Abstract
We find models of two dimensional gravity that resolve the factorization puzzle and have a discrete spectrum, whilst retaining a semiclassical description. A novelty of these models is that they contain non-trivially correlated spacetime branes or, equivalently, nonlocal interactions in their action. Such nonlocal correlations are motivated in the low-energy gravity theory by integrating out UV degrees of freedom. Demanding factorization fixes almost all brane correlators, and the exact geometric expansion of the partition function collapses to only two terms: the black hole saddle and a subleading “half-wormhole” geometry, whose sum yields the desired discrete spectrum. By mapping the insertion of correlated branes to a certain double-trace deformation in the dual matrix integral, we show that factorization and discreteness also persist non-perturbatively. While in our model all wormholes completely cancel, they are still computationally relevant: self-averaging quantities, like the Page curve, computed in the original theory with wormholes, accurately approximate observables in our theory, which accounts for UV corrections. Our models emphasize the importance of correlations between different disconnected components of spacetime, providing a possible resolution to the factorization puzzle in any number of dimensions.
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References
G. ‘t Hooft, Dimensional reduction in quantum gravity, Conf. Proc. C 930308 (1993) 284 [gr-qc/9310026] [INSPIRE].
L. Susskind, The World as a hologram, J. Math. Phys. 36 (1995) 6377 [hep-th/9409089] [INSPIRE].
J.M. Maldacena, The Large N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [hep-th/9711200] [INSPIRE].
D.N. Page, Average entropy of a subsystem, Phys. Rev. Lett. 71 (1993) 1291 [gr-qc/9305007] [INSPIRE].
A. Almheiri, T. Hartman, J. Maldacena, E. Shaghoulian and A. Tajdini, Replica Wormholes and the Entropy of Hawking Radiation, JHEP 05 (2020) 013 [arXiv:1911.12333] [INSPIRE].
G. Penington, S.H. Shenker, D. Stanford and Z. Yang, Replica wormholes and the black hole interior, JHEP 03 (2022) 205 [arXiv:1911.11977] [INSPIRE].
A. Almheiri, T. Hartman, J. Maldacena, E. Shaghoulian and A. Tajdini, The entropy of Hawking radiation, Rev. Mod. Phys. 93 (2021) 035002 [arXiv:2006.06872] [INSPIRE].
J.M. Maldacena and L. Maoz, Wormholes in AdS, JHEP 02 (2004) 053 [hep-th/0401024] [INSPIRE].
L.V. Iliesiu, M. Kologlu and G.J. Turiaci, Supersymmetric indices factorize, arXiv:2107.09062 [INSPIRE].
A. Maloney and E. Witten, Quantum Gravity Partition Functions in Three Dimensions, JHEP 02 (2010) 029 [arXiv:0712.0155] [INSPIRE].
J. Cotler and K. Jensen, AdS3 gravity and random CFT, JHEP 04 (2021) 033 [arXiv:2006.08648] [INSPIRE].
H. Maxfield and G.J. Turiaci, The path integral of 3D gravity near extremality; or, JT gravity with defects as a matrix integral, JHEP 01 (2021) 118 [arXiv:2006.11317] [INSPIRE].
J.M. Maldacena, Eternal black holes in anti-de Sitter, JHEP 04 (2003) 021 [hep-th/0106112] [INSPIRE].
J.S. Cotler, G. Gur-Ari, M. Hanada, J. Polchinski, P. Saad, S.H. Shenker et al., Black Holes and Random Matrices, JHEP 05 (2017) 118 [Erratum ibid. 09 (2018) 002] [arXiv:1611.04650] [INSPIRE].
P. Saad, S.H. Shenker and D. Stanford, A semiclassical ramp in SYK and in gravity, arXiv:1806.06840 [INSPIRE].
P. Saad, Late Time Correlation Functions, Baby Universes, and ETH in JT Gravity, arXiv:1910.10311 [INSPIRE].
A. Blommaert, T.G. Mertens and H. Verschelde, Clocks and Rods in Jackiw-Teitelboim Quantum Gravity, JHEP 09 (2019) 060 [arXiv:1902.11194] [INSPIRE].
