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Solving 3d Gravity with Virasoro TQFT
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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 Teichm\"uller 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.
Forward citations
Cited by 13 Pith papers
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On the Virasoro Crossing Kernels at Rational Central Charge
At rational central charge, the Virasoro crossing kernels decompose into two admissible square-root-branched kernels; the physical c≤1 kernels are derived for the first time.
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Elastic stiffness of three-dimensional black holes and wormholes from Liouville line defects
Shape and mass-density deformations of thin-shell AdS3 black holes and wormholes have stiffness kernels equal to two-point functions of defect-local displacement and mass-density operators, computed from linearized Li...
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Virasoro OPE and Conformal Blocks from the Inverse Shapovalov Form
A new explicit level-by-level series for four-point Virasoro conformal blocks on the sphere, with coefficients fixed by singular-vector weights, differing from Zamolodchikov recursion and AGT forms.
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Symmetry TFTs for Continuous Spacetime Symmetries
Continuous spacetime symmetries can be encoded in a (d+1)-dimensional BF/Chern-Simons topological field theory, whose boundary reproduces symmetry generators, symmetry breaking, and anomalies.
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A spool for every quotient: One-loop partition functions in AdS$_3$ gravity
One-loop partition functions of massive spinning fields on any smooth cusp-free hyperbolic 3-manifold are expressed as Wilson spools, sums over free loops of holonomy traces in lowest-weight sl(2,R) representations.
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A Holographic Map from AdS$_3$ to CFT$_2$
Semiclassical pure AdS3 gravity states, labelled by fixed-area geodesic networks, are mapped to CFT2 primary states whose wavefunctions are networks of OPE coefficients.
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Black Holes and Random Variables
High-energy CFT and black-hole interval counts are conjectured to obey the FHK extreme-value law; the resulting O(1) erratic fluctuations limit semiclassical AdS precision to e^{-S0}.
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The many facets of a hyperbolic tetrahedron: open and closed triangulations of 3d gravity
Open Virasoro TQFT equals fixed-length/angle 3d gravity path integrals on compact regions and yields the CTV–scalar Virasoro relation via open-closed duality.
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Microstate counting from defects in de Sitter
Counting defect microstates via Lorentzian wormholes reproduces the de Sitter and Schwarzschild-de Sitter entropy area laws.
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Triangulating quantum gravity in AdS$_3$
The fixed-angle gravitational path integral in AdS3 equals a Conformal Turaev-Viro partition function, the fixed-length path integral equals a Virasoro TQFT amplitude squared, and the semiclassical geometries are buil...
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Conformal Turaev-Viro Theory
Conformal Turaev-Viro theory is a triangulation-based dual to Virasoro TQFT whose partition function equals the modular S-transform of |Z_Vir|^2.
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It from ETH: Multi-interval Entanglement and Replica Wormholes from Large-$c$ BCFT Ensemble
The RT formula for entanglement in AdS3/CFT2, including phase transitions and multi-interval vacuum entropies, is derived from an assumed large-c ensemble of (B)CFT data, under the 'It from ETH' paradigm.
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Wilson Towers as Local Bulk Fields
A multi-winding Wilson loop in thermal AdS3 is re-expressed as a sum over single-winding Wilson loops, one per multi-trace primary, so a free bulk field becomes a tower of Wilson lines.
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