Abstract
We investigate in which sense, at the linearized level, one can extend the 3D topologically massive gravity theory beyond three dimensions. We show that, for each k=1,2,3,⋯ afreetopologicallymassivegaugetheoryin4k−1dimensionscanbedefined describing a massive “spin-2” particle provided one uses a non-standard representation of the massive “spin-2” state which makes use of a two-column Young tableau where each column is of height 2k − 1. We work out the case of k = 2, i.e. 7D, and show, by canonical analysis, that the model describes, unitarily, 35 massive “spin-2” degrees of freedom. The issue of interactions is discussed and compared with the three-dimensional situation.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
S. Deser, R. Jackiw and S. Templeton, Topologically massive gauge theories, Annals Phys. 140 (1982) 372 [Erratum ibid. 185 (1988) 406] [Annals Phys. 281 (2000) 409] [INSPIRE].
E.A. Bergshoeff, O. Hohm and P.K. Townsend, Massive gravity in three dimensions, Phys. Rev. Lett. 102 (2009) 201301 [arXiv:0901.1766] [INSPIRE].
E.A. Bergshoeff, J.J. Fernandez-Melgarejo, J. Rosseel and P.K. Townsend, On ‘new massive’ 4D gravity, JHEP 04 (2012) 070 [arXiv:1202.1501] [INSPIRE].
W. Siegel, Unextended superfields in extended supersymmetry, Nucl. Phys. B 156 (1979) 135 [INSPIRE].
J.F. Schonfeld, A mass term for three-dimensional gauge fields, Nucl. Phys. B 185 (1981) 157 [INSPIRE].
S. Deser, R. Jackiw and S. Templeton, Three-dimensional massive gauge theories, Phys. Rev. Lett. 48 (1982) 975 [INSPIRE].
S.J. Gates, M.T. Grisaru, M. Roček and W. Siegel, Superspace or one thousand and one lessons in supersymmetry, Front. Phys. 58 (1983) 1 [hep-th/0108200] [INSPIRE].
E.A. Bergshoeff, O. Hohm and P.K. Townsend, On higher derivatives in 3D gravity and higher spin gauge theories, Annals Phys. 325 (2010) 1118 [arXiv:0911.3061] [INSPIRE].
P.K. Townsend, K. Pilch and P. van Nieuwenhuizen, Selfduality in odd dimensions, Phys. Lett. B 136 (1984) 38 [Addendum ibid. B 137 (1984) 443] [INSPIRE].
S. Deser and R. Jackiw, ‘Selfduality’ of topologically massive gauge theories, Phys. Lett. B 139 (1984) 371 [INSPIRE].
E.A. Bergshoeff, M. Kovacevic, J. Rosseel, P.K. Townsend and Y. Yin, A spin-4 analog of 3D massive gravity, Class. Quant. Grav. 28 (2011) 245007 [arXiv:1109.0382] [INSPIRE].
T. Curtright, Generalized gauge fields, Phys. Lett. B 165 (1985) 304 [INSPIRE].
J.M.F. Labastida, Massless particles in arbitrary representations of the Lorentz group, Nucl. Phys. B 322 (1989) 185 [INSPIRE].
X. Bekaert and N. Boulanger, Tensor gauge fields in arbitrary representations of GL(D,R): duality and Poincaré lemma, Commun. Math. Phys. 245 (2004) 27 [hep-th/0208058] [INSPIRE].
H. Lü and Y. Pang, Seven-dimensional gravity with topological terms, Phys. Rev. D 81 (2010) 085016 [arXiv:1001.0042] [INSPIRE].
W. Fulton, Young tableaux, with applications to representation theory and geometry, Cambridge University Press, Cambridge U.K. (1997) [ISBN 978-0521567244].
M. Hamermesh, Group theory and its application to physical problems, Dover Publications (1989) [ISBN 978-0486661810].
D. Francia and C.M. Hull, Higher-spin gauge fields and duality, hep-th/0501236 [INSPIRE].
S. Deser, Ghost-free, finite, fourth order D = 3 (alas) gravity, Phys. Rev. Lett. 103 (2009) 101302 [arXiv:0904.4473] [INSPIRE].
A. Achúcarro and P.K. Townsend, A Chern-Simons action for three-dimensional anti-de Sitter supergravity theories, Phys. Lett. B 180 (1986) 89 [INSPIRE].
E. Witten, (2+1)-dimensional gravity as an exactly soluble system, Nucl. Phys. B 311 (1988) 46 [INSPIRE].
E.D. Skvortsov, Frame-like actions for massless mixed-symmetry fields in Minkowski space, Nucl. Phys. B 808 (2009) 569 [arXiv:0807.0903] [INSPIRE].
K. Peeters, A field-theory motivated approach to symbolic computer algebra, Comput. Phys. Commun. 176 (2007) 550 [cs/0608005] [INSPIRE].
K. Peeters, Introducing Cadabra: a symbolic computer algebra system for field theory problems, hep-th/0701238 [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1207.0192
Rights and permissions
About this article
Cite this article
Bergshoeff, E.A., Kovacevic, M., Rosseel, J. et al. On topologically massive spin-2 gauge theories beyond three dimensions. J. High Energ. Phys. 2012, 55 (2012). https://doi.org/10.1007/JHEP10(2012)055
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP10(2012)055