# Discrete gauging and Hasse diagrams

### Submission summary

 As Contributors: Antoine Bourget Arxiv Link: https://arxiv.org/abs/2105.08755v2 (pdf) Date accepted: 2021-08-04 Date submitted: 2021-07-27 17:16 Submitted by: Bourget, Antoine Submitted to: SciPost Physics Academic field: Physics Specialties: High-Energy Physics - Theory

### 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.

Published as SciPost Phys. 11, 026 (2021)

### List of changes

The following changes were made at the request of the referees (more explanations are given in the individual answers).
- Discussion of how to recognize slices at the beginning of Section 3
- Definition of wreathed product at the beginning of Section 4.1
- Paragraph added in Section 4.3 to explain the distinction between 3d mirror symmetry and magnetic quiver.
- Footnotes 5 and 7 added.