Reflection groups and 3d N$$ \mathcal{N} $$> 6 SCFTs

Yuji Tachikawa, Gabi Zafrir
2019 Journal of High Energy Physics  
We point out that the moduli spaces of all known 3d N = 8 and N = 6 SCFTs, after suitable gaugings of finite symmetry groups, have the form C 4r /Γ where Γ is a real or complex reflection group depending on whether the theory is N = 8 or N = 6, respectively. Real reflection groups are either dihedral groups, Weyl groups, or two sporadic cases H 3,4 . Since the BLG theories and the maximally supersymmetric Yang-Mills theories correspond to dihedral and Weyl groups, it is strongly suggested that
more » ... here are two yet-tobe-discovered 3d N = 8 theories for H 3,4 . We also show that all known N = 6 theories correspond to complex reflection groups collectively known as G(k, x, N ). Along the way, we demonstrate that two ABJM theories (SU(N ) k × SU(N ) −k )/Z N and (U(N ) k × U(N ) −k )/Z k are actually equivalent.
doi:10.1007/jhep12(2019)176 fatcat:lmvrqc7qafhm7b67cqsjpvz6ou