Discrete gauging and Hasse diagrams

TL;DR

This paper investigates the Higgs branches of 4d $ ext{N}=2$ SQCD theories with non-connected gauge groups, deriving Hasse diagrams and proposing magnetic quivers for the Higgs mechanism, supported by Hilbert series checks.

Contribution

It introduces a method to derive Hasse diagrams for non-connected gauge groups and proposes new magnetic quivers for the Higgs branches in discrete gauging cases.

Findings

Derived Hasse diagrams for non-connected gauge groups.

Proposed 3d $ ext{N}=4$ magnetic quivers using wreathed quivers.

Validated proposals with Coulomb branch Hilbert series computations.

Abstract

We analyse the Higgs branch of 4d $\mathcal{N}=2$ SQCD gauge theories with non-connected gauge groups $\widetilde{\mathrm{SU}}(N) = \mathrm{SU}(N) \rtimes_{I,II} \mathbb{Z}_2$ whose study was initiated in arXiv:1804.01108. We derive the Hasse diagrams corresponding to the Higgs mechanism using adapted characters for representations of non-connected groups. We propose 3d $\mathcal{N}=4$ magnetic quivers for the Higgs branches in the type $I$ discrete gauging case, in the form of recently introduced wreathed quivers, and provide extensive checks by means of Coulomb branch Hilbert series computations.