The Coulomb branch of an SQFT with eight supercharges is another maximal branch of the space of supersymmetric vacua. For 3D $\mathcal{N}=4$ the Coulomb branch is parametrized by VEVs of (dressed) monopole operators [36, 37] and is geometrically a symplectic singularity.

In mathematics, a quiver is a directed graph, defined as a set of vertices connected by arrows. The double quiver is obtained by adjoining the reverse arrow for each arrow—thus, an undirected edge arises. In physics, quivers (in string theory [42]) or mooses (in particle physics [43]) are graphs representing the matter content of (usually supersymmetric) gauge theories. Quivers $\mathsf{Q}$ for eight supercharge theories are undirected by convention. Expressing $\mathsf{Q}$ in four supercharges (e.g., a hyper becomes two chirals), $\mathsf{Q}$ becomes a double quiver.

This generalization was proposed in [50], in analogy with Dynkin diagrams. Each node can be given a length, and the nodes with maximal length are called long. Although this has no known Lagrangian description yet, it is motivated by brane systems with orientifolds [51], and the Coulomb branch has a working definition in terms of Hilbert series [50] and is mathematically understood [62].

Condition (i) means that every single unitary gauge node is good, i.e., having enough charged matter fields. Condition (ii) eliminates quivers that are a single U(1) node (plus some adjoint hypermultiplets). Condition (iii) detects moduli spaces of instantons on ${\mathbb{C}}^2$, which come with a free hypermultiplet and therefore have two monopole operators that saturate the unitarity bound [50]. With our definition, an affine Dynkin quiver for the simple algebra $\mathfrak{g}$ wherein all ranks equal the $k$ fold of the dual Coxeter labels, which we denote $k·\mathsf{Q}(\widehat{\mathfrak{g}})$, is good.