Abstract
We study aspects of Jackiw-Teitelboim (JT) quantum gravity in two-dimensional nearly de Sitter (dS) spacetime, as well as pure de Sitter quantum gravity in three dimensions. These are each theories of boundary modes, which include a reparameterization field on each connected component of the boundary as well as topological degrees of freedom. In two dimensions, the boundary theory is closely related to the Schwarzian path integral, and in three dimensions to the quantization of coadjoint orbits of the Virasoro group. Using these boundary theories we compute loop corrections to the wavefunction of the universe, and investigate gravitational contributions to scattering.
Along the way, we show that JT gravity in dS2 is an analytic continuation of JT gravity in Euclidean AdS2, and that pure gravity in dS3 is a continuation of pure gravity in Euclidean AdS3. We define a genus expansion for de Sitter JT gravity by summing over higher genus generalizations of surfaces used in the Hartle-Hawking construction. Assuming a conjecture regarding the volumes of moduli spaces of such surfaces, we find that the de Sitter genus expansion is the continuation of the recently discovered AdS genus expansion. Then both may be understood as coming from the genus expansion of the same double-scaled matrix model, which would provide a non-perturbative completion of de Sitter JT gravity.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
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. 126B (1983) 41 [INSPIRE].
R. Jackiw, Gauge theories for gravity on a line, Theor. Math. Phys. 92 (1992) 979 [hep-th/9206093] [INSPIRE].
J.B. Hartle and S.W. Hawking, Wave Function of the Universe, Phys. Rev. D 28 (1983) 2960 [INSPIRE].
J. Maldacena, Vacuum decay into Anti de Sitter space, arXiv:1012.0274 [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: Proceedings, Strings 2001 Conference, Tata Institute of Fundamental Research, Mumbai, India, January 5–10, 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].
P. McFadden and K. Skenderis, Holography for Cosmology, Phys. Rev. D 81 (2010) 021301 [arXiv:0907.5542] [INSPIRE].
D. Harlow and D. Stanford, Operator Dictionaries and Wave Functions in AdS/CFT and dS/CFT, arXiv:1104.2621 [INSPIRE].
D. Anninos and F. Denef, Cosmic clustering, JHEP 06 (2016) 181 [arXiv:1111.6061] [INSPIRE].
A. Castro, N. Lashkari and A. Maloney, A de Sitter Farey Tail, Phys. Rev. D 83 (2011) 124027 [arXiv:1103.4620] [INSPIRE].
A. Castro and A. Maloney, The Wave Function of Quantum de Sitter, JHEP 11 (2012) 096 [arXiv:1209.5757] [INSPIRE].
T. Hertog and J. Hartle, Holographic No-Boundary Measure, JHEP 05 (2012) 095 [arXiv:1111.6090] [INSPIRE].
S. Banerjee et al., Topology of Future Infinity in dS/CFT, JHEP 11 (2013) 026 [arXiv:1306.6629] [INSPIRE].
D. Anninos, F. Denef and D. Harlow, Wave function of Vasiliev’s universe: A few slices thereof, Phys. Rev. D 88 (2013) 084049 [arXiv:1207.5517] [INSPIRE].
D. Anninos, F. Denef, G. Konstantinidis and E. Shaghoulian, Higher Spin de Sitter Holography from Functional Determinants, JHEP 02 (2014) 007 [arXiv:1305.6321] [INSPIRE].
D. Anninos and D.M. Hofman, Infrared Realization of dS2 in AdS2, Class. Quant. Grav. 35 (2018) 085003 [arXiv:1703.04622] [INSPIRE].
D. Anninos, D.A. Galante and D.M. Hofman, De Sitter Horizons & Holographic Liquids, JHEP 07 (2019) 038 [arXiv:1811.08153] [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].
P. Saad, S.H. Shenker and D. Stanford, JT gravity as a matrix integral, arXiv:1903.11115 [INSPIRE].
J. Maldacena, G.J. Turiaci and Z. Yang, Two dimensional Nearly de Sitter gravity, arXiv:1904.01911 [INSPIRE].
K. Jensen, S. Kachru, A. Karch, J. Polchinski and E. Silverstein, Towards a holographic marginal Fermi liquid, Phys. Rev. D 84 (2011) 126002 [arXiv:1105.1772] [INSPIRE].
J.M. Maldacena, J. Michelson and A. Strominger, Anti-de Sitter fragmentation, JHEP 02 (1999) 011 [hep-th/9812073] [INSPIRE].
S. Aretakis, Horizon Instability of Extremal Black Holes, Adv. Theor. Math. Phys. 19 (2015) 507 [arXiv:1206.6598] [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].
