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Enhanced asymptotic symmetry algebra of AdS 3

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Abstract

A generalization of the Brown-Henneaux boundary conditions is introduced for pure gravity with negative cosmological constant in 3 dimensions. This leads to new degrees of freedom and to an enhancement of the symmetry algebra. Up to the zero modes, it consists of two copies of the semi-direct product of a Virasoro algebra with a U(1) current algebra. The associated surface charge algebra now contains three non-zero central charges: the two usual Brown-Henneaux central charges and one new quantity.

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References

  1. S. Deser and R. Jackiw, Three-dimensional cosmological gravity: dynamics of constant curvature, Annals Phys. 153 (1984) 405 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  2. 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].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  3. 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].

    ADS  Google Scholar 

  4. 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].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  5. A. Strominger, Black hole entropy from near horizon microstates, JHEP 02 (1998) 009 [hep-th/9712251] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  6. 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].

    Article  ADS  MATH  Google Scholar 

  7. 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] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  8. M. Rooman and P. Spindel, Holonomies, anomalies and the Fefferman-Graham ambiguity in AdS 3 gravity, Nucl. Phys. B 594 (2001) 329 [hep-th/0008147] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  9. G. Barnich and H.A. Gonzalez, Dual dynamics of three dimensional asymptotically flat Einstein gravity at null infinity, JHEP 05 (2013) 016 [arXiv:1303.1075] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  10. M. Bañados, Three-dimensional quantum geometry and black holes, hep-th/9901148 [INSPIRE].

  11. S. Carlip, Conformal field theory, (2 + 1)-dimensional gravity and the BTZ black hole, Class. Quant. Grav. 22 (2005) R85 [gr-qc/0503022] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  12. A. Maloney and E. Witten, Quantum gravity partition functions in three dimensions, JHEP 02 (2010) 029 [arXiv:0712.0155] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  13. A. Castro, M.R. Gaberdiel, T. Hartman, A. Maloney and R. Volpato, The Gravity Dual of the Ising Model, Phys. Rev. D 85 (2012) 024032 [arXiv:1111.1987] [INSPIRE].

    ADS  Google Scholar 

  14. A.P. Porfyriadis and F. Wilczek, Effective Action, Boundary Conditions and Virasoro Algebra for AdS 3, arXiv:1007.1031 [INSPIRE].

  15. G. Compère, W. Song and A. Strominger, New boundary conditions for AdS 3, JHEP 05 (2013) 152 [arXiv:1303.2662] [INSPIRE].

    Article  ADS  Google Scholar 

  16. G. Gibbons and S. Hawking, Action integrals and partition functions in quantum gravity, Phys. Rev. D 15 (1977) 2752 [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  17. J.D. Brown and J.W. York, Quasilocal energy and conserved charges derived from the gravitational action, Phys. Rev. D 47 (1993) 1407 [gr-qc/9209012] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  18. M. Henningson and K. Skenderis, Holography and the Weyl anomaly, Fortsch. Phys. 48 (2000) 125 [hep-th/9812032] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  19. V. Balasubramanian and P. Kraus, A stress tensor for Anti-de Sitter gravity, Commun. Math. Phys. 208 (1999) 413 [hep-th/9902121] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  20. S. de Haro, K. Skenderis and S.N. Solodukhin, Gravity in warped compactifications and the holographic stress tensor, Class. Quant. Grav. 18 (2001) 3171 [hep-th/0011230] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  21. I. Papadimitriou and K. Skenderis, Thermodynamics of asymptotically locally AdS spacetimes, JHEP 08 (2005) 004 [hep-th/0505190] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  22. G. Compere and D. Marolf, Setting the boundary free in AdS/CFT, Class. Quant. Grav. 25 (2008) 195014 [arXiv:0805.1902] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  23. G. Barnich and C. Troessaert, Aspects of the BMS/CFT correspondence, JHEP 05 (2010) 062 [arXiv:1001.1541] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  24. T. Regge and C. Teitelboim, Role of Surface Integrals in the Hamiltonian Formulation of General Relativity, Annals Phys. 88 (1974) 286 [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  25. R. Benguria, P. Cordero and C. Teitelboim, Aspects of the Hamiltonian Dynamics of Interacting Gravitational Gauge and Higgs Fields with Applications to Spherical Symmetry, Nucl. Phys. B 122 (1977) 61 [INSPIRE].

