Aires, December, 1998. v2: References added and minor corrections. v3: An incorrect statement about the sign of the Chern-Simons level erased. Extended (and in some cases modified) discussions in most sections. References added

Cited by in corpus (178)

• The Page curve of Hawking radiation from semiclassical geometry
• Liouville Action as Path-Integral Complexity: From Continuous Tensor Networks to AdS/CFT
• Entropy of three-dimensional asymptotically flat cosmological solutions
• Holographic Entanglement Entropy from 2d CFT: Heavy States and Local Quenches
• Quantum Computation as Gravity
• Quantum Gravity in 2+1 Dimensions: The Case of a Closed Universe
• $T\bar{T}$ and the mirage of a bulk cutoff
• Einstein's Equations from Varying Complexity
• Entanglement entropy in holographic moving mirror and Page curve
• Symplectic and Killing Symmetries of AdS${}_3$ Gravity: Holographic vs Boundary Gravitons
• Mutual information after a local quench in conformal field theory
• Complexity and the bulk volume, a new York time story
• Notes on the BMS group in three dimensions: II. Coadjoint representation
• Vacua of the gravitational field
• Quantum Information in Holographic Duality
• Black Hole Horizon Fluffs: Near Horizon Soft Hairs as Microstates of Three Dimensional Black Holes
• Stress tensor correlators in three-dimensional gravity
• Complexity measures from geometric actions on Virasoro and Kac-Moody orbits
• Holographic dual to charged SYK from 3D Gravity and Chern-Simons
• The (2+1)-dimensional gravastars
• Symmetry-Resolved Entanglement in AdS${}_3$/CFT${}_2$ coupled to $U(1)$ Chern-Simons Theory
• Two-dimensional fluids and their holographic duals
• Classical static final state of collapse with supertranslation memory
• Complexity change under conformal transformations in AdS${}_3$/CFT${}_2$
• An Exact Operator That Knows Its Location
• Newton-Hooke/Carrollian expansions of (A)dS and Chern-Simons gravity
• Energy Reflection and Transmission at 2D Holographic Interfaces
• Aspects of The First Law of Complexity
• A proposal for 3d quantum gravity and its bulk factorization
• CFT descriptions of bulk local states in the AdS black holes
• Charged Moments in $W_3$ Higher Spin Holography
• Geometric actions and flat space holography
• Subsystem eigenstate thermalization hypothesis for entanglement entropy in CFT
• Flat space (higher spin) gravity with chemical potentials
• WdW-patches in AdS${}_3$ and complexity change under conformal transformations II
• Holographic Lorentz and Carroll Frames
• AdS/BCFT with Brane-Localized Scalar Field
• Phases of Holographic Interfaces
• Comments on Thermalization in 2D CFT
• Brane Dynamics of Holographic BCFTs
• Near horizon dynamics of three dimensional black holes
• 3D Gravity in a Box
• Many-point classical conformal blocks and geodesic networks on the hyperbolic plane
• Wiggling Throat of Extremal Black Holes
• Extremal Rotating Black Holes in the Near-Horizon Limit: Phase Space and Symmetry Algebra
• Quantum Null Energy Condition and its (non)saturation in 2d CFTs
• $T\bar{T}$ in JT Gravity and BF Gauge Theory
• Bootstrapping holographic warped CFTs or: how I learned to stop worrying and tolerate negative norms
• Inside Out: Meet The Operators Inside The Horizon
• Local quantum energy conditions in non-Lorentz-invariant quantum field theories
• Exact Gravity Duals for Simple Quantum Circuits
• Cutoff Dependence and Complexity of the CFT${}_2$ Ground State
• Conserved Charges in Extended Theories of Gravity
• $T\bar{T}$-deformed conformal field theories out of equilibrium
• Quantization of conical spaces in 3D gravity
• Zoo of holographic moving mirrors
• Photons trajectories on a first order scale-dependent static BTZ black hole
• Entanglement and geometry from subalgebras of the Virasoro algebra
• Quantum information geometry of driven CFTs
