Unifying \( \mathcal{N} = 5 \) and \( \mathcal{N} = 6 \). (English) Zbl 1296.81066
Summary: We write the Lagrangian of the general \( \mathcal{N} = 5 \) three-dimensional superconformal Chern-Simons theory, based on a basic Lie superalgebra, in terms of our recently introduced \( \mathcal{N} = 5 \) three-algebras. These include \( \mathcal{N} = 6 \) and \( \mathcal{N} = 8 \) three-algebras as special cases. When we impose an antisymmetry condition on the triple product, the supersymmetry automatically enhances, and the \( \mathcal{N} = 5 \) Lagrangian reduces to that of the well known \( \mathcal{N} = 6 \) theory, including the ABJM and ABJ models.
MSC:
| 81T13 | Yang-Mills and other gauge theories in quantum field theory |
| 81T60 | Supersymmetric field theories in quantum mechanics |
| 58J28 | Eta-invariants, Chern-Simons invariants |
| 81T30 | String and superstring theories; other extended objects (e.g., branes) in quantum field theory |
| 17A70 | Superalgebras |
| 17B62 | Lie bialgebras; Lie coalgebras |
| 70S05 | Lagrangian formalism and Hamiltonian formalism in mechanics of particles and systems |
References:
| [1] | J. Bagger and N. Lambert, Modeling multiple M2’s, Phys. Rev.D 75 (2007) 045020 [hep-th/0611108] [SPIRES]. |
| [2] | J. Bagger and N. Lambert, Gauge Symmetry and Supersymmetry of Multiple M2-Branes, Phys. Rev.D 77 (2008) 065008 [arXiv:0711.0955] [SPIRES]. |
| [3] | J. Bagger and N. Lambert, Comments On Multiple M2-branes, JHEP02 (2008) 105 [arXiv:0712.3738] [SPIRES]. · doi:10.1088/1126-6708/2008/02/105 |
| [4] | A. Gustavsson, Algebraic structures on parallel M2-branes, Nucl. Phys.B 811 (2009) 66 [arXiv:0709.1260] [SPIRES]. · Zbl 1194.81205 · doi:10.1016/j.nuclphysb.2008.11.014 |
| [5] | O. Aharony, O. Bergman, D.L. Jafferis and J. Maldacena, N = 6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals, JHEP10 (2008) 091 [arXiv:0806.1218] [SPIRES]. · Zbl 1245.81130 · doi:10.1088/1126-6708/2008/10/091 |
| [6] | M. Benna, I. Klebanov, T. Klose and M. Smedbäck, Superconformal Chern-Simons Theories and AdS4/CFT3Correspondence, JHEP09 (2008) 072 [arXiv:0806.1519] [SPIRES]. · Zbl 1245.81263 · doi:10.1088/1126-6708/2008/09/072 |
| [7] | K. Hosomichi, K.-M. Lee, S. Lee, S. Lee and J. Park, N = 5, 6 Superconformal Chern-Simons Theories and M2-branes on Orbifolds, JHEP09 (2008) 002 [arXiv:0806.4977] [SPIRES]. · Zbl 1245.81094 · doi:10.1088/1126-6708/2008/09/002 |
| [8] | J. Bagger and N. Lambert, Three-Algebras and N = 6 Chern-Simons Gauge Theories, Phys. Rev.D 79 (2009) 025002 [arXiv:0807.0163] [SPIRES]. · Zbl 1222.81264 |
| [9] | E.A. Bergshoeff, O. Hohm, D. Roest, H. Samtleben and E. Sezgin, The Superconformal Gaugings in Three Dimensions, JHEP09 (2008) 101 [arXiv:0807.2841] [SPIRES]. · Zbl 1245.81081 · doi:10.1088/1126-6708/2008/09/101 |
