Abstract
We study the asymptotic dynamics of 3D gravity with Rindler boundary conditions both in flat and AdS spacetimes. We do this by using the angular quantization and Hamiltonian reduction of the action to the Wess-Zumino-Witten theory on the boundary. We then rewrite the boundary action as a functional of elements of the asymptotic symmetry group.
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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. B 126 (1983) 41 [INSPIRE].
A. Kitaev, A simple model of quantum holography. Part 2, talk given at the Entanglement in Strongly-Correlated Quantum Matter, Santa Barbara, CA, U.S.A., 6 April–2 July 2015, http://online.kitp.ucsb.edu/online/entangled15/kitaev2/.
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].
A. Almheiri and J. Polchinski, Models of AdS2 backreaction and holography, JHEP 11 (2015) 014 [arXiv:1402.6334] [INSPIRE].
J. Maldacena and D. Stanford, Remarks on the Sachdev-Ye-Kitaev model, Phys. Rev. D 94 (2016) 106002 [arXiv:1604.07818] [INSPIRE].
J. Maldacena, D. Stanford and Z. Yang, Conformal symmetry and its breaking in two dimensional Nearly Anti-de-Sitter space, Prog. Theor. Exp. Phys. 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. Jensen, Chaos in AdS2 Holography, Phys. Rev. Lett. 117 (2016) 111601 [arXiv:1605.06098] [INSPIRE].
C.G. Callan Jr., S.B. Giddings, J.A. Harvey and A. Strominger, Evanescent black holes, Phys. Rev. D 45 (1992) R1005(R) [hep-th/9111056] [INSPIRE].
D. Cangemi and R. Jackiw, Gauge invariant formulations of lineal gravity, Phys. Rev. Lett. 69 (1992) 233 [hep-th/9203056] [INSPIRE].
H. Afshar, H.A. González, D. Grumiller and D. Vassilevich, Flat space holography and the complex Sachdev-Ye-Kitaev model, Phys. Rev. D 101 (2020) 086024 [arXiv:1911.05739] [INSPIRE].
V. Godet and C. Marteau, New boundary conditions for AdS2, JHEP 12 (2020) 020 [arXiv:2005.08999] [INSPIRE].
H. Afshar, E. Esmaeili and H.R. Safari, Flat space holography in spin-2 extended dilaton-gravity, JHEP 07 (2021) 126 [arXiv:2012.15807] [INSPIRE].
V. Godet and C. Marteau, From black holes to baby universes in CGHS gravity, JHEP 07 (2021) 138 [arXiv:2103.13422] [INSPIRE].
H. Afshar and B. Oblak, Flat JT gravity and the BMS-Schwarzian, JHEP 11 (2022) 172 [arXiv:2112.14609] [INSPIRE].
H. Afshar and N. Aghamir, Holography in \( \textrm{C}\hat{\textrm{GH}}\textrm{S} \) supergravity, JHEP 03 (2023) 009 [arXiv:2211.00612] [INSPIRE].
H.R. Afshar, Warped Schwarzian theory, JHEP 02 (2020) 126 [arXiv:1908.08089] [INSPIRE].
H. Afshar, S. Detournay, D. Grumiller and B. Oblak, Near-Horizon Geometry and Warped Conformal Symmetry, JHEP 03 (2016) 187 [arXiv:1512.08233] [INSPIRE].
E. Witten, (2 + 1)-Dimensional Gravity as an Exactly Soluble System, Nucl. Phys. B 311 (1988) 46 [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, Three-Dimensional Gravity Revisited, arXiv:0706.3359 [INSPIRE].
E. Witten, Quantum Field Theory and the Jones Polynomial, Commun. Math. Phys. 121 (1989) 351 [INSPIRE].
G.W. Moore and N. Seiberg, Taming the Conformal Zoo, Phys. Lett. B 220 (1989) 422 [INSPIRE].
P. Salomonson, B.S. Skagerstam and A. Stern, ISO(2, 1) Chiral Models and Quantum Gravity in (2 + 1)-dimensions, Nucl. Phys. B 347 (1990) 769 [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].
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].
G. Barnich and H.A. González, Dual dynamics of three dimensional asymptotically flat Einstein gravity at null infinity, JHEP 05 (2013) 016 [arXiv:1303.1075] [INSPIRE].
