Advertisement

Journal of High Energy Physics

, 2010:70 | Cite as

Boundary stress tensor and counterterms for weakened AdS3 asymptotic in New Massive Gravity

  • Gaston Giribet
  • Mauricio Leston
Article

Abstract

Resorting to the notion of a stress-tensor induced on the boundary of a space-time, we compute the conserved charges associated to exact solutions of New Massive Gravity that obey weakened versions of AdS3 asymptotic boundary conditions. The computation requires the introduction of additional counterterms, which play the rôle of regularizing the semiclassical stress-tensor in the boundary theory. We show that, if treated appropriately, different ways of prescribing asymptotically AdS3 boundary conditions yield finite conserved charges for the solutions. The consistency of the construction manifests itself in that the charges of hairy asymptotically AdS3 black holes computed by this holography-inspired method exactly match the values required for the Cardy formula to reproduce the black hole entropy. We also consider new solutions to the equations of motion of New Massive Gravity, which happen to fulfill Brown-Henneaux boundary conditions despite not being Einstein manifolds. These solutions are shown to yield vanishing boundary stress-tensor. The results obtained in this paper can be regarded as consistency checks for the prescription proposed in [1].

Keywords

AdS-CFT Correspondence Black Holes 

References

  1. [1]
    O. Hohm and E. Tonni, A boundary stress tensor for higher-derivative gravity in AdS and Lifshitz backgrounds, JHEP 04 (2010) 093 [arXiv:1001.3598] [SPIRES].MathSciNetADSGoogle Scholar
  2. [2]
    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 [SPIRES].MathSciNetADSGoogle Scholar
  3. [3]
    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] [SPIRES].ADSGoogle Scholar
  4. [4]
    M. Henneaux, L. Maoz and A. Schwimmer, Asymptotic dynamics and asymptotic symmetries of three-dimensional extended AdS supergravity, Annals Phys. 282 (2000) 31 [hep-th/9910013] [SPIRES].MathSciNetADSGoogle Scholar
  5. [5]
    K. Krasnov, Λ < 0 quantum gravity in 2+1 dimensions. I: Quantum states and stringy S-matrix, Class. Quant. Grav. 19 (2002) 3977 [hep-th/0112164] [SPIRES].MathSciNetADSGoogle Scholar
  6. [6]
    K. Krasnov, 3D gravity, point particles and Liouville theory, Class. Quant. Grav. 18 (2001) 1291 [hep-th/0008253] [SPIRES].MathSciNetADSGoogle Scholar
  7. [7]
    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] [SPIRES].MathSciNetADSGoogle Scholar
  8. [8]
    E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [SPIRES].MathSciNetGoogle Scholar
  9. [9]
    S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from non-critical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [SPIRES].MathSciNetADSGoogle Scholar
  10. [10]
    E.J. Martinec, Conformal field theory, geometry and entropy, hep-th/9809021 [SPIRES].
  11. [11]
    S. Carlip, What we don’t know about BTZ black hole entropy, Class. Quant. Grav. 15 (1998) 3609 [hep-th/9806026] [SPIRES].MathSciNetADSGoogle Scholar
  12. [12]
    S. Carlip, Dynamics of asymptotic diffeomorphisms in (2+1)-dimensional gravity, Class. Quant. Grav. 22 (2005) 3055 [gr-qc/0501033] [SPIRES].MathSciNetADSGoogle Scholar