| [10] | O. Aharony, O. Bergman and D.L. Jafferis, Fractional M2-branes, JHEP11 (2008) 043 [arXiv:0807.4924] [SPIRES]. · doi:10.1088/1126-6708/2008/11/043 |
| [11] | P. de Medeiros, J. Figueroa-O’Farrill and E. Mendez-Escobar, Superpotentials for superconformal Chern-Simons theories from representation theory, J. Phys.A 42 (2009) 485204 [arXiv:0908.2125] [SPIRES]. · Zbl 1179.81144 |
| [12] | F.-M. Chen, Symplectic Three-Algebra Unifying N = 5, 6 Superconformal Chern-Simons-Matter Theories, JHEP08 (2010) 077 [arXiv:0908.2618] [SPIRES]. · Zbl 1290.81139 · doi:10.1007/JHEP08(2010)077 |
| [13] | J. Bagger and G. Bruhn, Three-Algebras in N = 5, 6 Superconformal Chern-Simons Theories: Representations and Relations, Phys. Rev.D 83 (2011) 025003 [arXiv:1006.0040] [SPIRES]. |
| [14] | A. Gustavsson, Monopoles, three-algebras and ABJM theories with N = 5, 6, 8 supersymmetry, JHEP01 (2011) 037 [arXiv:1012.4568] [SPIRES]. · Zbl 1214.81216 · doi:10.1007/JHEP01(2011)037 |
| [15] | S.-S. Kim and J. Palmkvist, N = 5 three-algebras and 5-graded Lie superalgebras, arXiv:1010.1457 [SPIRES]. · Zbl 1272.81175 |
| [16] | N. Cantarini and V.G. Kac, Classification of linearly compact simple N = 6 3-algebras, arXiv:1010.3599 [SPIRES]. · Zbl 1270.17002 |
| [17] | P. de Medeiros, J. Figueroa-O’Farrill, E. Mendez-Escobar and P. Ritter, On the Lie-algebraic origin of metric 3-algebras, Commun. Math. Phys.290 (2009) 871 [arXiv:0809.1086] [SPIRES]. · Zbl 1259.81081 · doi:10.1007/s00220-009-0760-1 |
| [18] | J. Figueroa-O’Farrill, Simplicity in the Faulkner construction, J. Phys.A 42 (2009) 445206 [arXiv:0905.4900] [SPIRES]. · Zbl 1176.81123 |
| [19] | J.A. de Azcárraga and J.M. Izquierdo, n-ary algebras: a review with applications, J. Phys.A 43 (2010) 293001 [arXiv:1005.1028] [SPIRES]. · Zbl 1202.81187 |
| [20] | B.E.W. Nilsson and J. Palmkvist, Superconformal M2-branes and generalized Jordan triple systems, Class. Quant. Grav.26 (2009) 075007 [arXiv:0807.5134] [SPIRES]. · Zbl 1161.83443 · doi:10.1088/0264-9381/26/7/075007 |
| [21] | J. Palmkvist, Three-algebras, triple systems and 3-graded Lie superalgebras, J. Phys.A 43 (2010) 015205 [arXiv:0905.2468] [SPIRES]. · Zbl 1180.81116 |
| [22] | V.G. Kac, A Sketch of Lie Superalgebra Theory, Commun. Math. Phys.53 (1977) 31 [SPIRES]. · Zbl 0359.17009 · doi:10.1007/BF01609166 |
| [23] | V.G. Kac, Lie Superalgebras, Adv. Math.26 (1977) 8 [SPIRES]. · Zbl 0366.17012 · doi:10.1016/0001-8708(77)90017-2 |
| [24] | L. Frappat, A. Sciarrino and P. Sorba, Dictionary on Lie algebras and superalgebras, Academic Press, London U.K. (2000). · Zbl 0965.17001 |
| [25] | J. Palmkvist, A realization of the Lie algebra associated to a Kantor triple system, J. Math. Phys. 47 (2006) 023505 [math/0504544]. · Zbl 1111.17011 · doi:10.1063/1.2168690 |
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