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].
S. Hadar, Near-extremal black holes at late times, backreacted, JHEP 01 (2019) 214 [arXiv:1811.01022] [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].
M. Cvetič and I. Papadimitriou, AdS2 holographic dictionary, JHEP 12 (2016) 008 [Erratum ibid. 01 (2017) 120] [arXiv:1608.07018] [INSPIRE].
K. Isler and C.A. Trugenberger, A Gauge Theory of Two-dimensional Quantum Gravity, Phys. Rev. Lett. 63 (1989) 834 [INSPIRE].
A.H. Chamseddine and D. Wyler, Gauge Theory of Topological Gravity in (1+1)-Dimensions, Phys. Lett. B 228 (1989) 75 [INSPIRE].
P. Saad, S.H. Shenker and D. Stanford, A semiclassical ramp in SYK and in gravity, arXiv:1806.06840 [INSPIRE].
J. Cotler and K. Jensen, A theory of reparameterizations for AdS3 gravity, JHEP 02 (2019) 079 [arXiv:1808.03263] [INSPIRE].
J. Kim and M. Porrati, On a Canonical Quantization of 3D Anti de Sitter Pure Gravity, JHEP 10 (2015) 096 [arXiv:1508.03638] [INSPIRE].
A. Alekseev and S.L. Shatashvili, Path Integral Quantization of the Coadjoint Orbits of the Virasoro Group and 2D Gravity, Nucl. Phys. B 323 (1989) 719 [INSPIRE].
B. Oblak, BMS Particles in Three Dimensions, Ph.D. thesis, Brussels U., 2016. arXiv:1610.08526 [DOI] [INSPIRE].
N.M.J. Woodhouse, Geometric quantization, Oxford University Press, (1997).
B. Khesin and R. Wendt, The geometry of infinite-dimensional groups, vol. 51, Springer Science & Business Media, (2008).
E. Witten, On quantum gauge theories in two-dimensions, Commun. Math. Phys. 141 (1991) 153 [INSPIRE].
E. Witten, Coadjoint Orbits of the Virasoro Group, Commun. Math. Phys. 114 (1988) 1 [INSPIRE].
D. Stanford and E. Witten, Fermionic Localization of the Schwarzian Theory, JHEP 10 (2017) 008 [arXiv:1703.04612] [INSPIRE].
D. Bagrets, A. Altland and A. Kamenev, Sachdev-Ye-Kitaev model as Liouville quantum mechanics, Nucl. Phys. B 911 (2016) 191 [arXiv:1607.00694] [INSPIRE].
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].
M. Mariño, Chern-Simons theory, matrix models, and topological strings, vol. 131, Oxford University Press, (2005).
N. Do, Moduli spaces of hyperbolic surfaces and their Weil-Petersson volumes arXiv:1103.4674.
M. Mirzakhani, Simple geodesics and Weil-Petersson volumes of moduli spaces of bordered Riemann surfaces, Invent. Math. 167 (2007) 179.
M. Mirzakhani, Weil-Petersson volumes and intersection theory on the moduli space of curves, J. Am. Math. Soc. 20 (2007) 1.
N. Do and P. Norbury, Weil-Petersson volumes and cone surfaces, math/0603406.
S. Peow Tan, Y. Loi Wong and Y. Zhang, Generalizations of McShane’s identity to hyperbolic cone-surfaces, math/0404226.
T. Nakanishi and M. Naatanen, Areas of two-dimensional moduli spaces, Proc. Am. Math. Soc. 129 (2001) 3241.
B. Eynard, Topological expansion for the 1-Hermitian matrix model correlation functions, JHEP 11 (2004) 031 [hep-th/0407261] [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 and N. Orantin, Weil-Petersson volume of moduli spaces, Mirzakhani’s recursion and matrix models, arXiv:0705.3600 [INSPIRE].
A. Achucarro and P.K. Townsend, A Chern-Simons Action for Three-Dimensional anti-de Sitter Supergravity Theories, Phys. Lett. B 180 (1986) 89 [INSPIRE].
E. Witten, (2+1)-Dimensional Gravity as an Exactly Soluble System, Nucl. Phys. B 311 (1988) 46 [INSPIRE].
E. Witten, Three-Dimensional Gravity Revisited, arXiv:0706.3359 [INSPIRE].
F.M. Haehl and M. Rozali, Effective Field Theory for Chaotic CFTs, JHEP 10 (2018) 118 [arXiv:1808.02898] [INSPIRE].
E. Witten, Quantization of Chern-Simons Gauge Theory With Complex Gauge Group, Commun. Math. Phys. 137 (1991) 29 [INSPIRE].
