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

Collier, Scott; Eberhardt, Lorenz; Zhang, Mengyang

doi:10.21468/SciPostPhys.17.5.134

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

Journal Article · Thu Nov 14 00:00:00 EST 2024 · SciPost Physics

DOI:https://doi.org/10.21468/SciPostPhys.17.5.134· OSTI ID:2477451

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We further develop the description of three-dimensional quantum gravity with negative cosmological constant in terms of Virasoro TQFT formulated in our previous paper [SciPost Phys. 15, 151 (2023)]. 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.

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Sponsoring Organization:: USDOE

Grant/Contract Number:: SC0009988; SC0012567; SC0021886

OSTI ID:: 2477451

Journal Information:: SciPost Physics, Journal Name: SciPost Physics Journal Issue: 5 Vol. 17; ISSN 2542-4653

Publisher:: Stichting SciPostCopyright Statement

Country of Publication:: Netherlands

Language:: English

References (52)

Conformal symmetry in two dimensions: An explicit recurrence formula for the conformal partial wave amplitude Zamolodchikov, Al. B. Communications in Mathematical Physics, Vol. 96, Issue 3 https://doi.org/10.1007/BF01214585	journal	September 1984
Classical and quantum conformal field theory Moore, Gregory; Seiberg, Nathan Communications in Mathematical Physics, Vol. 123, Issue 2 https://doi.org/10.1007/BF01238857	journal	June 1989
Mutation and volumes of knots inS 3 Ruberman, Daniel Inventiones Mathematicae, Vol. 90, Issue 1 https://doi.org/10.1007/BF01389038	journal	February 1987
Semi-classical Virasoro blocks: proof of exponentiation Beşken, Mert; Datta, Shouvik; Kraus, Per Journal of High Energy Physics, Vol. 2020, Issue 1 https://doi.org/10.1007/JHEP01(2020)109	journal	January 2020
The path integral of 3D gravity near extremality; or, JT gravity with defects as a matrix integral Maxfield, Henry; Turiaci, Gustavo J. Journal of High Energy Physics, Vol. 2021, Issue 1 https://doi.org/10.1007/JHEP01(2021)118	journal	January 2021
A theory of reparameterizations for AdS3 gravity Cotler, Jordan; Jensen, Kristan Journal of High Energy Physics, Vol. 2019, Issue 2 https://doi.org/10.1007/JHEP02(2019)079	journal	February 2019
A principle of maximum ignorance for semiclassical gravity de Boer, Jan; Liska, Diego; Post, Boris Journal of High Energy Physics, Vol. 2024, Issue 2 https://doi.org/10.1007/JHEP02(2024)003	journal	February 2024
Recursive representations of arbitrary Virasoro conformal blocks Cho, Minjae; Collier, Scott; Yin, Xi Journal of High Energy Physics, Vol. 2019, Issue 4 https://doi.org/10.1007/JHEP04(2019)018	journal	April 2019
AdS3 gravity and random CFT Cotler, Jordan; Jensen, Kristan Journal of High Energy Physics, Vol. 2021, Issue 4 https://doi.org/10.1007/JHEP04(2021)033	journal	April 2021
A universal Schwarzian sector in two-dimensional conformal field theories Ghosh, Animik; Maxfield, Henry; Turiaci, Gustavo J. Journal of High Energy Physics, Vol. 2020, Issue 5 https://doi.org/10.1007/JHEP05(2020)104	journal	May 2020
Toward random tensor networks and holographic codes in CFT Chandra, Jeevan; Hartman, Thomas Journal of High Energy Physics, Vol. 2023, Issue 5 https://doi.org/10.1007/JHEP05(2023)109	journal	May 2023
Non-Gaussianities in the statistical distribution of heavy OPE coefficients and wormholes Belin, Alexandre; de Boer, Jan; Liska, Diego Journal of High Energy Physics, Vol. 2022, Issue 6 https://doi.org/10.1007/JHEP06(2022)116	journal	June 2022
No ensemble averaging below the black hole threshold Schlenker, Jean-Marc; Witten, Edward Journal of High Energy Physics, Vol. 2022, Issue 7 https://doi.org/10.1007/JHEP07(2022)143	journal	July 2022
Solving the Schwarzian via the conformal bootstrap Mertens, Thomas G.; Turiaci, Gustavo J.; Verlinde, Herman L. Journal of High Energy Physics, Vol. 2017, Issue 8 https://doi.org/10.1007/JHEP08(2017)136	journal	August 2017