P. Forgacs, A. Wipf, J. Balog, L. Feher and L. O’Raifeartaigh, Liouville and Toda Theories as Conformally Reduced WZNW Theories, Phys. Lett. B 227 (1989) 214 [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].
M. Bershadsky and H. Ooguri, Hidden SL(n) Symmetry in Conformal Field Theories, Commun. Math. Phys. 126 (1989) 49 [INSPIRE].
J. Cotler and K. Jensen, A theory of reparameterizations for AdS3 gravity, JHEP 02 (2019) 079 [arXiv:1808.03263] [INSPIRE].
G. Barnich, H.A. González and P. Salgado-Rebolledo, Geometric actions for three-dimensional gravity, Class. Quant. Grav. 35 (2018) 014003 [arXiv:1707.08887] [INSPIRE].
T.G. Mertens, The Schwarzian theory — origins, JHEP 05 (2018) 036 [arXiv:1801.09605] [INSPIRE].
E. Witten, Coadjoint Orbits of the Virasoro Group, Commun. Math. Phys. 114 (1988) 1 [INSPIRE].
D.M. Hofman and A. Strominger, Chiral Scale and Conformal Invariance in 2D Quantum Field Theory, Phys. Rev. Lett. 107 (2011) 161601 [arXiv:1107.2917] [INSPIRE].
S. Detournay, T. Hartman and D.M. Hofman, Warped Conformal Field Theory, Phys. Rev. D 86 (2012) 124018 [arXiv:1210.0539] [INSPIRE].
A. Aggarwal, A. Castro and S. Detournay, Warped Symmetries of the Kerr Black Hole, JHEP 01 (2020) 016 [arXiv:1909.03137] [INSPIRE].
A. Aggarwal, A. Castro, S. Detournay and B. Mühlmann, Near-extremal limits of warped CFTs, SciPost Phys. 15 (2023) 056 [arXiv:2211.03770] [INSPIRE].
A. Aggarwal, A. Castro, S. Detournay and B. Mühlmann, Near-extremal limits of warped black holes, SciPost Phys. 15 (2023) 083 [arXiv:2304.10102] [INSPIRE].
S. Detournay, T. Smoes and R. Wutte, Boundary conditions for extremal black holes from 2d gravity, SciPost Phys. 16 (2024) 141 [arXiv:2312.08353] [INSPIRE].
G. Compère, W. Song and A. Strominger, New Boundary Conditions for AdS3, JHEP 05 (2013) 152 [arXiv:1303.2662] [INSPIRE].
G. Compère, W. Song and A. Strominger, Chiral Liouville Gravity, JHEP 05 (2013) 154 [arXiv:1303.2660] [INSPIRE].
C. Troessaert, Enhanced asymptotic symmetry algebra of AdS3, JHEP 08 (2013) 044 [arXiv:1303.3296] [INSPIRE].
G. Barnich, H. González and B. Oblak, The dual theory of AdS3 gravity with free boundary conditions, (2014).
G. Barnich and G. Compère, Classical central extension for asymptotic symmetries at null infinity in three spacetime dimensions, Class. Quant. Grav. 24 (2007) F15 [gr-qc/0610130] [INSPIRE].
W. Melton, F. Niewinski, A. Strominger and T. Wang, Hyperbolic Vacua in Minkowski Space, arXiv:2310.13663 [INSPIRE].
L. Donnay, G. Giribet, H.A. González and M. Pino, Supertranslations and Superrotations at the Black Hole Horizon, Phys. Rev. Lett. 116 (2016) 091101 [arXiv:1511.08687] [INSPIRE].
H. Afshar, D. Grumiller, W. Merbis, A. Perez, D. Tempo and R. Troncoso, Soft hairy horizons in three spacetime dimensions, Phys. Rev. D 95 (2017) 106005 [arXiv:1611.09783] [INSPIRE].
H. Afshar, D. Grumiller and M.M. Sheikh-Jabbari, Near horizon soft hair as microstates of three dimensional black holes, Phys. Rev. D 96 (2017) 084032 [arXiv:1607.00009] [INSPIRE].
L. Donnay, Asymptotic dynamics of three-dimensional gravity, PoS Modave2015 (2016) 001 [arXiv:1602.09021] [INSPIRE].
D. Grumiller and W. Merbis, Near horizon dynamics of three dimensional black holes, SciPost Phys. 8 (2020) 010 [arXiv:1906.10694] [INSPIRE].