A. Blommaert, Dissecting the ensemble in JT gravity, arXiv:2006.13971 [INSPIRE].
P. Saad, S.H. Shenker and D. Stanford, JT gravity as a matrix integral, arXiv:1903.11115 [INSPIRE].
D. Marolf and H. Maxfield, Transcending the ensemble: baby universes, spacetime wormholes, and the order and disorder of black hole information, JHEP 08 (2020) 044 [arXiv:2002.08950] [INSPIRE].
D. Stanford, More quantum noise from wormholes, arXiv:2008.08570 [INSPIRE].
A. Blommaert, T.G. Mertens and H. Verschelde, Eigenbranes in Jackiw-Teitelboim gravity, JHEP 02 (2021) 168 [arXiv:1911.11603] [INSPIRE].
J. Pollack, M. Rozali, J. Sully and D. Wakeham, Eigenstate Thermalization and Disorder Averaging in Gravity, Phys. Rev. Lett. 125 (2020) 021601 [arXiv:2002.02971] [INSPIRE].
N. Afkhami-Jeddi, H. Cohn, T. Hartman and A. Tajdini, Free partition functions and an averaged holographic duality, JHEP 01 (2021) 130 [arXiv:2006.04839] [INSPIRE].
A. Maloney and E. Witten, Averaging over Narain moduli space, JHEP 10 (2020) 187 [arXiv:2006.04855] [INSPIRE].
A. Belin and J. de Boer, Random statistics of OPE coefficients and Euclidean wormholes, Class. Quant. Grav. 38 (2021) 164001 [arXiv:2006.05499] [INSPIRE].
T. Anous, J. Kruthoff and R. Mahajan, Density matrices in quantum gravity, SciPost Phys. 9 (2020) 045 [arXiv:2006.17000] [INSPIRE].
Y. Chen, V. Gorbenko and J. Maldacena, Bra-ket wormholes in gravitationally prepared states, JHEP 02 (2021) 009 [arXiv:2007.16091] [INSPIRE].
H. Liu and S. Vardhan, Entanglement entropies of equilibrated pure states in quantum many-body systems and gravity, PRX Quantum 2 (2021) 010344 [arXiv:2008.01089] [INSPIRE].
D. Marolf and J.E. Santos, AdS Euclidean wormholes, Class. Quant. Grav. 38 (2021) 224002 [arXiv:2101.08875] [INSPIRE].
V. Meruliya, S. Mukhi and P. Singh, Poincaré Series, 3d Gravity and Averages of Rational CFT, JHEP 04 (2021) 267 [arXiv:2102.03136] [INSPIRE].
S.B. Giddings and G.J. Turiaci, Wormhole calculus, replicas, and entropies, JHEP 09 (2020) 194 [arXiv:2004.02900] [INSPIRE].
D. Stanford and E. Witten, JT gravity and the ensembles of random matrix theory, Adv. Theor. Math. Phys. 24 (2020) 1475 [arXiv:1907.03363] [INSPIRE].
K. Okuyama and K. Sakai, JT gravity, KdV equations and macroscopic loop operators, JHEP 01 (2020) 156 [arXiv:1911.01659] [INSPIRE].
A. Belin, J. De Boer, P. Nayak and J. Sonner, Charged eigenstate thermalization, Euclidean wormholes and global symmetries in quantum gravity, SciPost Phys. 12 (2022) 059 [arXiv:2012.07875] [INSPIRE].
H. Verlinde, Deconstructing the Wormhole: Factorization, Entanglement and Decoherence, arXiv:2105.02142 [INSPIRE].
S. Collier and A. Maloney, Wormholes and spectral statistics in the Narain ensemble, JHEP 03 (2022) 004 [arXiv:2106.12760] [INSPIRE].
