Solving 3d Gravity with Virasoro TQFT

Abstract

We propose a precise reformulation of 3d quantum gravity with negative cosmological constant in terms of a topological quantum field theory based on the quantization of the Teichmüller space of Riemann surfaces that we refer to as ``Virasoro TQFT.'' This TQFT is similar, but importantly not equivalent, to $\text{SL}(2,\mathbb{R})$ Chern-Simons theory. This sharpens the folklore that 3d gravity is related to $\text{SL}(2,\mathbb{R})$ Chern-Simons theory into a precise correspondence, and resolves some well-known issues with this lore at the quantum level. Our proposal is computationally very useful and provides a powerful tool for the further study of 3d gravity. In particular, we explain how together with standard TQFT surgery techniques this leads to a fully algorithmic procedure for the computation of the gravity partition function on a fixed topology exactly in the central charge. Mathematically, the relation leads to many nontrivial conjectures for hyperbolic 3-manifolds, Virasoro conformal blocks and crossing kernels.

arXiv comment72 pages

References in corpus (87)

• The Black Hole in Three Dimensional Space Time
• The Holographic Weyl anomaly
• Structure Constants and Conformal Bootstrap in Liouville Field Theory
• Black Holes and Random Matrices
• Quantum Gravity Partition Functions in Three Dimensions
• Asymptotic symmetries of three-dimensional gravity coupled to higher-spin fields
• Two and three-point functions in Liouville theory
• The asymptotic dynamics of three-dimensional Einstein gravity with a negative cosmological constant
• Three-Dimensional Gravity Revisited
• Universal Spectrum of 2d Conformal Field Theory in the Large c Limit
• Liouville theory revisited
• A Model of Three-Dimensional Lattice Gravity
• Analytic Continuation of Liouville Theory
• Three-Dimensional Quantum Gravity, Chern-Simons Theory, and the A-Polynomial
• Ponzano-Regge model revisited III: Feynman diagrams and Effective field theory
• Clebsch-Gordan and Racah-Wigner coefficients for a continuous series of representations of U_q(sl(2,R))
• One-loop Partition Functions of 3D Gravity
• Solvable Models of Quantum Black Holes: A Review on Jackiw-Teitelboim Gravity
• A Universal Inequality for CFT and Quantum Gravity
• Random Statistics of OPE Coefficients and Euclidean Wormholes
• Ponzano-Regge model revisited I: Gauge fixing, observables and interacting spinning particles
• Quantum Gravity in 2+1 Dimensions: The Case of a Closed Universe
• AdS${}_3$ gravity and random CFT
• Rolling Tachyons from Liouville theory
• The path integral of 3D gravity near extremality; or, JT gravity with defects as a matrix integral
• SL(2,R) Chern-Simons, Liouville, and Gauge Theory on Duality Walls
• Liouville bootstrap via harmonic analysis on a noncompact quantum group
• A theory of reparameterizations for AdS${}_3$ gravity
• Correlation functions in conformal Toda field theory I
• State sum constructions of spin-TFTs and string net constructions of fermionic phases of matter
• Boundary Liouville Field Theory: Boundary Three Point Function
• H(3)+ correlators from Liouville theory
• Poincare Series, 3D Gravity and CFT Spectroscopy
• Constraints on 2d CFT partition functions
• Semiclassical 3D gravity as an average of large-c CFTs
• Non-Perturbative Effects in Matrix Models and D-branes
• The Ponzano-Regge model
• An exact quantization of Jackiw-Teitelboim gravity
• Quantum Regge Trajectories and the Virasoro Analytic Bootstrap
• Lightcone Modular Bootstrap and Pure Gravity
• Random walks on the mapping class group
• Liouville theory with a central charge less than one
• Universal Dynamics of Heavy Operators in CFT${}_2$
• On the renormalized volume of hyperbolic 3-manifolds
• Minimal surfaces and particles in 3-manifolds
• Sphere Packing and Quantum Gravity
• Discrete and Continuum Approaches to Three-Dimensional Quantum Gravity
• Modular Invariance, Tauberian Theorems, and Microcanonical Entropy
• Light Cone Bootstrap in General 2D CFTs and Entanglement from Light Cone Singularity
• On the Three-point Function in Minimal Liouville Gravity
• Fine Structure of Jackiw-Teitelboim Quantum Gravity
• On canonical triangulations of once-punctured torus bundles and two-bridge link complements
• A de Sitter Farey Tail
• Holography in de Sitter Space via Chern-Simons Gauge Theory
• Bulk correlation functions in 2D quantum gravity
• Quantum three-dimensional de Sitter space
• Fast Conformal Bootstrap and Constraints on 3d Gravity
• On the relation between quantum Liouville theory and the quantized Teichm"uller spaces
• Ponzano-Regge model revisited II: Equivalence with Chern-Simons
• The minimal volume orientable hyperbolic 2-cusped 3-manifolds
• A proposal for 3d quantum gravity and its bulk factorization
• Non-Gaussianities in the Statistical Distribution of Heavy OPE Coefficients and Wormholes
• A conformal block Farey tail
• Rademacher Expansions and the Spectrum of 2d CFT
• Random Heegaard splittings
• Minimum-volume hyperbolic 3-manifolds
• Narain to Narnia
• Sphere and disk partition functions in Liouville and in matrix integrals
• Bootstrapping the Spectral Function: On the Uniqueness of Liouville and the Universality of BTZ
• Coupled minimal models revisited
• The Universal Phase Space of AdS3 Gravity
• Teichmuller TQFT vs Chern-Simons Theory
• Quantum Gravity on $d{S}_3$
• A new formulation of the Teichmüller TQFT
• Quantum Gravity from Timelike Liouville theory
• The universal Racah-Wigner symbol for Uq(osp(1|2))
• On the fusion matrix of the N=1 Neveu-Schwarz blocks
• JT gravity with matter, generalized ETH, and Random Matrices
• Braiding and fusion properties of the Neveu-Schwarz super-conformal blocks
• Geometric Microstates for the Three Dimensional Black Hole?
• The co-rank conjecture for 3-manifold groups
• On the relation between the modular double of U_q(sl(2,R)) and the quantum Teichmueller theory
• Resurgence, Conformal Blocks, and the Sum over Geometries in Quantum Gravity
• Liouville Quantum Gravity
• Gravitational Wilson Lines in 3D de Sitter
• Braiding properties of the N=1 super-conformal blocks (Ramond sector)
• Off-shell Partition Functions in 3d Gravity

