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Classification of N=6 superconformal theories of ABJM type · Around

2008

Classification of N=6 superconformal theories of ABJM type

Schnabl, Martin, Tachikawa, Yuji

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Studying the supersymmetry enhancement mechanism of Aharony, Bergman, Jafferis and Maldacena, we find a simple condition on the gauge group generators for the matter fields.

We analyze all possible compact Lie groups and their representations.
The only allowed gauge groups leading to the manifest N=6 supersymmetry are, up to discrete quotients, SU(n) x U(1), Sp(n) x U(1), SU(n) x SU(n), and SU(n) x SU(m) x U(1) with possibly additional U(1)'s.
Matter representations are restricted to be the (bi)fundamentals.

Built on

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P. Di Francesco, P. Mathieu and D. Senechal, “Conformal Field Theory,” Springer, 1997
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Similar

J. H. Schwarz, “Superconformal Chern-Simons theories,” JHEP
2004
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J. Bagger and N. Lambert, “Modeling multiple M2’s,” Phys. Rev. D
2007
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D. Gaiotto and X. Yin, “Notes on superconformal Chern-Simons-matter theories,” JHEP
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2007
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A. Gustavsson, “Algebraic structures on parallel M2-branes,” arXiv:0709.1260 [hep-th]
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D. Gaiotto and E. Witten, “Janus Configurations, Chern-Simons Couplings, and the Theta-Angle in 𝒩 = 4 {\mathcal{N}}\!=4 Super Yang-Mills Theory,” arXiv:0804.2907 [hep-th]
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K. Hosomichi, K. M. Lee, S. Lee, S. Lee and J. Park, “ 𝒩 = 4 {\mathcal{N}}\!=4 Superconformal Chern-Simons Theories with Hyper and Twisted Hyper Multiplets,” arXiv:0805.3662 [hep-th]
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O. Aharony, O. Bergman, D. L. Jafferis and J. Maldacena, “ 𝒩 = 6 {\mathcal{N}}\!=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals,” arXiv:0806.1218 [hep-th]
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M. Benna, I. Klebanov, T. Klose and M. Smedback, “Superconformal Chern-Simons Theories and AdS 4 \mathrm{AdS}_{4} /CFT 3 Correspondence,” arXiv:0806.1519 [hep-th]
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K. Hosomichi, K. M. Lee, S. Lee, S. Lee and J. Park, “ 𝒩 = 5 {\mathcal{N}}\!=5 ,6 Superconformal Chern-Simons Theories and M2-branes on Orbifolds,” arXiv:0806.4977 [hep-th]
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J. P. Gauntlett and J. B. Gutowski, “Constraining Maximally Supersymmetric Membrane Actions,” arXiv:0804.3078 [hep-th]
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J. Bagger and N. Lambert, “Three-Algebras and 𝒩 = 6 {\mathcal{N}}\!=6 Chern-Simons Gauge Theories,” arXiv:0807.0163 [hep-th]
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Cited in the paper.

Then

J. Bagger and N. Lambert, “Gauge Symmetry and Supersymmetry of Multiple M2-Branes,” Phys. Rev. D
Original
2008
Closest in time.
G. Papadopoulos, “M2-branes, 3-Lie Algebras and Plücker relations,” JHEP
Original
2008
Closest in time.
A. Gustavsson, “Selfdual strings and loop space Nahm equations,” JHEP
Original
2008
Closest in time.

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