E. Witten, Analytic Continuation Of Chern-Simons Theory, AMS/IP Stud. Adv. Math. 50 (2011) 347 [arXiv:1001.2933] [INSPIRE].
S. Gukov, M. Mariño and P. Putrov, Resurgence in complex Chern-Simons theory, arXiv:1605.07615 [INSPIRE].
M. Porrati and C. Yu, Kac-Moody and Virasoro Characters from the Perturbative Chern-Simons Path Integral, JHEP 05 (2019) 083 [arXiv:1903.05100] [INSPIRE].
T.P. Killingback, Quantization of SL(2, ℝ) Chern-Simons theory, Commun. Math. Phys. 145 (1992) 1 [INSPIRE].
H.L. Verlinde, Conformal Field Theory, 2-D Quantum Gravity and Quantization of Teichmüller Space, Nucl. Phys. B 337 (1990) 652 [INSPIRE].
A. Maloney, Geometric Microstates for the Three Dimensional Black Hole?, arXiv:1508.04079 [INSPIRE].
A. Castro, R. Gopakumar, M. Gutperle and J. Raeymaekers, Conical Defects in Higher Spin Theories, JHEP 02 (2012) 096 [arXiv:1111.3381] [INSPIRE].
J.D. Brown and M. Henneaux, Central Charges in the Canonical Realization of Asymptotic Symmetries: An Example from Three-Dimensional Gravity, Commun. Math. Phys. 104 (1986) 207 [INSPIRE].
M. Bañados, T. Brotz and M.E. Ortiz, Boundary dynamics and the statistical mechanics of the (2+1)-dimensional black hole, Nucl. Phys. B 545 (1999) 340 [hep-th/9802076] [INSPIRE].
S. Elitzur, G.W. Moore, A. Schwimmer and N. Seiberg, Remarks on the Canonical Quantization of the Chern-Simons-Witten Theory, Nucl. Phys. B 326 (1989) 108 [INSPIRE].
M.J. Bowick and S.G. Rajeev, The Holomorphic Geometry of Closed Bosonic String Theory and Diff S1/S1, Nucl. Phys. B 293 (1987) 348 [INSPIRE].
A. Castro, N. Lashkari and A. Maloney, Quantum Topologically Massive Gravity in de Sitter Space, JHEP 08 (2011) 040 [arXiv:1105.4733] [INSPIRE].
A. Maloney and E. Witten, Quantum Gravity Partition Functions in Three Dimensions, JHEP 02 (2010) 029 [arXiv:0712.0155] [INSPIRE].
S. Giombi, A. Maloney and X. Yin, One-loop Partition Functions of 3D Gravity, JHEP 08 (2008) 007 [arXiv:0804.1773] [INSPIRE].
D. Harlow and D. Jafferis, The Factorization Problem in Jackiw-Teitelboim Gravity, JHEP 02 (2020) 177 [arXiv:1804.01081] [INSPIRE].
A. Kitaev KITP strings seminar and Entanglement 2015 program, http://online.kitp.ucsb.edu/online/entangled15/.
J. Maldacena and D. Stanford, Remarks on the Sachdev-Ye-Kitaev model, Phys. Rev. D 94 (2016) 106002 [arXiv:1604.07818] [INSPIRE].
A. Kitaev and S.J. Suh, The soft mode in the Sachdev-Ye-Kitaev model and its gravity dual, JHEP 05 (2018) 183 [arXiv:1711.08467] [INSPIRE].
V. Balasubramanian and P. Kraus, A stress tensor for Anti-de Sitter gravity, Commun. Math. Phys. 208 (1999) 413 [hep-th/9902121] [INSPIRE].
G. Barnich, H.A. Gonzalez and P. Salgado-ReboLledó, Geometric actions for three-dimensional gravity, Class. Quant. Grav. 35 (2018) 014003 [arXiv:1707.08887] [INSPIRE].
O. Coussaert, M. Henneaux and P. van Driel, The asymptotic dynamics of three-dimensional Einstein gravity with a negative cosmological constant, Class. Quant. Grav. 12 (1995) 2961 [gr-qc/9506019] [INSPIRE].
H.L. Verlinde and E.P. Verlinde, Conformal Field Theory and Geometric Quantization, in Trieste School and Workshop on Superstrings Trieste, Italy, April 3–14, 1989, pp. 422–449.
D. Harlow, J. Maltz and E. Witten, Analytic Continuation of Liouville Theory, JHEP 12 (2011) 071 [arXiv:1108.4417] [INSPIRE].