Pure gravity and conical defects Benjamin, Nathan; Collier, Scott; Maloney, Alexander Journal of High Energy Physics, Vol. 2020, Issue 9 https://doi.org/10.1007/JHEP09(2020)034	journal	September 2020
Approximate CFTs and random tensor models Belin, Alexandre; de Boer, Jan; Jafferis, Daniel L. Journal of High Energy Physics, Vol. 2024, Issue 9 https://doi.org/10.1007/JHEP09(2024)163	journal	September 2024
Shockwave S-matrix from Schwarzian quantum mechanics Lam, Ho Tat; Mertens, Thomas G.; Turiaci, Gustavo J. Journal of High Energy Physics, Vol. 2018, Issue 11 https://doi.org/10.1007/JHEP11(2018)182	journal	November 2018
Semiclassical 3D gravity as an average of large-c CFTs Chandra, Jeevan; Collier, Scott; Hartman, Thomas Journal of High Energy Physics, Vol. 2022, Issue 12 https://doi.org/10.1007/JHEP12(2022)069	journal	December 2022
AdS3/RMT2 duality Di Ubaldo, Gabriele; Perlmutter, Eric Journal of High Energy Physics, Vol. 2023, Issue 12 https://doi.org/10.1007/JHEP12(2023)179	journal	December 2023
Clebsch–Gordan and Racah–Wigner Coefficients for a Continuous Series of Representations of ?q (??(2, ℝ)) Ponsot, B.; Teschner, J. Communications in Mathematical Physics, Vol. 224, Issue 3 https://doi.org/10.1007/PL00005590	journal	December 2001
Holomorphic factorization of determinants of Laplacians on Riemann surfaces and a higher genus generalization of Kronecker’s first limit formula McIntyre, A.; Takhtajan, L. A. GAFA Geometric And Functional Analysis, Vol. 16, Issue 6 https://doi.org/10.1007/s00039-006-0582-7	journal	October 2006
A TQFT from Quantum Teichmüller Theory Andersen, Jørgen Ellegaard; Kashaev, Rinat Communications in Mathematical Physics, Vol. 330, Issue 3 https://doi.org/10.1007/s00220-014-2073-2	journal	June 2014
Off-shell Partition Functions in 3d Gravity Eberhardt, Lorenz Communications in Mathematical Physics, Vol. 405, Issue 3 https://doi.org/10.1007/s00220-024-04963-2	journal	March 2024
6j Symbols for the Modular Double, Quantum Hyperbolic Geometry, and Supersymmetric Gauge Theories Teschner, Jörg; Vartanov, Grigory Letters in Mathematical Physics, Vol. 104, Issue 5 https://doi.org/10.1007/s11005-014-0684-3	journal	February 2014
Volumes of hyperbolic three-manifolds Neumann, Walter D.; Zagier, Don Topology, Vol. 24, Issue 3 https://doi.org/10.1016/0040-9383(85)90004-7	journal	January 1985
On the systematics of open-string theories Bianchi, Massimo; Sagnotti, Augusto Physics Letters B, Vol. 247, Issue 4 https://doi.org/10.1016/0370-2693(90)91894-H	journal	September 1990
Infinite conformal symmetry in two-dimensional quantum field theory Belavin, A. A.; Polyakov, A. M.; Zamolodchikov, A. B. Nuclear Physics B, Vol. 241, Issue 2 https://doi.org/10.1016/0550-3213(84)90052-X	journal	July 1984
Loss of incoherence and determination of coupling constants in quantum gravity Giddings, Steven B.; Strominger, Andrew Nuclear Physics B, Vol. 307, Issue 4 https://doi.org/10.1016/0550-3213(88)90109-5	journal	October 1988
Black holes as red herrings: Topological fluctuations and the loss of quantum coherence Coleman, Sidney Nuclear Physics B, Vol. 307, Issue 4 https://doi.org/10.1016/0550-3213(88)90110-1	journal	October 1988
Axion-induced topology change in quantum gravity and string theory Giddings, Steven B.; Strominger, Andrew Nuclear Physics B, Vol. 306, Issue 4 https://doi.org/10.1016/0550-3213(88)90446-4	journal	September 1988
Anyons in an exactly solved model and beyond Kitaev, Alexei Annals of Physics, Vol. 321, Issue 1 https://doi.org/10.1016/j.aop.2005.10.005	journal	January 2006
The volume conjecture, perturbative knot invariants, and recursion relations for topological strings Dijkgraaf, Robbert; Fuji, Hiroyuki; Manabe, Masahide Nuclear Physics B, Vol. 849, Issue 1 https://doi.org/10.1016/j.nuclphysb.2011.03.014	journal	August 2011
A parafermionic hypergeometric function and supersymmetric 6j-symbols Apresyan, Elena; Sarkissian, Gor; Spiridonov, Vyacheslav P. Nuclear Physics B, Vol. 990 https://doi.org/10.1016/j.nuclphysb.2023.116170	journal	May 2023
