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Asymptotic symmetries of colored gravity in three dimensions

Open Access
Regular Article - Theoretical Physics

Abstract

Three-dimensional colored gravity refers to nonabelian isospin extension of Einstein gravity. We investigate the asymptotic symmetry algebra of the SU(N)-colored gravity in (2+1)-dimensional anti-de Sitter spacetime. Formulated by the Chern-Simons theory with SU(N, N) × SU(N, N) gauge group, the theory contains graviton, SU(N) Chern-Simons gauge fields and massless spin-two multiplets in the SU(N) adjoint representation, thus extending diffeomorphism to colored, nonabelian counterpart. We identify the asymptotic symmetry as Poisson algebra of generators associated with the residual global symmetries of the nonabelian diffeomorphism set by appropriately chosen boundary conditions. The resulting asymptotic symmetry algebra is a nonlinear extension of \( \widehat{\mathfrak{su}(N)} \) Kac-Moody algebra, supplemented by additional generators corresponding to the massless spin-two adjoint matter fields.

Keywords

Chern-Simons Theories 1/N Expansion 

Notes

Open Access

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References

  1. [1]
    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].ADSMathSciNetCrossRefMATHGoogle Scholar
  2. [2]
    M.P. Blencowe, A Consistent Interacting Massless Higher Spin Field Theory in D = (2 + 1), Class. Quant. Grav. 6 (1989) 443 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  3. [3]
    S.F. Prokushkin and M.A. Vasiliev, Higher spin gauge interactions for massive matter fields in 3-D AdS space-time, Nucl. Phys. B 545 (1999) 385 [hep-th/9806236] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  4. [4]
    S. Gwak, E. Joung, K. Mkrtchyan and S.-J. Rey, Rainbow Valley of Colored (Anti) de Sitter Gravity in Three Dimensions, JHEP 04 (2016) 055 [arXiv:1511.05220] [INSPIRE].ADSMathSciNetMATHGoogle Scholar
  5. [5]
    S. Gwak, E. Joung, K. Mkrtchyan and S.-J. Rey, Rainbow vacua of colored higher-spin (A)dS 3 gravity, JHEP 05 (2016) 150 [arXiv:1511.05975] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  6. [6]
    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].ADSMathSciNetCrossRefGoogle Scholar
  7. [7]
    E. Witten, (2 + 1)-Dimensional Gravity as an Exactly Soluble System, Nucl. Phys. B 311 (1988) 46 [INSPIRE].
  8. [8]
    N. Boulanger, T. Damour, L. Gualtieri and M. Henneaux, Inconsistency of interacting, multigraviton theories, Nucl. Phys. B 597 (2001) 127 [hep-th/0007220] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  9. [9]
    N. Boulanger and L. Gualtieri, An Exotic theory of massless spin two fields in three-dimensions, Class. Quant. Grav. 18 (2001) 1485 [hep-th/0012003] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  10. [10]
    S. Deser and R.I. Nepomechie, Gauge Invariance Versus Masslessness in de Sitter Space, Annals Phys. 154 (1984) 396 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  11. [11]
    S. Deser and A. Waldron, Partial masslessness of higher spins in (A)dS, Nucl. Phys. B 607 (2001) 577 [hep-th/0103198] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  12. [12]
    A. Higuchi, Forbidden Mass Range for Spin-2 Field Theory in de Sitter Space-time, Nucl. Phys. B 282 (1987) 397 [INSPIRE].ADSCrossRefGoogle Scholar
  13. [13]
    S. Deser, E. Joung and A. Waldron, Partial Masslessness and Conformal Gravity, J. Phys. A 46 (2013) 214019 [arXiv:1208.1307] [INSPIRE].ADSMathSciNetMATHGoogle Scholar
  14. [14]