P. Betzios, E. Kiritsis and O. Papadoulaki, Interacting systems and wormholes, JHEP 02 (2022) 126 [arXiv:2110.14655] [INSPIRE].
A. Belin, J. de Boer and D. Liska, Non-Gaussianities in the statistical distribution of heavy OPE coefficients and wormholes, JHEP 06 (2022) 116 [arXiv:2110.14649] [INSPIRE].
P. Saad, S. Shenker and S. Yao, Comments on wormholes and factorization, arXiv:2107.13130 [INSPIRE].
A. Strominger and C. Vafa, Microscopic origin of the Bekenstein-Hawking entropy, Phys. Lett. B 379 (1996) 99 [hep-th/9601029] [INSPIRE].
L. Eberhardt, M.R. Gaberdiel and R. Gopakumar, The Worldsheet Dual of the Symmetric Product CFT, JHEP 04 (2019) 103 [arXiv:1812.01007] [INSPIRE].
L. Eberhardt, Partition functions of the tensionless string, JHEP 03 (2021) 176 [arXiv:2008.07533] [INSPIRE].
L. Eberhardt, Summing over Geometries in String Theory, JHEP 05 (2021) 233 [arXiv:2102.12355] [INSPIRE].
P. Saad, S.H. Shenker, D. Stanford and S. Yao, Wormholes without averaging, arXiv:2103.16754 [INSPIRE].
J. Maldacena and D. Stanford, Remarks on the Sachdev-Ye-Kitaev model, Phys. Rev. D 94 (2016) 106002 [arXiv:1604.07818] [INSPIRE].
A. Almheiri and B. Kang, Conformal Symmetry Breaking and Thermodynamics of Near-Extremal Black Holes, JHEP 10 (2016) 052 [arXiv:1606.04108] [INSPIRE].
P. Nayak, A. Shukla, R.M. Soni, S.P. Trivedi and V. Vishal, On the Dynamics of Near-Extremal Black Holes, JHEP 09 (2018) 048 [arXiv:1802.09547] [INSPIRE].
A. Castro, F. Larsen and I. Papadimitriou, 5D rotating black holes and the nAdS2/nCFT1 correspondence, JHEP 10 (2018) 042 [arXiv:1807.06988] [INSPIRE].
U. Moitra, S.K. Sake, S.P. Trivedi and V. Vishal, Jackiw-Teitelboim Gravity and Rotating Black Holes, JHEP 11 (2019) 047 [arXiv:1905.10378] [INSPIRE].
S. Sachdev, Universal low temperature theory of charged black holes with AdS2 horizons, J. Math. Phys. 60 (2019) 052303 [arXiv:1902.04078] [INSPIRE].
Z. Yang, The Quantum Gravity Dynamics of Near Extremal Black Holes, JHEP 05 (2019) 205 [arXiv:1809.08647] [INSPIRE].
L.V. Iliesiu and G.J. Turiaci, The statistical mechanics of near-extremal black holes, JHEP 05 (2021) 145 [arXiv:2003.02860] [INSPIRE].
M. Heydeman, L.V. Iliesiu, G.J. Turiaci and W. Zhao, The statistical mechanics of near-BPS black holes, J. Phys. A 55 (2022) 014004 [arXiv:2011.01953] [INSPIRE].
T.G. Mertens and G.J. Turiaci, Defects in Jackiw-Teitelboim Quantum Gravity, JHEP 08 (2019) 127 [arXiv:1904.05228] [INSPIRE].
E. Witten, Matrix Models and Deformations of JT Gravity, Proc. Roy. Soc. Lond. A 476 (2020) 20200582 [arXiv:2006.13414] [INSPIRE].
A. Blommaert and J. Kruthoff, Gravity without averaging, SciPost Phys. 12 (2022) 073 [arXiv:2107.02178] [INSPIRE].
P. Gao, D.L. Jafferis and D.K. Kolchmeyer, An effective matrix model for dynamical end of the world branes in Jackiw-Teitelboim gravity, JHEP 01 (2022) 038 [arXiv:2104.01184] [INSPIRE].
