Classification of $$ \mathcal{N} = 6 $$ superconformal theories of ABJM type

@article{Schnabl2008ClassificationO,
  title={Classification of \$\$ \mathcal\{N\} = 6 \$\$ superconformal theories of ABJM type},
  author={Martin Schnabl and Yuji Tachikawa},
  journal={Journal of High Energy Physics},
  year={2008},
  volume={2010},
  pages={1-18}
}
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 $$ \mathcal{N} = 6 $$ supersymmetry are, up to discrete quotients, SU(n) ×U(1), Sp(n) ×U(1), SU(n) ×SU(n), and SU(n) ×SU(m) ×U(1) with possibly additional U(1)’s. Matter representations are restricted… CONTINUE READING

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