×

zbMATH — the first resource for mathematics

The maximal \(D=5\) supergravities. (English) Zbl 1207.83073
Summary: The general Lagrangian for maximal supergravity in five spacetime dimensions is presented with vector potentials in the \(\overline{27}\) and tensor fields in the 27 representation of \(E_{6(6)}\). This novel tensor–vector system is subject to an intricate set of gauge transformations, describing \(3(27 - t)\) massless helicity degrees of freedom for the vector fields and \(3t\) massive spin degrees of freedom for the tensor fields, where the (even) value of \(t\) depends on the gauging. The kinetic term of the tensor fields is accompanied by a unique Chern–Simons coupling which involves both vector and tensor fields. The Lagrangians are completely encoded in terms of the embedding tensor which defines the \(E_{6(6)}\) subgroup that is gauged by the vectors. The embedding tensor is subject to two constraints which ensure the consistency of the combined vector–tensor gauge transformations and the supersymmetry of the full Lagrangian. This new formulation encompasses all possible gaugings.

MSC:
83E50 Supergravity
81T60 Supersymmetric field theories in quantum mechanics
Software:
LiE
PDF BibTeX XML Cite
Full Text: DOI arXiv
References:
[1] Cremmer, E., \(N = 8\) supergravity, (), 137
[2] Günaydin, M.; Romans, L.J.; Warner, N.P., Compact and non-compact gauged supergravity theories in five dimensions, Nucl. phys. B, 272, 598, (1986)
[3] Pernici, M.; Pilch, K.; van Nieuwenhuizen, P., Gauged maximally extended supergravity in seven dimension, Phys. lett. B, 143, 103, (1984)
[4] Townsend, P.K.; Pilch, K.; van Nieuwenhuizen, P., Self-duality in odd dimensions, Phys. lett. B, 136, 38, (1984)
[5] Andrianopoli, L.; Cordaro, F.; Fré, P.; Gualtieri, L., Non-semisimple gaugings of \(D = 5\), \(\mathcal{N} = 8\) supergravity and FDA.s, Class. quantum grav., 18, 395, (2001) · Zbl 0982.83042
[6] de Wit, B.; Samtleben, H.; Trigiante, M., On Lagrangians and gaugings of maximal supergravities, Nucl. phys. B, 655, 93, (2003) · Zbl 1009.83063
[7] de Wit, B.; Nicolai, H.; de Wit, B.; Nicolai, H., \(N = 8\) supergravity, Phys. lett. B, Nucl. phys. B, 208, 323, (1982)
[8] de Wit, B.; Samtleben, H.; Trigiante, M., Gauging maximal supergravities, Fortschr. phys., 52, 489-496, (2004) · Zbl 1055.83512
[9] de Wit, B.; Samtleben, H.; Trigiante, M., Maximal supergravity from IIB flux compactifications, Phys. lett. B, 583, 338, (2004) · Zbl 1246.83199
[10] M. van Leeuwen, A. Cohen, B. Lisser, LiE, a Computer Algebra Package for Lie Group Computations, Computer Algebra Nederland, Amsterdam, 1992
[11] Hull, C.M.; Catal-Ozer, A., Compactifications with S-duality twists, Jhep, 0310, 034, (2003)
[12] Andrianopoli, L.; Ferrara, S.; Lledo, M.A., No-scale \(D = 5\) supergravity from scherk – schwarz reduction of \(D = 6\) theories, Jhep, 0406, 018, (2004) · Zbl 1060.83055
[13] Bergshoeff, E.; Cucu, S.; de Wit, T.; Gheerardyn, J.; Vandoren, S.; Van Proeyen, A., \(N = 2\) supergravity in five dimensions revisited, Class. quantum grav., 21, 3015, (2004) · Zbl 1061.83061
[14] Cowdall, P.M., On gauged supergravity in six dimensions, Jhep, 9906, 018, (1999) · Zbl 0951.83057
[15] Alonso-Alberca, N.; Ortin, T., Gauged/massive supergravities in diverse dimensions, Nucl. phys. B, 651, 263, (2003) · Zbl 1008.83029
[16] Nicolai, H.; Samtleben, H.; Nicolai, H.; Samtleben, H., Compact and noncompact gauged maximal supergravities in three dimensions, Phys. rev. lett., Jhep, 0104, 022, (2001) · Zbl 0969.83548
[17] B. de Wit, H. Samtleben, M. Trigiante, The maximal \(D = 4\) supergravities, in preparation
[18] Sezgin, E.; Salam, A., Maximal extended supergravity theory in seven dimensions, Phys. lett. B, 118, 359, (1982)
[19] de Wit, B.; Samtleben, H., Gauged maximal supergravities and hierarchies of nonabelian vector-tensor systems, Fortschr. phys., 53, 586-591, (2005) · Zbl 1069.83509
[20] de Wit, B., M-theory duality and BPS-extended supergravity, Int. J. mod. phys. A, 16, 1002, (2001), Proc. Strings 2000, Ann Arbor · Zbl 0984.81132
[21] de Wit, B.; Nicolai, H., Hidden symmetries, central charges and all that, Class. quantum grav., 18, 3095-3112, (2001), Proc. Gürsey Memorial Conference II: M-Theory and Dualities, Istanbul · Zbl 0989.83061
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.