Abstract
We study Jackiw-Teitelboim gravity with positive cosmological constant as a model for de Sitter quantum gravity. We focus on the quantum mechanics of the model at past and future infinity. There is a Hilbert space of asymptotic states and an infinite-time evolution operator between the far past and far future. This evolution is not unitary, although we find that it acts unitarily on a subspace up to non-perturbative corrections. These corrections come from processes which involve changes in the spatial topology, including the nucleation of baby universes. There is significant evidence that this 1+1 dimensional model is dual to a 0+0 dimensional matrix integral in the double-scaled limit. So the bulk quantum mechanics, including the Hilbert space and approximately unitary evolution, emerge from a classical integral. We find that this emergence is a robust consequence of the level repulsion of eigenvalues along with the double scaling limit, and so is rather universal in random matrix theory.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
J.M. Maldacena, The large N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [Adv. Theor. Math. Phys. 2 (1998) 231] [hep-th/9711200] [INSPIRE].
S. Kachru, R. Kallosh, A.D. Linde and S.P. Trivedi, de Sitter vacua in string theory, Phys. Rev. D 68 (2003) 046005 [hep-th/0301240] [INSPIRE].
S. Kachru and S.P. Trivedi, A comment on effective field theories of flux vacua, Fortsch. Phys. 67 (2019) 1800086 [arXiv:1808.08971] [INSPIRE].
M.A. Vasiliev, Consistent equation for interacting gauge fields of all spins in (3+1)-dimensions, Phys. Lett. B 243 (1990) 378 [INSPIRE].
M.A. Vasiliev, Higher spin gauge theories: Star product and AdS space, hep-th/9910096 [INSPIRE].
C.M. Hull, Timelike T duality, de Sitter space, large N gauge theories and topological field theory, JHEP 07 (1998) 021 [hep-th/9806146] [INSPIRE].
A. Strominger, The dS/CFT correspondence, JHEP 10 (2001) 034 [hep-th/0106113] [INSPIRE].
E. Witten, Quantum gravity in de Sitter space, in Strings 2001: International Conference, (2001) [hep-th/0106109] [INSPIRE].
M. Alishahiha, A. Karch, E. Silverstein and D. Tong, The dS/dS correspondence, AIP Conf. Proc. 743 (2004) 393 [hep-th/0407125] [INSPIRE].
D. Anninos, T. Hartman and A. Strominger, Higher Spin Realization of the dS/CFT Correspondence, Class. Quant. Grav. 34 (2017) 015009 [arXiv:1108.5735] [INSPIRE].
X. Dong, B. Horn, E. Silverstein and G. Torroba, Micromanaging de Sitter holography, Class. Quant. Grav. 27 (2010) 245020 [arXiv:1005.5403] [INSPIRE].
V. Gorbenko, E. Silverstein and G. Torroba, dS/dS and T\( \overline{T} \), JHEP 03 (2019) 085 [arXiv:1811.07965] [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].
A. Almheiri and J. Polchinski, Models of AdS2 backreaction and holography, JHEP 11 (2015) 014 [arXiv:1402.6334] [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].
S. Sachdev and J. Ye, Gapless spin fluid ground state in a random, quantum Heisenberg magnet, Phys. Rev. Lett. 70 (1993) 3339 [cond-mat/9212030] [INSPIRE].
A. Kitaev KITP strings seminar and Entanglement 2015 program http://online.kitp.ucsb.edu/online/entangled15/.
J. Maldacena, G.J. Turiaci and Z. Yang, Two dimensional Nearly de Sitter gravity, JHEP 01 (2021) 139 [arXiv:1904.01911] [INSPIRE].
J. Cotler, K. Jensen and A. Maloney, Low-dimensional de Sitter quantum gravity, JHEP 06 (2020) 048 [arXiv:1905.03780] [INSPIRE].
D. Anninos, D.A. Galante and D.M. Hofman, de Sitter horizons & holographic liquids, JHEP 07 (2019) 038 [arXiv:1811.08153] [INSPIRE].
P. Saad, S.H. Shenker and D. Stanford, JT gravity as a matrix integral, arXiv:1903.11115 [INSPIRE].
D. Stanford and E. Witten, Fermionic Localization of the Schwarzian Theory, JHEP 10 (2017) 008 [arXiv:1703.04612] [INSPIRE].