B. Mukhametzhanov, Factorization and complex couplings in SYK and in Matrix Models, arXiv:2110.06221 [INSPIRE].
R. Jackiw, Lower Dimensional Gravity, Nucl. Phys. B 252 (1985) 343 [INSPIRE].
C. Teitelboim, Gravitation and Hamiltonian Structure in Two Space-Time Dimensions, Phys. Lett. B 126 (1983) 41 [INSPIRE].
K. Jensen, Chaos in AdS2 Holography, Phys. Rev. Lett. 117 (2016) 111601 [arXiv:1605.06098] [INSPIRE].
J. Maldacena, D. Stanford and Z. Yang, Conformal symmetry and its breaking in two dimensional Nearly Anti-de-Sitter space, PTEP 2016 (2016) 12C104 [arXiv:1606.01857] [INSPIRE].
J. Engelsöy, T.G. Mertens and H. Verlinde, An investigation of AdS2 backreaction and holography, JHEP 07 (2016) 139 [arXiv:1606.03438] [INSPIRE].
R. Dijkgraaf and E. Witten, Developments in Topological Gravity, Int. J. Mod. Phys. A 33 (2018) 1830029 [arXiv:1804.03275] [INSPIRE].
M. Mirzakhani, Simple geodesics and Weil-Petersson volumes of moduli spaces of bordered Riemann surfaces, Invent. Math. 167 (2007) 179.
D. Stanford and E. Witten, Fermionic Localization of the Schwarzian Theory, JHEP 10 (2017) 008 [arXiv:1703.04612] [INSPIRE].
B. Eynard and N. Orantin, Weil-Petersson volume of moduli spaces, Mirzakhani’s recursion and matrix models, arXiv:0705.3600 [INSPIRE].
A. Goel, L.V. Iliesiu, J. Kruthoff and Z. Yang, Classifying boundary conditions in JT gravity: from energy-branes to α-branes, JHEP 04 (2021) 069 [arXiv:2010.12592] [INSPIRE].
J.M. Maldacena, G.W. Moore, N. Seiberg and D. Shih, Exact vs. semiclassical target space of the minimal string, JHEP 10 (2004) 020 [hep-th/0408039] [INSPIRE].
V. Fateev, A.B. Zamolodchikov and A.B. Zamolodchikov, Boundary Liouville field theory. I. Boundary state and boundary two point function, hep-th/0001012 [INSPIRE].
B. Ponsot and J. Teschner, Boundary Liouville field theory: Boundary three point function, Nucl. Phys. B 622 (2002) 309 [hep-th/0110244] [INSPIRE].
T.G. Mertens and G.J. Turiaci, Liouville quantum gravity — holography, JT and matrices, JHEP 01 (2021) 073 [arXiv:2006.07072] [INSPIRE].
T.G. Mertens, Degenerate operators in JT and Liouville (super)gravity, JHEP 04 (2021) 245 [arXiv:2007.00998] [INSPIRE].
K. Hosomichi, Minimal Open Strings, JHEP 06 (2008) 029 [arXiv:0804.4721] [INSPIRE].
I.K. Kostov, Boundary correlators in 2-D quantum gravity: Liouville versus discrete approach, Nucl. Phys. B 658 (2003) 397 [hep-th/0212194] [INSPIRE].
K. Okuyama and K. Sakai, FZZT branes in JT gravity and topological gravity, JHEP 09 (2021) 191 [arXiv:2108.03876] [INSPIRE].
J. Teschner, Remarks on Liouville theory with boundary, PoS tmr2000 (2000) 041 [hep-th/0009138] [INSPIRE].
E. Witten, Deformations of JT Gravity and Phase Transitions, arXiv:2006.03494 [INSPIRE].
A. Blommaert and M. Usatyuk, Microstructure in matrix elements, arXiv:2108.02210 [INSPIRE].
M.L. Mehta, Random matrices, Elsevier (2004) [ISBN: 9780120884094].
