Abstract
There exists two distinct off-shell \( \mathcal{N} \) = 2 supergravities in three dimensions. They are also referred to as \( \mathcal{N} \) = (1, 1) and \( \mathcal{N} \) = (2, 0) supergravities, and they arise from the coupling of the Weyl multiplet to a compensating scalar or vector multiplet, respectively, followed by fixing of conformal symmetries. The \( \mathcal{N} \) = (p, q) terminology refers to the underlying anti-de Sitter superalgebras OSp(2, p) ⊕ OSp(2, q) with R-symmetry group SO(p) × SO(q). We construct off-shell invariants of these theories up to fourth order in derivatives. As an application of these results, we determine the special combinations of the \( \mathcal{N} \) = (1, 1) invariants that admit anti-de Sitter vacuum solution about which there is a ghost-free massive spin-2 multiplet of propagating modes. We also show that the \( \mathcal{N} \) =(2,0) invariants do not allow such possibility.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
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].
A. Achucarro and P.K. Townsend, Extended supergravities in d = (2 + 1) as Chern-Simons theories, Phys. Lett. B 229 (1989) 383 [INSPIRE].
P.S. Howe, J.M. Izquierdo, G. Papadopoulos and P.K. Townsend, New supergravities with central charges and Killing spinors in (2 + 1)-dimensions, Nucl. Phys. B 467 (1996) 183 [hep-th/9505032] [INSPIRE].
E.A. Bergshoeff, O. Hohm, J. Rosseel, E. Sezgin and P.K. Townsend, More on massive 3D supergravity, Class. Quant. Grav. 28 (2011) 015002 [arXiv:1005.3952] [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].
R. Andringa et al., Massive 3D supergravity, Class. Quant. Grav. 27 (2010) 025010 [arXiv:0907.4658] [INSPIRE].
E.A. Bergshoeff, O. Hohm, J. Rosseel, E. Sezgin and P.K. Townsend, On critical massive (super)gravity in AdS 3, J. Phys. Conf. Ser. 314 (2011) 012009 [arXiv:1011.1153] [INSPIRE].
M. Roček and P. van Nieuwenhuizen, N ≥ 2 supersymmetric Chern-Simons terms as D = 3 extended conformal supergravity, Class. Quant. Grav. 3 (1986) 43 [INSPIRE].
H. Nishino and S.J. Gates Jr., Chern-Simons theories with supersymmetries in three-dimensions, Int. J. Mod. Phys. A 8 (1993) 3371 [INSPIRE].
E. Bergshoeff, S. Cecotti, H. Samtleben and E. Sezgin, Superconformal σ-models in three dimensions, Nucl. Phys. B 838 (2010) 266 [arXiv:1002.4411] [INSPIRE].
B.M. Zupnik and D.G. Pak, Superfield formulation of the simplest three-dimensional gauge theories and conformal supergravities, Theor. Math. Phys. 77 (1988) 1070 [Teor. Mat. Fiz. 77 (1988) 97] [INSPIRE].
S.M. Kuzenko, U. Lindström, M. Roček, I. Sachs and G. Tartaglino-Mazzucchelli, Three-dimensional N = 2 supergravity theories: from superspace to components, Phys. Rev. D 89 (2014) 085028 [arXiv:1312.4267] [INSPIRE].
S.M. Kuzenko and G. Tartaglino-Mazzucchelli, Three-dimensional N = 2 (AdS) supergravity and associated supercurrents, JHEP 12 (2011) 052 [arXiv:1109.0496] [INSPIRE].
S.M. Kuzenko and J. Novak, Supergravity-matter actions in three dimensions and Chern-Simons terms, JHEP 05 (2014) 093 [arXiv:1401.2307] [INSPIRE].
S.M. Kuzenko, U. Lindström and G. Tartaglino-Mazzucchelli, Off-shell supergravity-matter couplings in three dimensions, JHEP 03 (2011) 120 [arXiv:1101.4013] [INSPIRE].
J.M. Izquierdo and P.K. Townsend, Supersymmetric space-times in (2 + 1) AdS supergravity models, Class. Quant. Grav. 12 (1995) 895 [gr-qc/9501018] [INSPIRE].
B. de Wit, A.K. Tollsten and H. Nicolai, Locally supersymmetric D = 3 nonlinear σ-models, Nucl. Phys. B 392 (1993) 3 [hep-th/9208074] [INSPIRE].
N.S. Deger, A. Kaya, E. Sezgin and P. Sundell, Matter coupled AdS 3 supergravities and their black strings, Nucl. Phys. B 573 (2000) 275 [hep-th/9908089] [INSPIRE].
N.S. Deger, A. Kaya, H. Samtleben and E. Sezgin, Supersymmetric warped AdS in extended topologically massive supergravity, Nucl. Phys. B 884 (2014) 106 [arXiv:1311.4583] [INSPIRE].
M.F. Sohnius and P.C. West, The new minimal formulation of N = 1 supergravity and its tensor calculus, in Proceedings, Quantum Structure Of Space and Time, London U.K. (1981), pg. 187 and TH. 3205, CERN, Geneva Switzerland (1981) [INSPIRE].
Y. Liu and Y.-W. Sun, On the generalized massive gravity in AdS 3, Phys. Rev. D 79 (2009) 126001 [arXiv:0904.0403] [INSPIRE].
H. Lü, C.N. Pope, E. Sezgin and L. Wulff, Critical and non-critical Einstein-Weyl supergravity, JHEP 10 (2011) 131 [arXiv:1107.2480] [INSPIRE].
C. Closset, T.T. Dumitrescu, G. Festuccia and Z. Komargodski, Supersymmetric field theories on three-manifolds, JHEP 05 (2013) 017 [arXiv:1212.3388] [INSPIRE].
C. Closset, T.T. Dumitrescu, G. Festuccia, Z. Komargodski and N. Seiberg, Comments on Chern-Simons contact terms in three dimensions, JHEP 09 (2012) 091 [arXiv:1206.5218] [INSPIRE].
C. Closset, T.T. Dumitrescu, G. Festuccia, Z. Komargodski and N. Seiberg, Contact terms, unitarity and F-maximization in three-dimensional superconformal theories, JHEP 10 (2012) 053 [arXiv:1205.4142] [INSPIRE].
N. Ohta, A complete classification of higher derivative gravity in 3D and criticality in 4D, Class. Quant. Grav. 29 (2012) 015002 [arXiv:1109.4458] [INSPIRE].
B. de Wit and F. Saueressig, Off-shell N = 2 tensor supermultiplets, JHEP 09 (2006) 062 [hep-th/0606148] [INSPIRE].
G. Festuccia and N. Seiberg, Rigid supersymmetric theories in curved superspace, JHEP 06 (2011) 114 [arXiv:1105.0689] [INSPIRE].
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].
H. Saida and J. Soda, Statistical entropy of BTZ black hole in higher curvature gravity, Phys. Lett. B 471 (2000) 358 [gr-qc/9909061] [INSPIRE].
P. Kraus and F. Larsen, Microscopic black hole entropy in theories with higher derivatives, JHEP 09 (2005) 034 [hep-th/0506176] [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1412.3118
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Alkaç, G., Basanisi, L., Bergshoeff, E.A. et al. Massive \( \mathcal{N} \) = 2 supergravity in three dimensions. J. High Energ. Phys. 2015, 125 (2015). https://doi.org/10.1007/JHEP02(2015)125
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP02(2015)125