Minimally unbalanced quivers

We develop a classification of minimally unbalanced 3d$N=4$ 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$N=4$ 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$N=1$ SQCD with gauge group SU(N_c) and 6d$N=(1,0)$ SQCD with gauge group Sp(N_c) at the respective UV fixed points.