Abstract
We propose Lobachevsky boundary conditions that lead to asymptotically \( {{\mathbb{H}}^2}\times \mathbb{R} \) solutions. As an example we check their consistency in conformal Chern-Simons gravity. The canonical charges are quadratic in the fields, but nonetheless integrable, conserved and finite. The asymptotic symmetry algebra consists of one copy of the Virasoro algebra with central charge c = 24k, where k is the Chern-Simons level, and an affine û(1). We find also regular non-perturbative states and show that none of them corresponds to black hole solutions. We attempt to calculate the one-loop partition function, find a remarkable separation between bulk and boundary modes, but conclude that the one-loop partition function is ill-defined due to an infinite degeneracy. We comment on the most likely resolution of this degeneracy.
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References
G. ’t Hooft, Dimensional reduction in quantum gravity, in Salamfestschrift, World Scientific (1993) [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 [Int. J. Theor. Phys. 38 (1999) 1113] [hep-th/9711200] [INSPIRE].
D. Son, Toward an AdS/cold atoms correspondence: A Geometric realization of the Schrödinger symmetry, Phys. Rev. D 78 (2008) 046003 [arXiv:0804.3972] [INSPIRE].
K. Balasubramanian and J. McGreevy, Gravity duals for non-relativistic CFTs, Phys. Rev. Lett. 101 (2008) 061601 [arXiv:0804.4053] [INSPIRE].
A. Adams, K. Balasubramanian and J. McGreevy, Hot Spacetimes for Cold Atoms, JHEP 11 (2008) 059 [arXiv:0807.1111] [INSPIRE].
M. Guica, K. Skenderis, M. Taylor and B.C. van Rees, Holography for Schrödinger backgrounds, JHEP 02 (2011) 056 [arXiv:1008.1991] [INSPIRE].
S. Kachru, X. Liu and M. Mulligan, Gravity Duals of Lifshitz-like Fixed Points, Phys. Rev. D 78 (2008) 106005 [arXiv:0808.1725] [INSPIRE].
D. Anninos, W. Li, M. Padi, W. Song and A. Strominger, Warped AdS 3 Black Holes, JHEP 03 (2009) 130 [arXiv:0807.3040] [INSPIRE].
D. Anninos, M. Esole and M. Guica, Stability of warped AdS 3 vacua of topologically massive gravity, JHEP 10 (2009) 083 [arXiv:0905.2612] [INSPIRE].
G. Compere and S. Detournay, Boundary conditions for spacelike and timelike warped AdS 3 spaces in topologically massive gravity, JHEP 08 (2009) 092 [arXiv:0906.1243] [INSPIRE].
D. Anninos, T. Hartman and A. Strominger, Higher Spin Realization of the dS/CFT Correspondence, arXiv:1108.5735 [INSPIRE].
G. Barnich and G. Compere, Classical central extension for asymptotic symmetries at null infinity in three spacetime dimensions, Class. Quant. Grav. 24 (2007) F15 [gr-qc/0610130] [INSPIRE].
A. Bagchi, S. Detournay and D. Grumiller, Flat-Space Chiral Gravity, Phys. Rev. Lett. 109 (2012) 151301 [arXiv:1208.1658] [INSPIRE].
A. Strominger, AdS 2 quantum gravity and string theory, JHEP 01 (1999) 007 [hep-th/9809027] [INSPIRE].
A. Sen, State Operator Correspondence and Entanglement in AdS 2 /CF T 1, Entropy 13 (2011) 1305 [arXiv:1101.4254] [INSPIRE].
H. Afshar, B. Cvetkovic, S. Ertl, D. Grumiller and N. Johansson, Holograms of Conformal Chern-Simons Gravity, Phys. Rev. D 84 (2011) 041502 [arXiv:1106.6299] [INSPIRE].
H. Afshar, B. Cvetkovic, S. Ertl, D. Grumiller and N. Johansson, Conformal Chern-Simons holography — lock, stock and barrel, Phys. Rev. D 85 (2012) 064033 [arXiv:1110.5644] [INSPIRE].
S. Deser, R. Jackiw and S. Templeton, Three-Dimensional Massive Gauge Theories, Phys. Rev. Lett. 48 (1982) 975 [INSPIRE].
S. Deser, R. Jackiw and S. Templeton, Topologically Massive Gauge Theories, Annals Phys. 140 (1982) 372 [Erratum ibid. 185 (1988) 406] [INSPIRE].
S. Detournay, T. Hartman and D.M. Hofman, Warped Conformal Field Theory, Phys. Rev. D 86 (2012) 124018 [arXiv:1210.0539] [INSPIRE].
M. Bañados, C. Teitelboim and J. Zanelli, The Black hole in three-dimensional space-time, Phys. Rev. Lett. 69 (1992) 1849 [hep-th/9204099] [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].
J.R. David, M.R. Gaberdiel and R. Gopakumar, The Heat Kernel on AdS 3 and its Applications, JHEP 04 (2010) 125 [arXiv:0911.5085] [INSPIRE].
M.R. Gaberdiel, D. Grumiller and D. Vassilevich, Graviton 1-loop partition function for 3-dimensional massive gravity, JHEP 11 (2010) 094 [arXiv:1007.5189] [INSPIRE].
M. Bertin, D. Grumiller, D. Vassilevich and T. Zojer, Generalised massive gravity one-loop partition function and AdS/(L)CFT, JHEP 06 (2011) 111 [arXiv:1103.5468] [INSPIRE].
D. Vassilevich, One loop quantum gravity on de Sitter space, Int. J. Mod. Phys. A 8 (1993) 1637 [INSPIRE].
R. Camporesi and A. Higuchi, Spectral functions and zeta functions in hyperbolic spaces, J. Math. Phys. 35 (1994) 4217 [INSPIRE].
M. Gary, D. Grumiller and R. Rashkov, Towards non-AdS holography in 3-dimensional higher spin gravity, JHEP 03 (2012) 022 [arXiv:1201.0013] [INSPIRE].
H. Afshar, M. Gary, D. Grumiller, R. Rashkov and M. Riegler, Non-AdS holography in 3-dimensional higher spin gravity — General recipe and example, JHEP 11 (2012) 099 [arXiv:1209.2860] [INSPIRE].
H. Afshar, M. Gary, D. Grumiller, R. Rashkov and M. Riegler, Semi-classical unitarity in 3-dimensional higher-spin gravity for non-principal embeddings, Class. Quant. Grav. 30 (2013) 104004 [arXiv:1211.4454] [INSPIRE].
M. Riegler, Asymptotic Symmetry Algebras in Non-Anti-de-Sitter Higher-Spin Gauge Theories, arXiv:1210.6500 [INSPIRE].
J.M. Maldacena and A. Strominger, AdS 3 black holes and a stringy exclusion principle, JHEP 12 (1998) 005 [hep-th/9804085] [INSPIRE].
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ArXiv ePrint: 1212.3335
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Bertin, M., Ertl, S., Ghorbani, H. et al. Lobachevsky holography in conformal Chern-Simons gravity. J. High Energ. Phys. 2013, 15 (2013). https://doi.org/10.1007/JHEP06(2013)015
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DOI: https://doi.org/10.1007/JHEP06(2013)015