    S. Gwak, J. Kim and S.-J. Rey, Massless and Massive Higher Spins from Anti-de Sitter Space Waveguide, JHEP 11 (2016) 024 [arXiv:1605.06526] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  15. [15]
    S. Gwak, J. Kim and S.J. Rey, Higgs Mechanism and Holography of Partially Massless Higher Spin Fields, in proceedings of International Workshop on Higher Spin Gauge Theories, 4–6 November 2015, Nanyang Institute for Advanced Study, pp. 317–352, World Scientific Pub, Singapore (2016) [INSPIRE].
  16. [16]
    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].ADSMathSciNetCrossRefMATHGoogle Scholar
  17. [17]
    M. Henneaux and S.-J. Rey, Nonlinear W as Asymptotic Symmetry of Three-Dimensional Higher Spin Anti-de Sitter Gravity, JHEP 12 (2010) 007 [arXiv:1008.4579] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  18. [18]
    A. Campoleoni, S. Fredenhagen, S. Pfenninger and S. Theisen, Asymptotic symmetries of three-dimensional gravity coupled to higher-spin fields, JHEP 11 (2010) 007 [arXiv:1008.4744] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  19. [19]
    M.R. Gaberdiel and R. Gopakumar, An AdS 3 Dual for Minimal Model CFTs, Phys. Rev. D 83 (2011) 066007 [arXiv:1011.2986] [INSPIRE].ADSGoogle Scholar
  20. [20]
    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].
  21. [21]
    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].ADSMathSciNetCrossRefMATHGoogle Scholar
  22. [22]
    J. Balog, L. Feher, L. O’Raifeartaigh, P. Forgacs and A. Wipf, Toda Theory and W Algebra From a Gauged WZNW Point of View, Annals Phys. 203 (1990) 76 [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  23. [23]
    A. Campoleoni, S. Fredenhagen and J. Raeymaekers, Quantizing higher-spin gravity in free-field variables, JHEP 02 (2018) 126 [arXiv:1712.08078] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  24. [24]
    M. Bañados, Global charges in Chern-Simons field theory and the (2 + 1) black hole, Phys. Rev. D 52 (1996) 5816 [hep-th/9405171] [INSPIRE].Google Scholar
  25. [25]
    M. Henneaux, G. Lucena Gómez, J. Park and S.-J. Rey, Super-W Asymptotic Symmetry of Higher-Spin AdS 3 Supergravity, JHEP 06 (2012) 037 [arXiv:1203.5152] [INSPIRE].ADSCrossRefGoogle Scholar
  26. [26]
    S.-J. Rey and Y. Hikida, Emergent AdS 3 and BTZ black hole from weakly interacting hot 2-D CFT, JHEP 07 (2006) 023 [hep-th/0604102] [INSPIRE].ADSCrossRefGoogle Scholar
  27. [27]
    M. Gary, D. Grumiller, S. Prohazka and S.-J. Rey, Lifshitz Holography with Isotropic Scale Invariance, JHEP 08 (2014) 001 [arXiv:1406.1468] [INSPIRE].ADSCrossRefGoogle Scholar
  28. [28]
    K. Lee, S.-J. Rey and J.A. Rosabal, A string theory which isn’t about strings, JHEP 11 (2017) 172 [arXiv:1708.05707] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  29. [29]
    A. Castro, E. Hijano and A. Lepage-Jutier, Unitarity Bounds in AdS 3 Higher Spin Gravity, JHEP 06 (2012) 001 [arXiv:1202.4467] [INSPIRE].ADSCrossRefGoogle Scholar
  30. [30]
    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].ADSMathSciNetCrossRefMATHGoogle Scholar
  31. [31]
    C. Candu, C. Peng and C. Vollenweider, Extended supersymmetry in AdS 3 higher spin theories, JHEP 12 (2014) 113 [arXiv:1408.5144] [INSPIRE].ADSCrossRefGoogle Scholar

Copyright information

© The Author(s) 2018

Authors and Affiliations

  1. 1.Department of Physics and Research Institute of Basic ScienceKyung Hee UniversitySeoulKorea
  2. 2.School of Physics & AstronomySeoul National UniversitySeoulKorea
  3. 3.Department of Emerging Materials ScienceDGISTDaeguKorea
  4. 4.Department of Physics and Center for Cosmology & Particle PhysicsNew York UniversityNew YorkU.S.A.

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