Magnetic quivers for rank 1 theories

TL;DR

This work builds magnetic quivers and Hasse diagrams for Higgs branches of rank-1 4d N=2 SCFTs and situates these theories within infinite families derived from higher-dimensional physics. By folding simply-laced 5d N=1 quivers with Z_k twists, the authors generate magnetic quivers for various rank-1 theories, compute their Higgs-branch Hilbert series via refined plethystic techniques, and illustrate the partial ordering of moduli spaces through Hasse diagrams. The paper confirms consistency with known class S and S-fold constructions, and extends the framework to higher ranks, including orbifold Higgs branches H^d/Z_k and explicit HWGs for the Coulomb branches. The approach provides a unifying, computationally checkable method to connect rank-1 SCFT data to higher-dimensional origins and to predict the structure of moduli spaces via quiver operations and symmetry considerations.

Abstract

Magnetic quivers and Hasse diagrams for Higgs branches of rank 1 $4d$ $\mathcal{N}=2$ SCFTs are provided. These rank 1 theories fit naturally into families of higher rank theories, originating from higher dimensions, which are addressed.