Abstract
We point out that the moduli spaces of all known 3d mathcal{N} = 8 and mathcal{N} = 6 SCFTs, after suitable gaugings of finite symmetry groups, have the form ℂ4r/Γ where Γ is a real or complex reflection group depending on whether the theory is mathcal{N} = 8 or mathcal{N} = 6, respectively. Real reflection groups are either dihedral groups, Weyl groups, or two sporadic cases H3,4 Since the BLG theories and the maximally supersymmetric Yang-Mills theories correspond to dihedral and Weyl groups, it is strongly suggested that there are two yet-tobe-discovered 3d mathcal{N} = 8 theories for H3,4. We also show that all known mathcal{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 x SU(N)-k)/ℤN and (U(N)k x U(N)-k) /ℤk are actually equivalent.
Published Version (
Free)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call