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• The Virasoro Minimal String
• Quantum complexity in gravity, quantum field theory, and quantum information science
• A principle of maximum ignorance for semiclassical gravity
• 3d gravity from Virasoro TQFT: Holography, wormholes and knots
• Multiboundary wormholes and OPE statistics
• A microscopic realization of dS${}_3$
• A note on the bulk interpretation of the Quantum Extremal Surface formula
• 3d Gravity as a random ensemble
• Hartle-Hawking state and its factorization in 3d gravity
• TQFT gravity and ensemble holography
• Multipartite edge modes and tensor networks
• Asymptotic safety, quantum gravity, and the swampland: a conceptual assessment
• Global Symmetries, Code Ensembles, and Sums Over Geometries
• Black hole wavefunctions and microcanonical states
• 3D $\mathcal{N}=1$ supergravity from Virasoro TQFT: Gravitational partition function and Out-of-time-order correlator
• Wormholes with Ends of the World
• Quantum Groups as Global Symmetries
• Deriving the non-perturbative gravitational dual of quantum Liouville theory from BCFT operator algebra
• Nambu-Goto equation from three-dimensional gravity
• Ryu-Takayanagi Formula for Multi-Boundary Black Holes from 2D Large-$c$ CFT Ensemble
• Anyon Condensation in Virasoro TQFT: Wormhole Factorization
• S-move matrix in the NS sector of $N=1$ super Liouville field theory
• On the Virasoro fusion kernel at $c=25$
• Space-time symmetry from the world-sheet
• The chiral SYK model in three-dimensional holography
• Entanglement in Typical States of Chern-Simons Theory
• Open-closed 3d gravity as a random ensemble
• Notes on solution phase space and BTZ black hole
• Minimal Factorization of Chern-Simons Theory -- Gravitational Anyonic Edge Modes
• Lecture notes on strings in AdS${}_3$ from the worldsheet and the AdS${}_3$/CFT${}_2$ duality
• A spool for every quotient: One-loop partition functions in AdS${}_3$ gravity
• QFT Realization of Non-Unitary $\mathfrak{sl}(2,\mathbb{C})$ WRT Invariants and Their Galois Conjugations
• A universal sum over topologies in 3d gravity
• Coarse-Grained Fixed-Point Tensor Networks and Holographic Reflected Entropy in 3D Gravity