E. Brézin, C. Itzykson, G. Parisi and J.-B. Zuber, Planar diagrams, in The Large N Expansion In Quantum Field Theory And Statistical Physics: From Spin Systems to 2-Dimensional Gravity, World Scientific, Singapore (1993), pp. 567–583 [DOI].
A.A. Migdal, Loop Equations and 1/N Expansion, Phys. Rept. 102 (1983) 199 [INSPIRE].
R. Dijkgraaf and C. Vafa, Toda Theories, Matrix Models, Topological Strings, and N = 2 Gauge Systems, arXiv:0909.2453 [INSPIRE].
I. Dumitriu and A. Edelman, Eigenvalues of hermite and laguerre ensembles: large beta asymptotics, Ann. I. H. P. Probab. Stat. 41 (2005) 1083.
T.G. Mertens, G.J. Turiaci and H.L. Verlinde, Solving the Schwarzian via the Conformal Bootstrap, JHEP 08 (2017) 136 [arXiv:1705.08408] [INSPIRE].
T.G. Mertens, The Schwarzian theory — origins, JHEP 05 (2018) 036 [arXiv:1801.09605] [INSPIRE].
A. Kitaev and S.J. Suh, Statistical mechanics of a two-dimensional black hole, JHEP 05 (2019) 198 [arXiv:1808.07032] [INSPIRE].
A. Blommaert, T.G. Mertens and H. Verschelde, Fine Structure of Jackiw-Teitelboim Quantum Gravity, JHEP 09 (2019) 066 [arXiv:1812.00918] [INSPIRE].
L.V. Iliesiu, S.S. Pufu, H. Verlinde and Y. Wang, An exact quantization of Jackiw-Teitelboim gravity, JHEP 11 (2019) 091 [arXiv:1905.02726] [INSPIRE].
A. Blommaert, T.G. Mertens and H. Verschelde, The Schwarzian Theory — A Wilson Line Perspective, JHEP 12 (2018) 022 [arXiv:1806.07765] [INSPIRE].
L.V. Iliesiu, M. Mezei and G. Sárosi, The volume of the black hole interior at late times, JHEP 07 (2022) 073 [arXiv:2107.06286] [INSPIRE].
L. Susskind, Three Lectures on Complexity and Black Holes, SpringerBriefs in Physics, Springer, Berlin, Germany (2018), DOI [arXiv:1810.11563] [INSPIRE].
P.-S. Hsin, L.V. Iliesiu and Z. Yang, A violation of global symmetries from replica wormholes and the fate of black hole remnants, Class. Quant. Grav. 38 (2021) 194004 [arXiv:2011.09444] [INSPIRE].
S.B. Giddings and A. Strominger, Loss of Incoherence and Determination of Coupling Constants in Quantum Gravity, Nucl. Phys. B 307 (1988) 854 [INSPIRE].
S.R. Coleman, Black Holes as Red Herrings: Topological Fluctuations and the Loss of Quantum Coherence, Nucl. Phys. B 307 (1988) 867 [INSPIRE].
S.R. Das, A. Dhar, A.M. Sengupta and S.R. Wadia, New Critical Behavior in d = 0 Large N Matrix Models, Mod. Phys. Lett. A 5 (1990) 1041 [INSPIRE].
G.T. Horowitz and E. Silverstein, The Inside story: Quasilocal tachyons and black holes, Phys. Rev. D 73 (2006) 064016 [hep-th/0601032] [INSPIRE].
A. Adams, X. Liu, J. McGreevy, A. Saltman and E. Silverstein, Things fall apart: Topology change from winding tachyons, JHEP 10 (2005) 033 [hep-th/0502021] [INSPIRE].
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Blommaert, A., Iliesiu, L.V. & Kruthoff, J. Gravity factorized. J. High Energ. Phys. 2022, 80 (2022). https://doi.org/10.1007/JHEP09(2022)080
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DOI: https://doi.org/10.1007/JHEP09(2022)080