D. Harlow and D. Jafferis, The Factorization Problem in Jackiw-Teitelboim Gravity, JHEP 02 (2020) 177 [arXiv:1804.01081] [INSPIRE].
J. Cotler and K. Jensen, AdS3 gravity and random CFT, JHEP 04 (2021) 033 [arXiv:2006.08648] [INSPIRE].
M. Henneaux, W. Merbis and A. Ranjbar, Asymptotic dynamics of AdS3 gravity with two asymptotic regions, JHEP 03 (2020) 064 [arXiv:1912.09465] [INSPIRE].
S. Carlip, The Statistical mechanics of the (2 + 1)-dimensional black hole, Phys. Rev. D 51 (1995) 632 [gr-qc/9409052] [INSPIRE].
A.P. Balachandran, L. Chandar and A. Momen, Edge states in gravity and black hole physics, Nucl. Phys. B 461 (1996) 581 [gr-qc/9412019] [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. Banados and F. Mendez, A Note on covariant action integrals in three-dimensions, Phys. Rev. D 58 (1998) 104014 [hep-th/9806065] [INSPIRE].
M. Banados, R. Canto and S. Theisen, The Action for higher spin black holes in three dimensions, JHEP 07 (2012) 147 [arXiv:1204.5105] [INSPIRE].
D.P. Zelobenko, Compact Lie groups and their representations, American Mathematical Society Providence (1973) (English translation).
W. Merbis and M. Riegler, Geometric actions and flat space holography, JHEP 02 (2020) 125 [arXiv:1912.08207] [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].
M. Gutperle and P. Kraus, Higher Spin Black Holes, JHEP 05 (2011) 022 [arXiv:1103.4304] [INSPIRE].
M. Ammon, M. Gutperle, P. Kraus and E. Perlmutter, Spacetime Geometry in Higher Spin Gravity, JHEP 10 (2011) 053 [arXiv:1106.4788] [INSPIRE].
P. Kraus and E. Perlmutter, Partition functions of higher spin black holes and their CFT duals, JHEP 11 (2011) 061 [arXiv:1108.2567] [INSPIRE].
C. Bunster, M. Henneaux, A. Perez, D. Tempo and R. Troncoso, Generalized Black Holes in Three-dimensional Spacetime, JHEP 05 (2014) 031 [arXiv:1404.3305] [INSPIRE].
A. Castro, R. Gopakumar, M. Gutperle and J. Raeymaekers, Conical Defects in Higher Spin Theories, JHEP 02 (2012) 096 [arXiv:1111.3381] [INSPIRE].
R. Laflamme, Entropy of a Rindler Wedge, Phys. Lett. B 196 (1987) 449 [INSPIRE].
P. Saad, S.H. Shenker and D. Stanford, JT gravity as a matrix integral, arXiv:1903.11115 [INSPIRE].
J.-M. Schlenker and E. Witten, No ensemble averaging below the black hole threshold, JHEP 07 (2022) 143 [arXiv:2202.01372] [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].
A. Achucarro and M.E. Ortiz, Relating black holes in two-dimensions and three-dimensions, Phys. Rev. D 48 (1993) 3600 [hep-th/9304068] [INSPIRE].
Acknowledgments
We thank the anonymous referee for his/her valuable comments. We thank Daniel Grumiller for his comments on the draft. NA would like to thank Monica Guica, Pavel Putrov and Cumrun Vafa for discussions on general aspects of holography and the Hamiltonian reduction in 3D gravity during her participation in the Spring School on Superstring Theory and Related Topics 2023, the New Pathways in Exploration of Quantum Field Theory 2023, and Quantum Gravity beyond Supersymmetry III and String-Math 2024 at ICTP. She also appreciates the Abdus Salam International Centre for Theoretical Physics (ICTP) for providing financial support throughout her stay. This research was supported by the Iran National Science Foundation (INSF), project No. 4000132.
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Afshar, H., Aghamir, N. The near horizon dynamics in three-dimensional Einstein gravity. J. High Energ. Phys. 2024, 99 (2024). https://doi.org/10.1007/JHEP08(2024)099
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DOI: https://doi.org/10.1007/JHEP08(2024)099