Abstract
We study the asymptotic symmetries of three-dimensional Warped Anti-de Sitter (WAdS) spaces in three-dimensional New Massive Gravity (NMG). For a specific choice of asymptotic boundary conditions, we find that the algebra of charges is infinite dimensional and coincides with the semidirect sum of Virasoro algebra with non-vanishing central charge and an affine û(1) k Kač-Moody algebra. We show that the WAdS black hole configurations organize in terms of two commuting Virasoro algebras. We identify the Virasoro generators that expand the associated representations in the dual Warped Conformal Field Theory (WCFT) and, by applying the Warped version of the Cardy formula, we prove that the microscopic WCFT computation exactly reproduces the entropy of black holes in WAdS space.
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References
I. Bengtsson and P. Sandin, Anti de Sitter space, squashed and stretched, Class. Quant. Grav. 23 (2006) 971 [gr-qc/0509076] [INSPIRE].
M. Guica, T. Hartman, W. Song and A. Strominger, The Kerr/CFT correspondence, Phys. Rev. D 80 (2009) 124008 [arXiv:0809.4266] [INSPIRE].
D.M. Hofman and B. Rollier, Warped conformal field theory as lower spin gravity, Nucl. Phys. B 897 (2015) 1 [arXiv:1411.0672] [INSPIRE].
D. Anninos, J. Samani and E. Shaghoulian, Warped entanglement entropy, JHEP 02 (2014) 118 [arXiv:1309.2579] [INSPIRE].
K.A. Moussa, G. Clément and C. Leygnac, The black holes of topologically massive gravity, Class. Quant. Grav. 20 (2003) L277 [gr-qc/0303042] [INSPIRE].
D. Anninos, W. Li, M. Padi, W. Song and A. Strominger, Warped AdS3 black holes, JHEP 03 (2009) 130 [arXiv:0807.3040] [INSPIRE].
W. Song and A. Strominger, Warped AdS3/Dipole-CFT Duality, JHEP 05 (2012) 120 [arXiv:1109.0544] [INSPIRE].
S. Detournay, T. Hartman and D.M. Hofman, Warped conformal field theory, Phys. Rev. D 86 (2012) 124018 [arXiv:1210.0539] [INSPIRE].
E.A. Bergshoeff, O. Hohm and P.K. Townsend, Massive gravity in three dimensions, Phys. Rev. Lett. 102 (2009) 201301 [arXiv:0901.1766] [INSPIRE].
G. Clément, Warped AdS3 black holes in new massive gravity, Class. Quant. Grav. 26 (2009) 105015 [arXiv:0902.4634] [INSPIRE].
M. Bañados, G. Barnich, G. Compère and A. Gomberoff, Three dimensional origin of Godel spacetimes and black holes, Phys. Rev. D 73 (2006) 044006 [hep-th/0512105] [INSPIRE].
L. Donnay, J.J. Fernández-Melgarejo, G. Giribet, A. Goya and E. Lavia, Conserved charges in timelike warped AdS 3 spaces, Phys. Rev. D 91 (2015) 125006 [arXiv:1504.05212] [INSPIRE].
G. Giribet and A. Goya, The Brown-York mass of black holes in Warped Anti-de Sitter space, JHEP 03 (2013) 130 [arXiv:1212.2100] [INSPIRE].
S. Nam, J.-D. Park and S.-H. Yi, Mass and Angular momentum of Black Holes in New Massive Gravity, Phys. Rev. D 82 (2010) 124049 [arXiv:1009.1962] [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].
M. Bañados, M. Henneaux, C. Teitelboim and J. Zanelli, Geometry of the (2 + 1) black hole, Phys. Rev. D 48 (1993) 1506 [gr-qc/9302012] [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].
M. Henneaux, C. Martinez and R. Troncoso, Asymptotically warped anti-de Sitter spacetimes in topologically massive gravity, Phys. Rev. D 84 (2011) 124016 [arXiv:1108.2841] [INSPIRE].
G. Compère, M. Guica and M.J. Rodr´ıguez, Two Virasoro symmetries in stringy warped AdS 3, JHEP 12 (2014) 012 [arXiv:1407.7871] [INSPIRE].
G. Barnich and F. Brandt, Covariant theory of asymptotic symmetries, conservation laws and central charges, Nucl. Phys. B 633 (2002) 3 [hep-th/0111246] [INSPIRE].
G. Barnich and G. Compère, Surface charge algebra in gauge theories and thermodynamic integrability, J. Math. Phys. 49 (2008) 042901 [arXiv:0708.2378] [INSPIRE].
V. Iyer and R.M. Wald, Some properties of Noether charge and a proposal for dynamical black hole entropy, Phys. Rev. D 50 (1994) 846 [gr-qc/9403028] [INSPIRE].
G. Compère and S. Detournay, Semi-classical central charge in topologically massive gravity, Class. Quant. Grav. 26 (2009) 012001 [arXiv:0808.1911] [INSPIRE].
G. Compère and S. Detournay, Centrally extended symmetry algebra of asymptotically Godel spacetimes, JHEP 03 (2007) 098 [hep-th/0701039] [INSPIRE].
M. Blagojevic and B. Cvetkovic, Asymptotic structure of topologically massive gravity in spacelike stretched AdS sector, JHEP 09 (2009) 006 [arXiv:0907.0950] [INSPIRE].
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Donnay, L., Giribet, G. Holographic entropy of Warped-AdS3 black holes. J. High Energ. Phys. 2015, 99 (2015). https://doi.org/10.1007/JHEP06(2015)099
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DOI: https://doi.org/10.1007/JHEP06(2015)099