  13. [13]
    S. Carlip, Liouville lost, Liouville regained: Central charge in a dynamical background, Phys. Lett. B 508 (2001) 168 [gr-qc/0103100] [SPIRES].MathSciNetADSGoogle Scholar
  14. [14]
    M. Bañados, C. Teitelboim and J. Zanelli, The Black hole in three-dimensional space-time, Phys. Rev. Lett. 69 (1992) 1849 [hep-th/9204099] [SPIRES].MathSciNetADSGoogle Scholar
  15. [15]
    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] [SPIRES].ADSGoogle Scholar
  16. [16]
    A. Strominger, Black hole entropy from near-horizon microstates, JHEP 02 (1998) 009 [hep-th/9712251] [SPIRES].MathSciNetADSGoogle Scholar
  17. [17]
    M. Kleban, M. Porrati and R. Rabadán, Poincaré recurrences and topological diversity, JHEP 10 (2004) 030 [hep-th/0407192] [SPIRES].ADSGoogle Scholar
  18. [18]
    E. Witten, Three-Dimensional Gravity Revisited, arXiv:0706.3359 [SPIRES].
  19. [19]
    A. Maloney and E. Witten, Quantum Gravity Partition Functions in Three Dimensions, JHEP 02 (2010) 029 [arXiv:0712.0155] [SPIRES].MathSciNetADSGoogle Scholar
  20. [20]
    M.R. Gaberdiel, Constraints on extremal self-dual CFTs, JHEP 11 (2007) 087 [arXiv:0707.4073] [SPIRES].ADSGoogle Scholar
  21. [21]
    M.R. Gaberdiel and C.A. Keller, Modular differential equations and null vectors, JHEP 09 (2008) 079 [arXiv:0804.0489] [SPIRES].MathSciNetADSGoogle Scholar
  22. [22]
    D. Gaiotto, Monster symmetry and Extremal CFTs, arXiv:0801.0988 [SPIRES].
  23. [23]
    W. Li, W. Song and A. Strominger, Chiral Gravity in Three Dimensions, JHEP 04 (2008) 082 [arXiv:0801.4566] [SPIRES].MathSciNetADSGoogle Scholar
  24. [24]
    A. Strominger, A Simple Proof of the Chiral Gravity Conjecture, arXiv:0808.0506 [SPIRES].
  25. [25]
    S. Deser, R. Jackiw and S. Templeton, Topologically massive gauge theories, Ann. Phys. 140 (1982) 372 [Erratum ibid. 185 (1988) 406] [SPIRES].MathSciNetADSGoogle Scholar
  26. [26]
    S. Deser, R. Jackiw and S. Templeton, Topologically massive gauge theories, Ann. Phys. 140 (1982) 372 [SPIRES].MathSciNetADSGoogle Scholar
  27. [27]
    S. Deser, R. Jackiw and S. Templeton, Three-Dimensional Massive Gauge Theories, Phys. Rev. Lett. 48 (1982) 975 [SPIRES].ADSGoogle Scholar
  28. [28]
    S. Carlip, S. Deser, A. Waldron and D.K. Wise, Topologically Massive AdS Gravity, Phys. Lett. B 666 (2008) 272 [arXiv:0807.0486] [SPIRES].MathSciNetADSGoogle Scholar
  29. [29]
    S. Carlip, S. Deser, A. Waldron and D.K. Wise, Cosmological topologically massive gravitons and photons, Class. Quant. Grav. 26 (2009) 075008. MathSciNetADSGoogle Scholar
  30. [30]
    W. Li, W. Song and A. Strominger, Comment on ’Cosmological Topological Massive Gravitons and Photons’, arXiv:0805.3101 [SPIRES].
  31. [31]
    G. Giribet, M. Kleban and M. Porrati, Topologically Massive Gravity at the Chiral Point is Not Chiral, JHEP 10 (2008) 045 [arXiv:0807.4703] [SPIRES].MathSciNetADSGoogle Scholar
  32. [32]
    D. Grumiller, R. Jackiw and N. Johansson, Canonical analysis of cosmological topologically massive gravity at the chiral point, in Wolfgang Kummer memorial volume, [arXiv:0806.4185] [SPIRES].
  33. [33]