L. Susskind, The Census taker’s hat, in Quantum Mechanics of Fundamental Systems: The Quest for Beauty and Simplicity, pp. 1–53. Springer, 2009, arXiv:0710.1129 [INSPIRE].
Y. Sekino and L. Susskind, Census Taking in the Hat: FRW/CFT Duality, Phys. Rev. D 80 (2009) 083531 [arXiv:0908.3844] [INSPIRE].
M. Van Raamsdonk, Building up spacetime with quantum entanglement, Gen. Rel. Grav. 42 (2010) 2323 [arXiv:1005.3035] [INSPIRE].
S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett. 96 (2006) 181602 [hep-th/0603001] [INSPIRE].
B. Czech, J.L. Karczmarek, F. Nogueira and M. Van Raamsdonk, The Gravity Dual of a Density Matrix, Class. Quant. Grav. 29 (2012) 155009 [arXiv:1204.1330] [INSPIRE].
J. Maldacena and L. Susskind, Cool horizons for entangled black holes, Fortsch. Phys. 61 (2013) 781 [arXiv:1306.0533] [INSPIRE].
T. Faulkner, A. Lewkowycz and J. Maldacena, Quantum corrections to holographic entanglement entropy, JHEP 11 (2013) 074 [arXiv:1307.2892] [INSPIRE].
N. Lashkari, M.B. McDermott and M. Van Raamsdonk, Gravitational dynamics from entanglement ‘thermodynamics’, JHEP 04 (2014) 195 [arXiv:1308.3716] [INSPIRE].
T. Faulkner, M. Guica, T. Hartman, R.C. Myers and M. Van Raamsdonk, Gravitation from Entanglement in Holographic CFTs, JHEP 03 (2014) 051 [arXiv:1312.7856] [INSPIRE].
A. Almheiri, X. Dong and D. Harlow, Bulk Locality and Quantum Error Correction in AdS/CFT, JHEP 04 (2015) 163 [arXiv:1411.7041] [INSPIRE].
D.L. Jafferis, A. Lewkowycz, J. Maldacena and S.J. Suh, Relative entropy equals bulk relative entropy, JHEP 06 (2016) 004 [arXiv:1512.06431] [INSPIRE].
X. Dong, D. Harlow and A.C. Wall, Reconstruction of Bulk Operators within the Entanglement Wedge in Gauge-Gravity Duality, Phys. Rev. Lett. 117 (2016) 021601 [arXiv:1601.05416] [INSPIRE].
P. Gao, D.L. Jafferis and A.C. Wall, Traversable Wormholes via a Double Trace Deformation, JHEP 12 (2017) 151 [arXiv:1608.05687] [INSPIRE].
V. Balasubramanian, J. de Boer and D. Minic, Notes on de Sitter space and holography, Class. Quant. Grav. 19 (2002) 5655 [hep-th/0207245] [INSPIRE].
J. de Boer, M.P. Heller, R.C. Myers and Y. Neiman, Holographic de Sitter Geometry from Entanglement in Conformal Field Theory, Phys. Rev. Lett. 116 (2016) 061602 [arXiv:1509.00113] [INSPIRE].
J. Cotler, C.-M. Jian, X.-L. Qi and F. Wilczek, Superdensity Operators for Spacetime Quantum Mechanics, JHEP 09 (2018) 093 [arXiv:1711.03119] [INSPIRE].
J. Cotler, X. Han, X.-L. Qi and Z. Yang, Quantum Causal Influence, JHEP 07 (2019) 042 [arXiv:1811.05485] [INSPIRE].
X. Dong, E. Silverstein and G. Torroba, de Sitter Holography and Entanglement Entropy, JHEP 07 (2018) 050 [arXiv:1804.08623] [INSPIRE].
A.L. Fitzpatrick, J. Kaplan and M.T. Walters, Universality of Long-Distance AdS Physics from the CFT Bootstrap, JHEP 08 (2014) 145 [arXiv:1403.6829] [INSPIRE].
A.L. Fitzpatrick, J. Kaplan and M.T. Walters, Virasoro Conformal Blocks and Thermality from Classical Background Fields, JHEP 11 (2015) 200 [arXiv:1501.05315] [INSPIRE].
E. Perlmutter, Virasoro conformal blocks in closed form, JHEP 08 (2015) 088 [arXiv:1502.07742] [INSPIRE].
A.L. Fitzpatrick and J. Kaplan, Conformal Blocks Beyond the Semi-Classical Limit, JHEP 05 (2016) 075 [arXiv:1512.03052] [INSPIRE].
M. Beccaria, A. Fachechi and G. Macorini, Virasoro vacuum block at next-to-leading order in the heavy-light limit, JHEP 02 (2016) 072 [arXiv:1511.05452] [INSPIRE].
