Discrete gauging and Hasse diagrams

Abstract

We analyse the Higgs branch of 4d \mathcal{N}=2𝒩=2 SQCD gauge theories with non-connected gauge groups \widetilde{\mathrm{SU}}(N) = \mathrm{SU}(N) \rtimes_{I,II} \mathbb{Z}_2SŨ(N)=SU(N)⋊I,IIℤ2 whose study was initiated in . We derive the Hasse diagrams corresponding to the Higgs mechanism using adapted characters for representations of non-connected groups. We propose 3d \mathcal{N}=4𝒩=4 magnetic quivers for the Higgs branches in the type II discrete gauging case, in the form of recently introduced wreathed quivers, and provide extensive checks by means of Coulomb branch Hilbert series computations.