Abstract
A consistent theory of massive gravity, where the graviton acquires mass by spontaneously breaking diffeomorphism invariance, is now well established. We supersymmetrize this construction using N=1 fields. Coupling to N=1 supergravity is done by applying the rules of tensor calculus to construct an action invariant under local N=1 supersymmetry. The supersymmetric action is shown, at the quadratic level, to be free of ghosts and have as its spectrum a massive graviton, two gravitinos (with different masses) and a massive vector.
References
H. van Dam, M.J.G. Veltman, Massive and massless Yang–Mills and gravitational fields. Nucl. Phys. B 22, 397 (1970)
V.I. Zakharov, Linearized gravitation theory and the graviton mass. JETP Lett. 12, 312 (1970)
M. Fierz, W. Pauli, On relativistic wave equations for particles of arbitrary spin in an electromagnetic field. Proc. R. Soc. Lond. A 173, 211 (1939)
D.G. Boulware, S. Deser, Can gravity have a finite range? Phys. Rev. D 6, 3368 (1972)
A.I. Vainshtein, To the problem of nonvanishing graviton mass. Phys. Lett. B 39, 393 (1972)
C.J. Isham, A. Salam, J.A. Strathdee, F-dominance of gravity. Phys. Rev. D 3, 867 (1971)
A.H. Chamseddine, A. Salam, J.A. Strathdee, Strong gravity and supersymmetry. Nucl. Phys. B 136, 248 (1978)
G.R. Dvali, G. Gabadadze, M. Porrati, 4D gravity on a brane in 5D Minkowski space. Phys. Lett. B 485, 208 (2000)
N. Arkani-Hamed, H. Georgi, M.D. Schwartz, Effective field theory for massive gravitons and gravity in theory space. Ann. Phys. 305, 96 (2003)
W. Siegel, Hidden gravity in open-string field theory. Phys. Rev. D 49, 4144 (1994)
G. ’t Hooft, Unitarity in the Brout–Englert–Higgs mechanism for gravity, arXiv:0708.3184 (2007)
Z. Kakushadze, Massless limit of gravitational Higgs mechanism. Int. J. Geom. Methods Mod. Phys. 05, 157 (2008)
A. Chamseddine, V. Mukhanov, Higgs for graviton: simple and elegant solution. J. High Energy Phys. 08, 11 (2010)
L. Alberte, A. Chamseddine, V. Mukhanov, Massive gravity: resolving the puzzle. J. High Energy Phys. 12, 23 (2010)
A. Chamseddine, V. Mukhanov, Massive gravity simplified: a quadratic action. J. High Energy Phys. 08, 91 (2011)
C. de Rham, G. Gabadadze, Generalization of the Fierz–Pauli action. Phys. Rev. D 82, 4 (2010)
C. de Rham, G. Gabadadze, A.J. Tolley, Resummation of massive gravity. Phys. Rev. Lett. 106, 231101 (2011)
S.F. Hassan, R.A. Rosen, Resolving the ghost problem in nonlinear massive gravity. Phys. Rev. Lett. 108(108), 041101 (2012)
S.F. Hassan, R.A. Rosen, A. Schmidt-May, Ghost-free massive gravity with a general reference metric. J. High Energy Phys. 02, 026 (2012)
S. Deser, A. Waldron, Acausality of massive gravity. Phys. Rev. Lett. 110, 111101 (2013)
J. Wess, J. Bagger, Supersymmetry and Supergravity (Princeton University Press, Princeton, 1992)
O. Malaeb, Supersymmetrizing massive gravity. Phys. Rev. D 88, 025002 (2013). doi:10:1103/PhysRevD.88.025002
E. Cremmer, S. Ferrara, L. Girardello, A. Van Proeyen, Yang–Mills theories with local supersymmetry: Lagrangian, transformation laws and super-Higgs effect. Nucl. Phys. B 212, 413 (1983)
P. Nath, R. Arnowitt, A. Chamseddine, Applied N=1 Supergravity (World Scientific, Singapore, 1984)
Acknowledgements
I would like to thank Professor Ali Chamseddine for suggesting the problem and for his many helpful discussions on the subject. I would like to thank the American University of Beirut (Faculty of Science) for support.
Open Access
This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Malaeb, O. Massive gravity with N=1 local supersymmetry. Eur. Phys. J. C 73, 2549 (2013). https://doi.org/10.1140/epjc/s10052-013-2549-9
Received:
Revised:
Published:
DOI: https://doi.org/10.1140/epjc/s10052-013-2549-9