    Article  ADS  Google Scholar 

  26. C. Imbimbo, A. Schwimmer, S. Theisen and S. Yankielowicz, Diffeomorphisms and holographic anomalies, Class. Quant. Grav. 17 (2000) 1129 [hep-th/9910267] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  27. 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].

    ADS  Google Scholar 

  28. 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].

    Article  MathSciNet  ADS  Google Scholar 

  29. S. Detournay, T. Hartman and D.M. Hofman, Warped conformal field theory, Phys. Rev. D 86 (2012) 124018 [arXiv:1210.0539] [INSPIRE].

    ADS  Google Scholar 

  30. J. Navarro-Salas and P. Navarro, A note on Einstein gravity on AdS 3 and boundary conformal field theory, Phys. Lett. B 439 (1998) 262 [hep-th/9807019] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  31. C. Fefferman and C. Graham, Conformal invariants, Elie Cartan et les Mathématiques d’aujourd’hui, Asterisque Num. Hors Ser. (1985), pg. 95.

  32. C. Graham and J. Lee, Einstein metrics with prescribed conformal infinity on the ball, Adv. Math. 87 (1991) 186.

    Article  MathSciNet  MATH  Google Scholar 

  33. K. Skenderis and S.N. Solodukhin, Quantum effective action from the AdS/CFT correspondence, Phys. Lett. B 472 (2000) 316 [hep-th/9910023] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  34. C.R. Graham, Volume and area renormalizations for conformally compact Einstein metrics, math/9909042 [INSPIRE].

  35. M. Rooman and P. Spindel, Aspects of (2 + 1)-dimensional gravity: AdS 3 asymptotic dynamics in the framework of Fefferman-Graham-Lee theorems, Annalen Phys. 9 (2000) 161 [hep-th/9911142] [INSPIRE].

    Google Scholar 

  36. K. Bautier, F. Englert, M. Rooman and P. Spindel, The Fefferman-Graham ambiguity and AdS black holes, Phys. Lett. B 479 (2000) 291 [hep-th/0002156] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  37. 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].

    Article  MathSciNet  ADS  Google Scholar 

  38. G. Barnich and G. Compere, Surface charge algebra in gauge theories and thermodynamic integrability, J. Math. Phys. 49 (2008) 042901 [arXiv:0708.2378] [INSPIRE].

    Article  MathSciNet  Google Scholar 

  39. S. Carlip, Liouville lost, Liouville regained: central charge in a dynamical background, Phys. Lett. B 508 (2001) 168 [gr-qc/0103100] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  40. A. Castro, E. Hijano and A. Lepage-Jutier, Unitarity bounds in AdS 3 higher spin gravity, JHEP 06 (2012) 001 [arXiv:1202.4467] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  41. 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].

    Article  MathSciNet  ADS  Google Scholar 

  42. L. Brink and M. Henneaux, Principles of string theory, Plenum, New York U.S.A. (1988).

    Book  Google Scholar 

  43. J.A. de Azcárraga and J.M. Izquierdo, Lie Groups, Lie algebras, cohomology, and some applications in physics, Cambridge University Press, Cambridge U.K. (1995).

    Book  MATH  Google Scholar 

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  1. Centro de Estudios Científicos (CECs), Arturo Prat 514, Valdivia, Chile

    Cédric Troessaert

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  1. Cédric Troessaert
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Correspondence to Cédric Troessaert.

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ArXiv ePrint: 1303.3296

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Troessaert, C. Enhanced asymptotic symmetry algebra of AdS 3 . J. High Energ. Phys. 2013, 44 (2013). https://doi.org/10.1007/JHEP08(2013)044

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  • DOI: https://doi.org/10.1007/JHEP08(2013)044

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