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

Yuji Tachikawa; Gabi Zafrir

doi:10.1007/JHEP12(2019)176

paper

Reflection groups and 3d $N \geq$ 6 SCFTs

arXiv:1908.03346 · doi:10.1007/JHEP12(2019)176

Abstract

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 $C^{4 r} /Γ$ 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 there are two yet-to-be-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 $(S U (N)_{k} \times S U (N)_{- k}) / Z_{N}$ and $(U (N)_{k} \times U (N)_{- k}) / Z_{k}$ are actually equivalent.

arXiv comment37 pages

Reflection groups and 3d $N \geq$ 6 SCFTs

Abstract

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Reflection groups and 3d N≥ 6 SCFTs

Abstract

References in corpus (45)

Cited by in corpus (14)

Reflection groups and 3d $N \geq$ 6 SCFTs