Abstract
We study Vasiliev’s higher-spin gravity in 3+1d. We formulate the theory in the so-called compensator formalism, where the local isometry group SO(4, 1) is reduced to the Lorentz group SO(3, 1) by a choice of spacelike direction in an internal 4+1d space. We present a consistent extension of Vasiliev’s equations that allows this internal direction to become spacetime-dependent. This allows a new point of view on the theory, where spacetime is identified with the de Sitter space of possible internal directions. We thus obtain an interacting theory of higher-spin massless gauge fields on a fixed, maximally symmetric background spacetime. We expect implications for the physical interpretation of higher-spin gravity, for the search for a Lagrangian formulation and/or quantization, as well as for higher-spin holography.
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References
M.A. Vasiliev, Higher spin gauge theories in four-dimensions, three-dimensions and two-dimensions, Int. J. Mod. Phys. D 5 (1996) 763 [hep-th/9611024] [INSPIRE].
M.A. Vasiliev, Higher spin gauge theories: Star product and AdS space, in Y. Golfand and M.A. Shifman, The Many Faces of the Superworld: Yuri Golfand Memorial Volume, World Scientific Pub. Co. Inc. (1999), pp. 533-610, [hep-th/9910096] [INSPIRE].
I.R. Klebanov and A.M. Polyakov, AdS dual of the critical O(N ) vector model, Phys. Lett. B 550 (2002) 213 [hep-th/0210114] [INSPIRE].
E. Sezgin and P. Sundell, Holography in 4D (super) higher spin theories and a test via cubic scalar couplings, JHEP 07 (2005) 044 [hep-th/0305040] [INSPIRE].
S. Giombi and X. Yin, The Higher Spin/Vector Model Duality, J. Phys. A 46 (2013) 214003 [arXiv:1208.4036] [INSPIRE].
D. Anninos, T. Hartman and A. Strominger, Higher Spin Realization of the dS/CFT Correspondence, arXiv:1108.5735 [INSPIRE].
C.-M. Chang, S. Minwalla, T. Sharma and X. Yin, ABJ Triality: from Higher Spin Fields to Strings, J. Phys. A 46 (2013) 214009 [arXiv:1207.4485] [INSPIRE].
M.A. Vasiliev, Cubic interactions of bosonic higher spin gauge fields in AdS 5, Nucl. Phys. B 616 (2001) 106 [Erratum ibid. B 652 (2003) 407] [hep-th/0106200] [INSPIRE].
V.E. Didenko and E.D. Skvortsov, Towards higher-spin holography in ambient space of any dimension, J. Phys. A 46 (2013) 214010 [arXiv:1207.6786] [INSPIRE].
Y. Neiman, Twistors and antipodes in de Sitter space, Phys. Rev. D 89 (2014) 063521 [arXiv:1312.7842] [INSPIRE].
R. Penrose and W. Rindler, Spinors And Space-time. Volume 2. Spinor And Twistor Methods In Space-time Geometry, Cambridge University Press, Cambridge U.K. (1986).
R.S. Ward and R.O. Wells, Twistor geometry and field theory, Cambridge University Press, Cambridge U.K. (1990).
Y. Neiman, Antipodally symmetric gauge fields and higher-spin gravity in de Sitter space, JHEP 10 (2014) 153 [arXiv:1406.3291] [INSPIRE].
M.A. Vasiliev, Holography, Unfolding and Higher-Spin Theory, J. Phys. A 46 (2013) 214013 [arXiv:1203.5554] [INSPIRE].
J.M. Maldacena and A. Zhiboedov, Constraining Conformal Field Theories with A Higher Spin Symmetry, J. Phys. A 46 (2013) 214011 [arXiv:1112.1016] [INSPIRE].
S. Giombi and X. Yin, Higher Spin Gauge Theory and Holography: The Three-Point Functions, JHEP 09 (2010) 115 [arXiv:0912.3462] [INSPIRE].
S. Giombi and X. Yin, Higher Spins in AdS and Twistorial Holography, JHEP 04 (2011) 086 [arXiv:1004.3736] [INSPIRE].
N. Colombo and P. Sundell, Higher Spin Gravity Amplitudes From Zero-form Charges, arXiv:1208.3880 [INSPIRE].
V.E. Didenko and E.D. Skvortsov, Exact higher-spin symmetry in CFT: all correlators in unbroken Vasiliev theory, JHEP 04 (2013) 158 [arXiv:1210.7963] [INSPIRE].
V.E. Didenko, J. Mei and E.D. Skvortsov, Exact higher-spin symmetry in CFT: free fermion correlators from Vasiliev Theory, Phys. Rev. D 88 (2013) 046011 [arXiv:1301.4166] [INSPIRE].
N. Boulanger and P. Sundell, An action principle for Vasiliev’s four-dimensional higher-spin gravity, J. Phys. A 44 (2011) 495402 [arXiv:1102.2219] [INSPIRE].
N. Boulanger, N. Colombo and P. Sundell, A minimal BV action for Vasiliev’s four-dimensional higher spin gravity, JHEP 10 (2012) 043 [arXiv:1205.3339] [INSPIRE].
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ArXiv ePrint: 1502.06685
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Neiman, Y. Higher-spin gravity as a theory on a fixed (anti) de Sitter background. J. High Energ. Phys. 2015, 144 (2015). https://doi.org/10.1007/JHEP04(2015)144
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DOI: https://doi.org/10.1007/JHEP04(2015)144