H. Chen, A.L. Fitzpatrick, J. Kaplan, D. Li and J. Wang, Degenerate Operators and the 1/c Expansion: Lorentzian Resummations, High Order Computations and Super-Virasoro Blocks, JHEP 03 (2017) 167 [arXiv:1606.02659] [INSPIRE].
S. Collier, Y. Gobeil, H. Maxfield and E. Perlmutter, Quantum Regge Trajectories and the Virasoro Analytic Bootstrap, JHEP 05 (2019) 212 [arXiv:1811.05710] [INSPIRE].
A. Bhatta, P. Raman and N.V. Suryanarayana, Holographic Conformal Partial Waves as Gravitational Open Wilson Networks, JHEP 06 (2016) 119 [arXiv:1602.02962] [INSPIRE].
M. Beşken, A. Hegde, E. Hijano and P. Kraus, Holographic conformal blocks from interacting Wilson lines, JHEP 08 (2016) 099 [arXiv:1603.07317] [INSPIRE].
A.L. Fitzpatrick, J. Kaplan, D. Li and J. Wang, Exact Virasoro Blocks from Wilson Lines and Background-Independent Operators, JHEP 07 (2017) 092 [arXiv:1612.06385] [INSPIRE].
M. Beşken, A. Hegde and P. Kraus, Anomalous dimensions from quantum Wilson lines, arXiv:1702.06640 [INSPIRE].
Y. Hikida and T. Uetoko, Conformal blocks from Wilson lines with loop corrections, Phys. Rev. D 97 (2018) 086014 [arXiv:1801.08549] [INSPIRE].
M. Beşken, E. D’Hoker, A. Hegde and P. Kraus, Renormalization of gravitational Wilson lines, JHEP 06 (2019) 020 [arXiv:1810.00766] [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].
E.A. Bergshoeff, D.Z. Freedman, R. Kallosh and A. Van Proeyen, Pure de Sitter Supergravity, Phys. Rev. D 92 (2015) 085040 [Erratum ibid. D 93 (2016) 069901] [arXiv:1507.08264] [INSPIRE].
W. Fu, D. Gaiotto, J. Maldacena and S. Sachdev, Supersymmetric Sachdev-Ye-Kitaev models, Phys. Rev. D 95 (2017) 026009 [arXiv:1610.08917] [INSPIRE].
I. Bakas, Conformal Invariance, the KdV Equation and Coadjoint Orbits of the Virasoro Algebra, Nucl. Phys. B 302 (1988) 189 [INSPIRE].
H. Aratyn, E. Nissimov, S. Pacheva and S. Solomon, Superspace Actions on Coadjoint Orbits of Graded Infinite Dimensional Groups, Phys. Lett. B 234 (1990) 307 [INSPIRE].
G.W. Delius, P. van Nieuwenhuizen and V.G.J. Rodgers, The Method of Coadjoint Orbits: An Algorithm for the Construction of Invariant Actions, Int. J. Mod. Phys. A 5 (1990) 3943 [INSPIRE].
K. Krasnov, Holography and Riemann surfaces, Adv. Theor. Math. Phys. 4 (2000) 929 [hep-th/0005106] [INSPIRE].
D. Gaiotto and X. Yin, Genus two partition functions of extremal conformal field theories, JHEP 08 (2007) 029 [arXiv:0707.3437] [INSPIRE].
X. Yin, Partition Functions of Three-Dimensional Pure Gravity, Commun. Num. Theor. Phys. 2 (2008) 285 [arXiv:0710.2129] [INSPIRE].
K. Skenderis and B.C. van Rees, Holography and wormholes in 2+1 dimensions, Commun. Math. Phys. 301 (2011) 583 [arXiv:0912.2090] [INSPIRE].
T.G. Mertens, The Schwarzian theory — origins, JHEP 05 (2018) 036 [arXiv:1801.09605] [INSPIRE].
V.I. Arnold and B.A. Khesin, Topological methods in hydrodynamics, vol. 125, Springer Science & Business Media, (1999).
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
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: 1905.03780
Rights and permissions
This article is published under an open access license. Please check the 'Copyright Information' section either on this page or in the PDF for details of this license and what re-use is permitted. If your intended use exceeds what is permitted by the license or if you are unable to locate the licence and re-use information, please contact the Rights and Permissions team.
About this article
Cite this article
Cotler, J., Jensen, K. & Maloney, A. Low-dimensional de Sitter quantum gravity. J. High Energ. Phys. 2020, 48 (2020). https://doi.org/10.1007/JHEP06(2020)048
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP06(2020)048