3d gravity from Virasoro TQFT: Holography, wormholes and knots

Abstract

We further develop the description of three-dimensional quantum gravity with negative cosmological constant in terms of Virasoro TQFT formulated in our previous paper arXiv:2304.13650. We compare the partition functions computed in the Virasoro TQFT formalism to the semiclassical evaluation of Euclidean gravity partition functions. This matching is highly non-trivial, but can be checked directly in some examples. We then showcase the formalism in action, by computing the gravity partition functions of many relevant topologies. For holographic applications, we focus on the partition functions of Euclidean multi-boundary wormholes with three-punctured spheres as boundaries. This precisely quantifies the higher moments of the structure constants in the proposed ensemble boundary dual and subjects the proposal to thorough checks. Finally, we investigate in detail the example of the figure eight knot complement as a hyperbolic 3-manifold. We show that the Virasoro TQFT partition function is identical to the partition function computed in Teichmüller theory, thus giving strong evidence for the equivalence of these TQFTs. We also show how to produce a large class of manifolds via Dehn surgery on the figure eight knot.

arXiv comment54 pages

References in corpus (26)

• Anyons in an exactly solved model and beyond
• The Holographic Weyl anomaly
• Liouville Field Theory -- A decade after the revolution
• Solving the Schwarzian via the Conformal Bootstrap
• 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
• Random Statistics of OPE Coefficients and Euclidean Wormholes
• AdS${}_3$ gravity and random CFT
• The path integral of 3D gravity near extremality; or, JT gravity with defects as a matrix integral
• Liouville bootstrap via harmonic analysis on a noncompact quantum group
• A theory of reparameterizations for AdS${}_3$ gravity
• Semiclassical 3D gravity as an average of large-c CFTs
• The Volume Conjecture, Perturbative Knot Invariants, and Recursion Relations for Topological Strings
• A universal Schwarzian sector in two-dimensional conformal field theories
• Shockwave S-matrix from Schwarzian Quantum Mechanics
• Solving 3d Gravity with Virasoro TQFT
• The Virasoro Minimal String
• On the relation between quantum Liouville theory and the quantized Teichm"uller spaces
• Non-Gaussianities in the Statistical Distribution of Heavy OPE Coefficients and Wormholes
• Semi-classical Virasoro blocks: proof of exponentiation
• On Non-handlebody Instantons in 3D Gravity
• A principle of maximum ignorance for semiclassical gravity
• Toward random tensor networks and holographic codes in CFT
• Liouville Field Theory on an Unoriented Surface
• Notes on crossing transformations of Virasoro conformal blocks
• A parafermionic hypergeometric function and supersymmetric 6j-symbols

Cited by in corpus (14)

• A microscopic realization of dS${}_3$
• 3d Gravity as a random ensemble
• TQFT gravity and ensemble holography
• Global Symmetries, Code Ensembles, and Sums Over Geometries
• 3D $\mathcal{N}=1$ supergravity from Virasoro TQFT: Gravitational partition function and Out-of-time-order correlator
• Deriving the non-perturbative gravitational dual of quantum Liouville theory from BCFT operator algebra
• Wormholes with Ends of the World
• Anyon Condensation in Virasoro TQFT: Wormhole Factorization
• Space-time symmetry from the world-sheet
• Open-closed 3d gravity as a random ensemble
• 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
• Coarse-Grained Fixed-Point Tensor Networks and Holographic Reflected Entropy in 3D Gravity
• A universal sum over topologies in 3d gravity