A solvable 3d quantum gravity model is defined by summing Virasoro TQFT copies over all topologies, shown to be dual to a 2d CFT ensemble and to exhibit semiclassical features such as cured negative density of states and Hawking-Page transition in the large-c limit.
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Quantum Gravity Partition Functions in Three Dimensions
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abstract
We consider pure three-dimensional quantum gravity with a negative cosmological constant. The sum of known contributions to the partition function from classical geometries can be computed exactly, including quantum corrections. However, the result is not physically sensible, and if the model does exist, there are some additional contributions. One possibility is that the theory may have long strings and a continuous spectrum. Another possibility is that complex geometries need to be included, possibly leading to a holomorphically factorized partition function. We analyze the subleading corrections to the Bekenstein-Hawking entropy and show that these can be correctly reproduced in such a holomorphically factorized theory. We also consider the Hawking-Page phase transition between a thermal gas and a black hole and show that it is a phase transition of Lee-Yang type, associated with a condensation of zeros in the complex temperature plane. Finally, we analyze pure three-dimensional supergravity, with similar results.
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hep-th 23representative citing papers
Non-orientable topological gravity produces a resummed topological expansion whose late-time behavior matches the GOE universality class of random matrix theory for time-reversal invariant chaotic systems.
The Hartle-Hawking state for toroidal quantum cosmologies is expressed in the Langlands decomposition as a sum over zeta zeros whose near-singularity dynamics follow the Hilbert-Pólya Hamiltonian and as a Möbius average of CFT partition functions.
Near-extremal BTZ and warped BTZ in TMG receive log-T corrections from Schwarzian and rotational zero modes whose full-geometry eigenvalues match the throat after non-normalizable eigenfunction corrections and BC specification.
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}.
Unitary QFTs are determined up to unitary isomorphism by closed-manifold partition functions; every reflection-positive partition function comes from a unitary QFT, so spatial wormholes do not break Hilbert-space factorization once the full charged spectrum is included.
Using worldline formalism and geometric quantization, the partition function for 3D gravity with matter on thermal AdS3 is computed via equivariant localization, reproducing the Wilson spool and conjecturing the all-orders result.
Proposes an SL(2,Z) sum of Kerr-lens geometries in 3d dS gravity whose spectral density is computed via crosscap amplitudes in CLS ⊗ CLS, matching semi-classical predictions and reducing in a simple case to GΣ ⊗ GΣ on the observer worldline.
Proposal that compact d-manifolds with elliptic data prepare boundary quantum states |J>, with Rényi entropies from path integrals agreeing with minimal-surface formulas after analytic continuation.
Symmetry reduction of 3D AdS Chern-Simons gravity on toroidal boundary yields two inequivalent 1D boundary theories: standard Schwarzian and affine-deformed Schwarzian with Kac-Moody extensions.
A Lorentzian path integral contour for charged AdS black holes selects a finite subset of complex saddles via Picard-Lefschetz theory, ensuring the semiclassical sum converges at finite β.
3d gravity on Σ_{g,n} × I with EOW branes equals the Virasoro minimal string random matrix model, with exact match for g=0 n=2 and inner-product formulation for negative Euler characteristic.
Introduces RMT surgery to relate off-shell 3D gravity partition functions to CFT spectral statistics via Euclidean wormholes with four-punctured sphere and trumpet boundaries.
The paper shows that Euclidean axion wormholes remain regular and stable in AdS3 for any mouth radius to AdS radius ratio and across topologies, with computable actions that can be included in the 3D gravitational path integral.
Inner horizon saddles supply the semiclassical correction -exp(A_inner/4G) to near-extremal black-hole entropy and motivate a spectral KSW criterion for well-defined one-loop effects around complex gravitational saddles.
Spinning states scaled with central charge cancel negative densities in 3D gravity, reinterpreted as bulk defects or overspinning BTZ quotients of AdS3 that preserve the gap but exhibit causal pathologies.
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.
One-loop partition function from boundary graviton zero modes in the near-horizon AdS2 x S1 geometry produces logarithmic corrections to the semiclassical entropy of near-extremal black holes in New Massive Gravity.
Finite cutoff in JT gravity causes faster ERB-length saturation, deformation-dependent baby-universe emission only under Lorentzian evolution, and possible one-cut universality corrections in the matrix dual.
The Zamolodchikov metric in Narain CFTs is realized using the Cartan matrix K_g and its inverse from finite-dimensional Lie algebras g.
From the de Sitter partition function in various approximations, the volume probability distribution concentrates around the classical value but shifts to favor smaller universes as quantum effects increase.
Applies Lindblad open quantum system methods to quantum-corrected 3d AdS black holes to analyze Page curve zig-zag, greybody factors, and Lyapunov exponents in Cotler-Jensen theory.
Lecture notes deliver a self-contained pedagogical overview of worldsheet strings in AdS3 with NSNS flux, summarizing 25 years of results with emphasis on spectrally flowed correlation functions.
citing papers explorer
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A solvable model of 3d quantum gravity
A solvable 3d quantum gravity model is defined by summing Virasoro TQFT copies over all topologies, shown to be dual to a 2d CFT ensemble and to exhibit semiclassical features such as cured negative density of states and Hawking-Page transition in the large-c limit.
