Abstract
We study the canonical structure of the Bergshoeff-Hohm-Townsend massive gravity, linearized around a maximally symmetric background. At the critical point in the space of parameters, defined by Λ 0/m 2 = −1, we discover an extra gauge symmetry, which reflects the existence of the partially massless mode. The number of the Lagrangian degrees of freedom is found to be 1. We show that the canonical structure of the theory at the critical point is unstable under linearization.
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E.A. Bergshoeff, O. Hohm and P.K. Townsend, Massive Gravity in Three Dimensions, Phys. Rev. Lett. 102 (2009) 201301 [arXiv:0901.1766] [SPIRES].
E.A. Bergshoeff, O. Hohm and P.K. Townsend, More on Massive 3D Gravity, Phys. Rev. D 79 (2009) 124042 [arXiv:0905.1259] [SPIRES].
M. Fierz and W. Pauli, On relativistic wave equations for particles of arbitrary spin in an electromagnetic field, Proc. Roy. Soc. Lond. A 173 (1939) 211 [SPIRES].
M. Nakasone and I. Oda, On Unitarity of Massive Gravity in Three Dimensions, Prog. Theor. Phys. 121 (2009) 1389 [arXiv:0902.3531] [SPIRES].
S. Deser, Ghost-free, finite, fourth order D = 3 (alas) gravity, Phys. Rev. Lett. 103 (2009) 101302 [arXiv:0904.4473] [SPIRES].
I. Oda, Renormalizability of Massive Gravity in Three Dimensions, JHEP 05 (2009) 064 [arXiv:0904.2833] [SPIRES].
Y. Liu and Y.-w. Sun, Note on New Massive Gravity in AdS 3, JHEP 04 (2009) 106 [arXiv:0903.0536] [SPIRES].
Y. Liu and Y.-W. Sun, Consistent Boundary Conditions for New Massive Gravity in AdS 3, JHEP 05 (2009) 039 [arXiv:0903.2933] [SPIRES].
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].
A. Sinha, On the new massive gravity and AdS/CFT, JHEP 06 (2010) 061 [arXiv:1003.0683] [SPIRES].
P.A.M. Dirac, Lectures on quantum mechanics, Belfer Graduate School of Science, Yeshiva University, New York U.S.A. (1964).
M. Blagojevic and B. Cvetkovic, Hamiltonian analysis of BHT massive gravity, JHEP 01 (2011) 082 [arXiv:1010.2596] [SPIRES].
M. Sadegh and A. Shirzad, Constraint structure of the three dimensional massive gravity, arXiv:1010.2887 [SPIRES].
S. Deser and A. Waldron, Gauge invariances and phases of massive higher spins in (A)dS, Phys. Rev. Lett. 87 (2001) 031601 [hep-th/0102166] [SPIRES].
S. Deser and A. Waldron, Partial masslessness of higher spins in (A)dS, Nucl. Phys. B 607 (2001) 577 [hep-th/0103198] [SPIRES].
B. Tekin, Partially massless spin-2 fields in string generated models, hep-th/0306178 [SPIRES].
I. Gullu, T.C. Sisman and B. Tekin, Canonical Structure of Higher Derivative Gravity in 3D, Phys. Rev. D 81 (2010) 104017 [arXiv:1002.3778] [SPIRES].
M. Blagojević, Gravitation and gauge symmetries, IoP Publishing, Bristol U.K. (2002).
T. Ortín, Gravity and strings, Cambridge University Press, Cambridge U.K. (2004).
H. Afshar, B. Cvetković, S. Ertl, D. Grumiller and N. Johansson, Chern-Simons gravity, partial masslessness and holography, in preparation.
L. Castellani, Symmetries in constrained hamiltonian systems, Ann. Phys. 143 (1982) 357 [SPIRES].
H. Chen, J.M. Nester and H.-J. Yo, Acausal PGT modes and the nonlinear constraint effect, Acta Phys. Polon. B 29 (1998) 961.
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Blagojević, M., Cvetković, B. Extra gauge symmetries in BHT gravity. J. High Energ. Phys. 2011, 139 (2011). https://doi.org/10.1007/JHEP03(2011)139
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DOI: https://doi.org/10.1007/JHEP03(2011)139