$$ \mathcal{N} $$ = 5 SCFTs and quaternionic reflection groups

Abstract

Abstract It was previously noted that for 3d SCFTs with $$ \mathcal{N} $$ N ≥ 6 the moduli space has the form of ℂ4r/Γ, where Γ is a complex reflection group, at least following suitable gauging of finite symmetries. Here we argue that this observation can be extended also to 3d SCFTs with $$ \mathcal{N} $$ N ≥ 5 SUSY, where Γ is now a quaternionic reflection group. To do this, we study the moduli space of the known 3d $$ \mathcal{N} $$ N = 5 SCFTs. For Lagrangian cases, the results for the moduli space are further checked using the superconformal index.