    S. Carlip, Chiral Topologically Massive Gravity and Extremal B-F Scalars, JHEP 09 (2009) 083 [arXiv:0906.2384] [SPIRES].MathSciNetADSGoogle Scholar
  34. [34]
    S. Carlip, The Constraint Algebra of Topologically Massive AdS Gravity, JHEP 10 (2008) 078 [arXiv:0807.4152] [SPIRES].ADSGoogle Scholar
  35. [35]
    M. Becker, P. Bruillard and S. Downes, Chiral Supergravity, JHEP 10 (2009) 004 [arXiv:0906.4822] [SPIRES].MathSciNetADSGoogle Scholar
  36. [36]
    M. Henneaux, C. Martinez and R. Troncoso, More on Asymptotically Anti-de Sitter Spaces in Topologically Massive Gravity, arXiv:1006.0273 [SPIRES].
  37. [37]
    M. Henneaux, C. Martinez, R. Troncoso and J. Zanelli, Black holes and asymptotics of 2+1 gravity coupled to a scalar field, Phys. Rev. D 65 (2002) 104007 [hep-th/0201170] [SPIRES].MathSciNetADSGoogle Scholar
  38. [38]
    M. Henneaux, C. Martinez, R. Troncoso and J. Zanelli, Asymptotically anti-de Sitter spacetimes and scalar fields with a logarithmic branch, Phys. Rev. D 70 (2004) 044034 [hep-th/0404236] [SPIRES].MathSciNetADSGoogle Scholar
  39. [39]
    M. Henneaux, C. Martinez, R. Troncoso and J. Zanelli, Asymptotic behavior and Hamiltonian analysis of anti-de Sitter gravity coupled to scalar fields, Annals Phys. 322 (2007) 824 [hep-th/0603185] [SPIRES].MathSciNetADSGoogle Scholar
  40. [40]
    D. Grumiller and N. Johansson, Instability in cosmological topologically massive gravity at the chiral point, JHEP 07 (2008) 134 [arXiv:0805.2610] [SPIRES].ADSGoogle Scholar
  41. [41]
    D. Grumiller and N. Johansson, Consistent boundary conditions for cosmological topologically massive gravity at the chiral point, Int. J. Mod. Phys. D 17 (2009) 2367 [arXiv:0808.2575] [SPIRES]. MathSciNetADSGoogle Scholar
  42. [42]
    S. Ertl, D. Grumiller and N. Johansson, Erratum to ‘Instability in cosmological topologically massive gravity at the chiral point’, arXiv:0805.2610, arXiv:0910.1706 [SPIRES].
  43. [43]
    A. Maloney, W. Song and A. Strominger, Chiral Gravity, Log Gravity and Extremal CFT, Phys. Rev. D 81 (2010) 064007 [arXiv:0903.4573] [SPIRES].MathSciNetADSGoogle Scholar
  44. [44]
    D. Grumiller and I. Sachs, AdS 3 /LCFT 2 — Correlators in Cosmological Topologically Massive Gravity, JHEP 03 (2010) 012 [arXiv:0910.5241] [SPIRES].MathSciNetADSGoogle Scholar
  45. [45]
    D. Grumiller and N. Johansson, Gravity duals for logarithmic conformal field theories, J. Phys. Conf. Ser. 222 (2010) 012047 [arXiv:1001.0002] [SPIRES]. ADSGoogle Scholar
  46. [46]
    E.A. Bergshoeff, O. Hohm and P.K. Townsend, Massive Gravity in Three Dimensions, Phys. Rev. Lett. 102 (2009) 201301 [arXiv:0901.1766] [SPIRES].MathSciNetADSGoogle Scholar
  47. [47]
    E.A. Bergshoeff, O. Hohm and P.K. Townsend, More on Massive 3D Gravity, Phys. Rev. D 79 (2009) 124042 [arXiv:0905.1259] [SPIRES].MathSciNetADSGoogle Scholar
  48. [48]
    E. Bergshoeff, O. Hohm and P. Townsend, On massive gravitons in 2+1 dimensions, J. Phys. Conf. Ser. 229 (2010) 012005 [arXiv:0912.2944] [SPIRES]. ADSGoogle Scholar
  49. [49]
    R. Andringa, E. Bergshoeff, M. de Roo, O. Hohm and E. Sezgin, Massive 3D supergravity, Class. Quant. Grav. 27 (2010) 025010. ADSGoogle Scholar
  50. [50]
    E.A. Bergshoeff, O. Hohm, J. Rosseel, E. Sezgin and P.K. Townsend, More on Massive 3D Supergravity, arXiv:1005.3952 [SPIRES].