• Quantizing higher-spin gravity in free-field variables
• Asymptotic dynamics of AdS${}_3$ gravity with two asymptotic regions
• Thermal transport in $T\bar{T}$-deformed conformal field theories: from integrability to holography
• Wilson Lines and Ishibashi States in AdS${}_3$/CFT${}_2$
• Glue-on AdS holography for $T\bar{T}$-deformed CFTs
• Root-$T\overline{T}$ Deformed Boundary Conditions in Holography
• Scrambling and Recovery of Quantum Information in Inhomogeneous Quenches in Two-dimensional Conformal Field Theories
• Interpolating Between Asymptotic and Near Horizon Symmetries
• Holographic torus correlators of stress tensor in $Ad{S}_3/CF{T}_2$
• The inside outs of AdS(3)/CFT(2): Exact AdS wormholes with entangled CFT duals
• The Sagnac effect on a scale-dependent rotating BTZ black hole background
• Note on ETH of descendant states in 2D CFT
• Steady States of Holographic Interfaces
• Scalar Blocks as Gravitational Wilson Networks
• Gluing AdS/CFT
• Semi-simple enlargement of the ${\mathfrak{bms}}_3$ algebra from a $\mathfrak{so}(2,2)\oplus \mathfrak{so}(2,1)$ Chern-Simons theory
• Liouville Quantum Gravity
• Asymptotic Symmetries of Maxwell Chern-Simons Gravity with Torsion
• Quantum thermodynamics of holographic quenches and bounds on the growth of entanglement from the QNEC
• On asymptotic charges in 3D gravity
• Berry phases, wormholes and factorization in AdS/CFT
• Holographic entanglement entropy in $T\overline{T}$-deformed AdS${}_3$
• Path Integral Complexity and Kasner singularities
• Complexity in a moving mirror model
• Chaos in Celestial CFT
• Cosmic footballs from superrotations
• Symmetries and Charges in Weyl-Fefferman-Graham Gauge
• The AdS${}_3$ Propagator and the Fate of Locality
• 4-d Chern-Simons Theory: Higher Gauge Symmetry and Holographic Aspects
• Entanglement negativity in $\text{T}\bar{\text{T}}$-deformed CFT${}_2$s
• Local quenches and quantum chaos from higher spin perturbations
• More on Wilson toroidal networks and torus blocks
• Multi-centered higher spin solutions from $W_N$ conformal blocks
• Virasoro Entanglement Berry Phases
• Erasure tolerant quantum memory and the quantum null energy condition in holographic systems
• Entwinement as a possible alternative to complexity
• $T\bar{T}/J\bar{T}$-deformed WZW models from Chern-Simons AdS${}_3$ gravity with mixed boundary conditions
• Islands and dynamics at the interface
• Surface charges in Chern-Simons gravity with $T\bar{T}$ deformation
• Reflected Entropy and Entanglement Negativity for Holographic Moving Mirrors
• QNEC2 in deformed holographic CFTs
• Hartle-Hawking state and its factorization in 3d gravity
• Bridging two quantum quench problems -- local joining quantum quench and Möbius quench -- and their holographic dual descriptions
• Holographic Dual of Conformal Field Theories with Very Special $T\bar{J}$ Deformations
• Wilson line networks in $p$-adic AdS/CFT
• Chiral Higher Spin Gravity
• Combing gravitational hair in 2+1 dimensions
• Twisted String Theory in Anti-de Sitter Space
• Exploring new Boundary Conditions for $\mathcal{N}=(1,1)$ Extended Higher Spin $Ad{S}_3$ Supergravity
• Higher-spin gauge theories in three spacetime dimensions
• Quantum Correction of the Wilson Line and Entanglement Entropy in the Pure AdS${}_3$ Einstein Gravity Theory
• On the entanglement contour of excited states in the holographic CFT
• New black hole solutions in three-dimensional $f(R)$ gravity
• On the universality of late-time correlators in semi-classical 2d CFTs
• Non-geometric States in a Holographic Conformal Field Theory
• Four-point conformal blocks with three heavy background operators
• Freelance Holography, Part II: Moving Boundary in Gauge/Gravity Correspondence
• Modular Hamiltonians and large diffeomorphisms in $Ad{S}_3$
• On-shell versus Off-shell Equivalence in 3D Gravity
