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

A bstract It was previously noted that for 3d SCFTs with $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> ≥ 6 the moduli space has the form of ℂ 4 r / 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 $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> ≥ 5 SUSY, where Γ is now a quaternionic reflection group. To do this, we study the moduli space of the known 3d $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 5 SCFTs. For Lagrangian cases, the results for the moduli space are further checked using the superconformal index.