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Unifying \( \mathcal{N} = 5 \) and \( \mathcal{N} = 6 \)

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Abstract

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.

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References

  1. J. Bagger and N. Lambert, Modeling multiple M2’s, Phys. Rev. D 75 (2007) 045020 [hep-th/0611108] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  2. J. Bagger and N. Lambert, Gauge Symmetry and Supersymmetry of Multiple M2-Branes, Phys. Rev. D 77 (2008) 065008 [arXiv:0711.0955] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  3. J. Bagger and N. Lambert, Comments On Multiple M2-branes, JHEP 02 (2008) 105 [arXiv:0712.3738] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  4. A. Gustavsson, Algebraic structures on parallel M2-branes, Nucl. Phys. B 811 (2009) 66 [arXiv:0709.1260] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  5. O. Aharony, O. Bergman, D.L. Jafferis and J. Maldacena, N = 6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals, JHEP 10 (2008) 091 [arXiv:0806.1218] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  6. M. Benna, I. Klebanov, T. Klose and M. Smedbäck, Superconformal Chern-Simons Theories and AdS 4 /CFT 3 Correspondence, JHEP 09 (2008) 072 [arXiv:0806.1519] [SPIRES].

    Article  ADS  Google Scholar 

  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, JHEP 09 (2008) 002 [arXiv:0806.4977] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  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].

    MathSciNet  ADS  Google Scholar 

  9. E.A. Bergshoeff, O. Hohm, D. Roest, H. Samtleben and E. Sezgin, The Superconformal Gaugings in Three Dimensions, JHEP 09 (2008) 101 [arXiv:0807.2841] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  10. O. Aharony, O. Bergman and D.L. Jafferis, Fractional M2-branes, JHEP 11 (2008) 043 [arXiv:0807.4924] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  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].

    Google Scholar 

  12. F.-M. Chen, Symplectic Three-Algebra Unifying N = 5, 6 Superconformal Chern-Simons-Matter Theories, JHEP 08 (2010) 077 [arXiv:0908.2618] [SPIRES].

    Article  ADS  Google Scholar 

  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].

    ADS  Google Scholar 

  14. A. Gustavsson, Monopoles, three-algebras and ABJM theories with N = 5, 6, 8 supersymmetry, JHEP 01 (2011) 037 [arXiv:1012.4568] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  15. S.-S. Kim and J. Palmkvist, N = 5 three-algebras and 5-graded Lie superalgebras, arXiv:1010.1457 [SPIRES].

  16. N. Cantarini and V.G. Kac, Classification of linearly compact simple N = 6 3-algebras, arXiv:1010.3599 [SPIRES].

  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].

    Article  ADS  MATH  Google Scholar 

  18. J. Figueroa-O’Farrill, Simplicity in the Faulkner construction, J. Phys. A 42 (2009) 445206 [arXiv:0905.4900] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  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].

    Google Scholar 

  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].

    Article  MathSciNet  ADS  Google Scholar 

  21. J. Palmkvist, Three-algebras, triple systems and 3-graded Lie superalgebras, J. Phys. A 43 (2010) 015205 [arXiv:0905.2468] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  22. V.G. Kac, A Sketch of Lie Superalgebra Theory, Commun. Math. Phys. 53 (1977) 31 [SPIRES].

    Article  ADS  MATH  Google Scholar 

  23. V.G. Kac, Lie Superalgebras, Adv. Math. 26 (1977) 8 [SPIRES].

    Article  MATH  Google Scholar 

  24. L. Frappat, A. Sciarrino and P. Sorba, Dictionary on Lie algebras and superalgebras, Academic Press, London U.K. (2000).

    MATH  Google Scholar 

  25. J. Palmkvist, A realization of the Lie algebra associated to a Kantor triple system, J. Math. Phys. 47 (2006) 023505 [math/0504544].

    Article  MathSciNet  ADS  Google Scholar 

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Correspondence to Jakob Palmkvist.

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ArXiv ePrint: 1103.4860

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Palmkvist, J. Unifying \( \mathcal{N} = 5 \) and \( \mathcal{N} = 6 \) . J. High Energ. Phys. 2011, 88 (2011). https://doi.org/10.1007/JHEP05(2011)088

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