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Mind the crosscap: $\tau$-scaling in non-orientable gravity and time-reversal-invariant systems
Non-orientable topological gravity produces a resummed topological expansion whose late-time behavior matches the GOE universality class of random matrix theory for time-reversal invariant chaotic systems.
-
M\"obius randomness in the Hartle-Hawking state
The Hartle-Hawking state for toroidal quantum cosmologies is expressed in the Langlands decomposition as a sum over zeta zeros whose near-singularity dynamics follow the Hilbert-Pólya Hamiltonian and as a Möbius average of CFT partition functions.
-
Quantum corrections to the near-extremal thermodynamics of (warped) BTZ black holes
Near-extremal BTZ and warped BTZ in TMG receive log-T corrections from Schwarzian and rotational zero modes whose full-geometry eigenvalues match the throat after non-normalizable eigenfunction corrections and BC specification.
-
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}.
-
Wormholes as red herrings: reflection positivity and the reconstruction of unitary quantum field theories
Unitary QFTs are determined up to unitary isomorphism by closed-manifold partition functions; every reflection-positive partition function comes from a unitary QFT, so spatial wormholes do not break Hilbert-space factorization once the full charged spectrum is included.
-
What's the Matter with 3D Gravity?
Using worldline formalism and geometric quantization, the partition function for 3D gravity with matter on thermal AdS3 is computed via equivariant localization, reproducing the Wilson spool and conjecturing the all-orders result.
-
An observer's quantization of 3d de Sitter
Proposes an SL(2,Z) sum of Kerr-lens geometries in 3d dS gravity whose spectral density is computed via crosscap amplitudes in CLS ⊗ CLS, matching semi-classical predictions and reducing in a simple case to GΣ ⊗ GΣ on the observer worldline.
-
Quantum State of a Gravitating Region
Proposal that compact d-manifolds with elliptic data prepare boundary quantum states |J>, with Rényi entropies from path integrals agreeing with minimal-surface formulas after analytic continuation.
-
Dimensional reduction of AdS3 Chern-Simons gravity: Schwarzian and affine boundary theories
Symmetry reduction of 3D AdS Chern-Simons gravity on toroidal boundary yields two inequivalent 1D boundary theories: standard Schwarzian and affine-deformed Schwarzian with Kac-Moody extensions.
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How to tame your (black hole) saddles: Lessons from the Lorentzian Gravitational Path Integral
A Lorentzian path integral contour for charged AdS black holes selects a finite subset of complex saddles via Picard-Lefschetz theory, ensuring the semiclassical sum converges at finite β.
-
On random matrix statistics of 3d gravity
3d gravity on Σ_{g,n} × I with EOW branes equals the Virasoro minimal string random matrix model, with exact match for g=0 n=2 and inner-product formulation for negative Euler characteristic.
-
Surgery and statistics in 3d gravity
Introduces RMT surgery to relate off-shell 3D gravity partition functions to CFT spectral statistics via Euclidean wormholes with four-punctured sphere and trumpet boundaries.
-
AdS3 axion wormholes as stable contributions to the Euclidean gravitational path integral
The paper shows that Euclidean axion wormholes remain regular and stable in AdS3 for any mouth radius to AdS radius ratio and across topologies, with computable actions that can be included in the 3D gravitational path integral.
-
Inner Horizon Saddles and a Spectral KSW Criterion
Inner horizon saddles supply the semiclassical correction -exp(A_inner/4G) to near-extremal black-hole entropy and motivate a spectral KSW criterion for well-defined one-loop effects around complex gravitational saddles.
-
Spinning States and Unitarity in 3D Gravity
Spinning states scaled with central charge cancel negative densities in 3D gravity, reinterpreted as bulk defects or overspinning BTZ quotients of AdS3 that preserve the gap but exhibit causal pathologies.
-
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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Logarithmic corrections to the entropy of near-extremal black holes in New Massive Gravity
One-loop partition function from boundary graviton zero modes in the near-horizon AdS2 x S1 geometry produces logarithmic corrections to the semiclassical entropy of near-extremal black holes in New Massive Gravity.
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Finite cutoff JT gravity: Baby universes, Matrix dual, and (Krylov) Complexity
Finite cutoff in JT gravity causes faster ERB-length saturation, deformation-dependent baby-universe emission only under Lorentzian evolution, and possible one-cut universality corrections in the matrix dual.
-
Algebraic Realisation of the Zamolodchikov Metric in Narain Theories
The Zamolodchikov metric in Narain CFTs is realized using the Cartan matrix K_g and its inverse from finite-dimensional Lie algebras g.
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Euclidean volume fluctuations in de Sitter quantum gravity
From the de Sitter partition function in various approximations, the volume probability distribution concentrates around the classical value but shifts to favor smaller universes as quantum effects increase.
-
Black holes with quantum corrections in $3d$: The case of Page curve in Lindblad, greybody factor, and Lyapunov exponent
Applies Lindblad open quantum system methods to quantum-corrected 3d AdS black holes to analyze Page curve zig-zag, greybody factors, and Lyapunov exponents in Cotler-Jensen theory.
-
Lecture notes on strings in AdS$_3$ from the worldsheet and the AdS$_3$/CFT$_2$ duality
Lecture notes deliver a self-contained pedagogical overview of worldsheet strings in AdS3 with NSNS flux, summarizing 25 years of results with emphasis on spectrally flowed correlation functions.