Reflection groups and 3d N > 6 SCFTs

Yuji Tachikawa, Gabi Zafrir

Research output: Contribution to journalArticlepeer-review


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 ℂ4r/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 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-to­ be-discovered 3d N = 8 theories for H3,4. 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 x SU(N)-k)/ℤN and (U(N)k x U(N)-k) /ℤk are actually equivalent.

Original languageEnglish
Article number176
JournalJournal of High Energy Physics
Issue number12
StatePublished - 1 Dec 2019
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2020, The Author(s).


  • Discrete Symmetries
  • Extended Supersymmetry
  • Supersymmetry and Duality

ASJC Scopus subject areas

  • Nuclear and High Energy Physics


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