:{unav) Kashaev, R. M. Letters in Mathematical Physics, Vol. 39, Issue 3, p. 269-275 https://doi.org/10.1023/A:1007364912784	journal	January 1997
On Uniformization of Riemann Surfaces and the Weil-Petersson Metric on TeichmÜLler and Schottky Spaces Zograf, P. G.; Takhtadzhyan, L. A. Mathematics of the USSR-Sbornik, Vol. 60, Issue 2 https://doi.org/10.1070/SM1988v060n02ABEH003170	journal	February 1988
The holographic Weyl anomaly Henningson, M.; Skenderis, K. Journal of High Energy Physics, Vol. 1998, Issue 07 https://doi.org/10.1088/1126-6708/1998/07/023	journal	July 1998
Liouville field theory on an unoriented surface Hikida, Yasuaki Journal of High Energy Physics, Vol. 2003, Issue 05 https://doi.org/10.1088/1126-6708/2003/05/002	journal	May 2003
One-loop partition functions of 3D gravity Giombi, Simone; Maloney, Alexander; Yin, Xi Journal of High Energy Physics, Vol. 2008, Issue 08 https://doi.org/10.1088/1126-6708/2008/08/007	journal	August 2008
On non-handlebody instantons in 3D gravity Yin, Xi Journal of High Energy Physics, Vol. 2008, Issue 09 https://doi.org/10.1088/1126-6708/2008/09/120	journal	September 2008
Random statistics of OPE coefficients and Euclidean wormholes Belin, Alexandre; de Boer, Jan Classical and Quantum Gravity, Vol. 38, Issue 16 https://doi.org/10.1088/1361-6382/ac1082	journal	July 2021
Jackiw-Teitelboim gravity with matter, generalized eigenstate thermalization hypothesis, and random matrices Jafferis, Daniel Louis; Kolchmeyer, David K.; Mukhametzhanov, Baur Physical Review D, Vol. 108, Issue 6 https://doi.org/10.1103/PhysRevD.108.066015	journal	September 2023
Liouville Field Theory: a Decade After the Revolution Nakayama, Yu International Journal of Modern Physics A, Vol. 19, Issue 17n18 https://doi.org/10.1142/S0217751X04019500	journal	July 2004
On the Relation Between Quantum Liouville Theory and the Quantized TeichmÜLler Spaces Teschner, J. International Journal of Modern Physics A, Vol. 19, Issue supp02 https://doi.org/10.1142/S0217751X04020579	journal	May 2004
Solving 3d gravity with Virasoro TQFT Collier, Scott; Eberhardt, Lorenz; Zhang, Mengyang SciPost Physics, Vol. 15, Issue 4 https://doi.org/10.21468/SciPostPhys.15.4.151	journal	October 2023
The Virasoro minimal string Collier, Scott; Eberhardt, Lorenz; Mühlmann, Beatrix SciPost Physics, Vol. 16, Issue 2 https://doi.org/10.21468/SciPostPhys.16.2.057	journal	February 2024
Holography and Riemann surfaces Krasnov, Kirill Advances in Theoretical and Mathematical Physics, Vol. 4, Issue 4 https://doi.org/10.4310/ATMP.2000.v4.n4.a5	journal	January 2000
Quantum Riemann surfaces in Chern-Simons theory Dimofte, Tudor Advances in Theoretical and Mathematical Physics, Vol. 17, Issue 3 https://doi.org/10.4310/ATMP.2013.v17.n3.a1	journal	January 2013
Supersymmetric gauge theories, quantization of $\mathcal{M}_{\mathrm{flat}}$, and conformal field theory Teschner, J.; Vartanov, G. S. Advances in Theoretical and Mathematical Physics, Vol. 19, Issue 1 https://doi.org/10.4310/ATMP.2015.v19.n1.a1	journal	January 2015
Partition functions of three-dimensional pure gravity Yin, Xi Communications in Number Theory and Physics, Vol. 2, Issue 2 https://doi.org/10.4310/CNTP.2008.v2.n2.a1	journal	January 2008
Exact results for perturbative Chern–Simons theory with complex gauge group Dimofte, Tudor; Gukov, Sergei; Lenells, Jonatan Communications in Number Theory and Physics, Vol. 3, Issue 2 https://doi.org/10.4310/CNTP.2009.v3.n2.a4	journal	January 2009
Notes on crossing transformations of Virasoro conformal blocks Eberhardt, Lorenz arXiv https://doi.org/10.48550/arXiv.2309.11540	preprint	January 2023
Liouville bootstrap via harmonic analysis on a noncompact quantum group Ponsot, B.; Teschner, J. arXiv https://doi.org/10.48550/arXiv.hep-th/9911110	preprint	January 1999

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