Minimally Unbalanced Quivers

TL;DR

This paper classifies minimally unbalanced 3d N=4 quiver gauge theories, revealing their Coulomb branch isometry groups and providing a framework to understand hyperk"ahler cones relevant for Higgs branch descriptions across various dimensions.

Contribution

It offers a classification of minimally unbalanced 3d N=4 quiver gauge theories with specific isometry groups, linking Coulomb and Higgs branch constructions.

Findings

Classification of minimally unbalanced quivers with classical and exceptional Lie groups.

Identification of Coulomb branch isometry groups as single factors.

Application to Higgs branch descriptions in higher-dimensional theories.

Abstract

We develop a classification of \emph{minimally unbalanced} $3d~\mathcal{N}=4$ quiver gauge theories. These gauge theories are important because the isometry group $G$ of their Coulomb branch contains a single factor, which is either a classical or an exceptional Lie group. Concurrently, this provides a classification of hyperk\"ahler cones with isometry group $G$ which are obtainable by Coulomb branch constructions. HyperK\"ahler cones such as Coulomb branches of $3d~\mathcal{N}=4$ quivers are indispensable tools for describing Higgs branches of different theories in various dimensions. In particular, they are used to describe Higgs branches of $5d~\mathcal{N}=1$ SQCD with gauge group $SU(N_c)$ and $6d~\mathcal N = (1,0)$ SQCD with gauge group $Sp(N_c)$ at the respective UV fixed points.