Minimally unbalanced quivers

Abstract We develop a classification of minimally unbalanced 3d N = 4 $$ \mathcal{N}=4 $$ 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 hyperkähler cones with isometry group G which are obtainable by Coulomb branch constructions. HyperKähler cones such as Coulomb branches of 3d N = 4 $$ \mathcal{N}=4 $$ 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 N = 1 $$ \mathcal{N}=1 $$ SQCD with gauge group SU(N c ) and 6d N = 1 0 $$ \mathcal{N}=\left(1,0\right) $$ SQCD with gauge group Sp(N c) at the respective UV fixed points