  51. [51]
    S. Deser, Ghost-free, finite, fourth order D = 3 (alas) gravity, Phys. Rev. Lett. 103 (2009) 101302 [arXiv:0904.4473] [SPIRES].MathSciNetADSGoogle Scholar
  52. [52]
    A. Sinha, On the new massive gravity and AdS/CFT, JHEP 06 (2010) 061 [arXiv:1003.0683] [SPIRES].ADSGoogle Scholar
  53. [53]
    M.F. Paulos, New massive gravity, extended, arXiv:1005.1646 [SPIRES].
  54. [54]
    I. Gullu, T.C. Sisman and B. Tekin, Born-Infeld extension of new massive gravity, Class. Quant. Grav. 27 (2010) 162001 [arXiv:1003.3935] [SPIRES].MathSciNetADSGoogle Scholar
  55. [55]
    I. Gullu, T.C. Sisman and B. Tekin, c-functions in the Born-Infeld extended New Massive Gravity, Phys. Rev. D 82 (2010) 024032 [arXiv:1005.3214] [SPIRES].ADSGoogle Scholar
  56. [56]
    E. Ayón-Beato, G. Giribet and M. Hassaine, Bending AdS Waves with New Massive Gravity, JHEP 05 (2009) 029 [arXiv:0904.0668] [SPIRES].ADSGoogle Scholar
  57. [57]
    E. Ayón-Beato, A. Garbarz, G. Giribet and M. Hassaine, Lifshitz Black Hole in Three Dimensions, Phys. Rev. D 80 (2009) 104029 [arXiv:0909.1347] [SPIRES].ADSGoogle Scholar
  58. [58]
    E. Ayón-Beato, A. Garbarz, G. Giribet and M. Hassaine, Analytic Lifshitz black holes in higher dimensions, JHEP 04 (2010) 030 [arXiv:1001.2361] [SPIRES].ADSGoogle Scholar
  59. [59]
    A. Garbarz, G. Giribet and Y. Vasquez, Asymptotically AdS 3 Solutions to Topologically Massive Gravity at Special Values of the Coupling Constants, Phys. Rev. D 79 (2009) 044036 [arXiv:0811.4464] [SPIRES].MathSciNetADSGoogle Scholar
  60. [60]
    G. Clément, Black holes with a null Killing vector in three-dimensional massive gravity, Class. Quant. Grav. 26 (2009) 165002. ADSGoogle Scholar
  61. [61]
    J. Oliva, D. Tempo and R. Troncoso, Three-dimensional black holes, gravitational solitons, kinks and wormholes for BHT masive gravity, JHEP 07 (2009) 011 [arXiv:0905.1545] [SPIRES]. ADSGoogle Scholar
  62. [62]
    M. Alishahiha and A. Naseh, Holographic Renormalization of New Massive Gravity, arXiv:1005.1544 [SPIRES].
  63. [63]
    G. Giribet, J. Oliva, D. Tempo and R. Troncoso, Microscopic entropy of the three-dimensional rotating black hole of BHT massive gravity, Phys. Rev. D 80 (2009) 124046 [arXiv:0909.2564] [SPIRES].ADSGoogle Scholar
  64. [64]
    Y. Liu and Y.-W. Sun, On the Generalized Massive Gravity in AdS 3, Phys. Rev. D 79 (2009) 126001 [arXiv:0904.0403] [SPIRES].MathSciNetADSGoogle Scholar
  65. [65]
    Y. Liu and Y.-w. Sun, Note on New Massive Gravity in AdS 3, JHEP 04 (2009) 106 [arXiv:0903.0536] [SPIRES].
  66. [66]
    Y. Liu and Y.-W. Sun, Consistent Boundary Conditions for New Massive Gravity in AdS 3, JHEP 05 (2009) 039 [arXiv:0903.2933] [SPIRES].MathSciNetADSGoogle Scholar
  67. [67]
    P. Kraus, Lectures on black holes and the AdS 3 /CFT 2 correspondence, Lect. Notes Phys. 755 (2008) 193 [hep-th/0609074] [SPIRES].MathSciNetADSGoogle Scholar
  68. [68]
    J.D. Brown and J.W. York, Jr., Quasilocal energy and conserved charges derived from the gravitational action, Phys. Rev. D 47 (1993) 1407 [gr-qc/9209012] [SPIRES].MathSciNetADSGoogle Scholar
  69. [69]