J.M. Maldacena and L. Maoz, Wormholes in AdS, JHEP 02 (2004) 053 [hep-th/0401024] [INSPIRE].
N. Arkani-Hamed, J. Orgera and J. Polchinski, Euclidean wormholes in string theory, JHEP 12 (2007) 018 [arXiv:0705.2768] [INSPIRE].
J. Lin, Entanglement entropy in Jackiw-Teitelboim Gravity, arXiv:1807.06575 [INSPIRE].
B. Eynard and N. Orantin, Invariants of algebraic curves and topological expansion, Commun. Num. Theor. Phys. 1 (2007) 347 [math-ph/0702045] [INSPIRE].
B. Eynard, T. Kimura and S. Ribault, Random matrices, arXiv:1510.04430 [INSPIRE].
E. Witten, Two-dimensional gravity and intersection theory on moduli space, Surveys Diff. Geom. 1 (1991) 243 [INSPIRE].
M. Kontsevich, Intersection theory on the moduli space of curves and the matrix Airy function, Commun. Math. Phys. 147 (1992) 1 [INSPIRE].
R. Dijkgraaf and E. Witten, Developments in Topological Gravity, Int. J. Mod. Phys. A 33 (2018) 1830029 [arXiv:1804.03275] [INSPIRE].
A. Altland and M.R. Zirnbauer, Nonstandard symmetry classes in mesoscopic normal-superconducting hybrid structures, Phys. Rev. B 55 (1997) 1142 [cond-mat/9602137] [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].
L.V. Iliesiu, On 2D gauge theories in Jackiw-Teitelboim gravity, arXiv:1909.05253 [INSPIRE].
J.A. Wheeler, Information, physics, quantum: The search for links, in Complexity, entropy, and the physics of information, CRC Press (1990).
J. Cotler and K. Jensen, A theory of reparameterizations for AdS3 gravity, JHEP 02 (2019) 079 [arXiv:1808.03263] [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].
P. Saad, Late Time Correlation Functions, Baby Universes, and ETH in JT Gravity, arXiv:1910.10311 [INSPIRE].
G. Barnich and C. Troessaert, Aspects of the BMS/CFT correspondence, JHEP 05 (2010) 062 [arXiv:1001.1541] [INSPIRE].
G. Barnich, A. Gomberoff and H.A. González, The flat limit of three dimensional asymptotically anti-de Sitter spacetimes, Phys. Rev. D 86 (2012) 024020 [arXiv:1204.3288] [INSPIRE].
G. Barnich, A. Gomberoff and H.A. González, Three-dimensional Bondi-Metzner-Sachs invariant two-dimensional field theories as the flat limit of Liouville theory, Phys. Rev. D 87 (2013) 124032 [arXiv:1210.0731] [INSPIRE].
A. Bagchi and R. Gopakumar, Non-relativistic AdS/CFT and the GCA, J. Phys. Conf. Ser. 462 (2013) 012017 [INSPIRE].
T. Andrade and D. Marolf, Asymptotic Symmetries from finite boxes, Class. Quant. Grav. 33 (2016) 015013 [arXiv:1508.02515] [INSPIRE].
B. Oblak, BMS Particles in Three Dimensions, Ph.D. Thesis, Brussels University, 2016. arXiv:1610.08526. https://doi.org/10.1007/978-3-319-61878-4 [INSPIRE].
G. Barnich, H.A. González and P. Salgado-ReboLledó, Geometric actions for three-dimensional gravity, Class. Quant. Grav. 35 (2018) 014003 [arXiv:1707.08887] [INSPIRE].
E. Hijano, Flat space physics from AdS/CFT, JHEP 07 (2019) 132 [arXiv:1905.02729] [INSPIRE].
J. Cotler and K. Jensen, forthcoming.
D. Anninos, F. Denef, R. Monten and Z. Sun, Higher Spin de Sitter Hilbert Space, JHEP 10 (2019) 071 [arXiv:1711.10037] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 1911.12358
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Cotler, J., Jensen, K. Emergent unitarity in de Sitter from matrix integrals. J. High Energ. Phys. 2021, 89 (2021). https://doi.org/10.1007/JHEP12(2021)089
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP12(2021)089