• Symmetric space $\lambda$-model exchange algebra from 4d holomorphic Chern-Simons theory
• Holographic Reflected Entropy and Islands in Interface CFTs
• Black Flowers and Real Forms of Higher Spin Symmetries
• Holographic relations for OPE blocks in excited states
• $\mathcal{N}=(2,2)$ extended $\mathfrak{sl}(3|2)$ Chern-Simons $Ad{S}_3$ supergravity with new boundaries
• Odd entanglement entropy in $\text{T}\bar{\text{T}}$ deformed CFT${}_2$s and holography
• Embedding formalism for $(p,q)$ AdS superspaces in three dimensions
• Pure and Twisted Holography
• Towards Holographic Quantum Energy Teleportation
• Systematics of Boundary Actions in Gauge Theory and Gravity
• One-loop partition functions in $T\overline{T}$-deformed AdS${}_3$
• Banados and SUSY: On Supersymmetry and Minimal Surfaces of Locally AdS3 Geometries
• Vacuum block thermalization in semi-classical 2d CFT
• Entanglement entropy in inhomogeneous quenches in AdS${}_3$/CFT${}_2$
• Adiabatic analysis of the rotating BTZ black hole
• Warped Flatland
• Non-Einsteinian Black Holes in Generic 3D Gravity Theories
• The covariant action of higher spin black holes in three dimensions
• Asymptotic Symmetries of Three-Dimensional Black Strings
• On the Explicit Asymptotic ${\mathcal{W}}_5$ Symmetry of 3D Chern-Simons Higher Spin $Ad{S}_3$ Gravity
• Extreme Kerr black hole microstates with horizon fluff
• Holographic moving mirrors
• Collisions of massive particles, timelike thin shells and formation of black holes in three dimensions
• Nambu-Goto equation from three-dimensional gravity
• AdS${}_3$ Reconstruction with General Gravitational Dressings
• Fluctuating Ensemble Averages and the BTZ Threshold
• Near-extremal dynamics away from the horizon
• Negative R$\acute{\text{e}}$nyi entropy and Brane intersection
• Black hole solutions of three dimensional E${}_6$-gravity
• Phase space holography with no strings attached
• On the symmetry of $T\bar{T}$ deformed CFT
• Strings from 3D gravity: asymptotic dynamics of AdS${}_3$ gravity with free boundary conditions
• A Microscopic Model of Black Hole Evaporation in Two Dimensions
• Generalized Clausius inequalities and entanglement production in holographic two-dimensional CFTs
• Entanglement in conformal field theory and holography
• Schwarzian for colored Jackiw-Teitelboim gravity
• Root-$T\overline{T}$ deformed CFT partition functions at large central charge
• Entanglement Entropy with a Time-dependent Hamiltonian
• Three-dimensional $\mathrm{SL}(2,\mathbb{R})$ Yang-Mills theory is three-dimensional gravity with background sources
• Reconstructing bulk equation of motion using CFT modular Hamiltonians
• Two Splits, Three Ways: Advances in Double Splitting Quenches
• Information recovery from pure state geometries in 3D
• Holography for bulk states in 3D quantum gravity
• DC conductance and memory in 3D gravity
• Near-Horizon Extremal Geometries: Coadjoint Orbits and Quantization
• Large gravitons and near-horizon diffeomorphisms
• The chiral SYK model in three-dimensional holography
• Asymptotic structure of three-dimensional Maxwell Chern-Simons gravity coupled to spin-3 fields
• Hietarinta Chern-Simons supergravity and its asymptotic structure
• Entanglement Entropy and Conformal Collider Physics in 2D CFTs
• 1/c deformations of AdS${}_3$ boundary conditions and the Dym hierarchy
• Virasoro algebras, kinematic space and the spectrum of modular Hamiltonians in CFT${}_2$
• Quantum null energy condition in quenched 2d CFTs
• Notes on solution phase space and BTZ black hole
• The degrees of freedom of multiway junctions in three dimensional gravity
• Holographic Black Hole Formation and Scrambling in Time-Ordered Correlators
• On Acceleration in Three Dimensions
• Spacetime Bananas with EOW Branes and Spins
• Disorder in AdS${}_3$/CFT${}_2$
• Geodesics and Bending of Light around a BTZ Black Hole Surrounded by Quintessential Matter