    V. Balasubramanian and P. Kraus, A stress tensor for anti-de Sitter gravity, Commun. Math. Phys. 208 (1999) 413 [hep-th/9902121] [SPIRES].MathSciNetADSGoogle Scholar
  70. [70]
    S. Kachru, X. Liu and M. Mulligan, Gravity Duals of Lifshitz-like Fixed Points, Phys. Rev. D 78 (2008) 106005 [arXiv:0808.1725] [SPIRES].MathSciNetADSGoogle Scholar
  71. [71]
    S.F. Ross and O. Saremi, Holographic stress tensor for non-relativistic theories, JHEP 09 (2009) 009 [arXiv:0907.1846] [SPIRES].MathSciNetADSGoogle Scholar
  72. [72]
    K.A. Moussa, G. Clement and C. Leygnac, The black holes of topologically massive gravity, Class. Quant. Grav. 20 (2003) L277 [gr-qc/0303042] [SPIRES].ADSGoogle Scholar
  73. [73]
    G. Clément, Black hole mass and angular momentum in 2+1 gravity, Phys. Rev. D 68 (2003) 024032 [gr-qc/0301129] [SPIRES].ADSGoogle Scholar
  74. [74]
    J.L. Cardy, Operator Content of Two-Dimensional Conformally Invariant Theories, Nucl. Phys. B 270 (1986) 186 [SPIRES].MathSciNetADSGoogle Scholar
  75. [75]
    G. Compere, S. de Buyl and S. Detournay, Non-Einstein geometries in Chiral Gravity, arXiv:1006.3099 [SPIRES].
  76. [76]
    D. Grumiller and O. Hohm, AdS 3 /LCFT 2 — Correlators in New Massive Gravity, Phys. Lett. B 686 (2010) 264 [arXiv:0911.4274] [SPIRES].MathSciNetADSGoogle Scholar
  77. [77]
    G. Compère and S. Detournay, Semi-classical central charge in topologically massive gravity, Class. Quant. Grav. 26 (2009) 012001 [Erratum ibid. 26 (2009) 139801].ADSGoogle Scholar
  78. [78]
    D. Anninos, W. Li, M. Padi, W. Song and A. Strominger, Warped AdS 3 Black Holes, JHEP 03 (2009) 130 [arXiv:0807.3040] [SPIRES].MathSciNetADSGoogle Scholar
  79. [79]
    D. Anninos, Sailing from Warped AdS 3 to Warped dS 3 in Topologically Massive Gravity, JHEP 02 (2010) 046 [arXiv:0906.1819] [SPIRES].MathSciNetADSGoogle Scholar
  80. [80]
    D. Anninos, M. Esole and M. Guica, Stability of warped AdS 3 vacua of topologically massive gravity, JHEP 10 (2009) 083 [arXiv:0905.2612] [SPIRES].MathSciNetADSGoogle Scholar
  81. [81]
    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] [SPIRES].MathSciNetADSGoogle Scholar
  82. [82]
    M. Blagojevic and B. Cvetkovic, Asymptotic Chern-Simons formulation of spacelike stretched AdS gravity, Class. Quant. Grav. 27 (2010) 185022 [arXiv:0912.5154] [SPIRES].MathSciNetADSGoogle Scholar
  83. [83]
    M. Blagojevic and B. Cvetkovic, Asymptotic structure of topologically massive gravity in spacelike stretched AdS sector, JHEP 09 (2009) 006 [arXiv:0907.0950] [SPIRES].ADSGoogle Scholar
  84. [84]
    D. Anninos, G. Compere, S. de Buyl, S. Detournay and M. Guica, The Curious Case of Null Warped Space, arXiv:1005.4072 [SPIRES].
  85. [85]
    G. Clément, Warped AdS 3 black holes in new massive gravity, Class. Quant. Grav. 26 (2009) 105015. ADSGoogle Scholar
  86. [86]
    O. Mišković and R. Olea, Background-independent charges in Topologically Massive Gravity, JHEP 12 (2009) 046 [arXiv:0909.2275] [SPIRES].ADSGoogle Scholar

Copyright information

© SISSA, Trieste, Italy 2010

Authors and Affiliations

  1. 1.Universidad de Buenos Aires FCEN-UBA and IFIBA -CONICETBuenos AiresArgentina
  2. 2.Instituto de A stronomíay Física del Espacio IAFE-CONICETBuenos AiresArgentina

Personalised recommendations