Abstract
We develop a classification of 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 hyperkähler cones with isometry group G which are obtainable by Coulomb branch constructions. HyperKähler 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(Nc) and 6d mathcal{N}=left(1,0right) SQCD with gauge group Sp(Nc) at the respective UV fixed points.
Highlights
The study of the vacuum structure of SQED and SQCD with eight supercharges [1,2,3,4,5] constitutes a prodigious bridge between physics and mathematics
In this paper we present a classification of 3d N = 4 gauge theories that have a common property: their Coulomb branch has an isometry group G which has a single factor, but need not necessarily be a closure of a nilpotent orbit of Lie(G)
To D-type, minimally unbalanced quivers with SO(2n + 1) global symmetry divide into cases based on two parameters, a and n, where a is the position of the extra unbalanced node and n is the total number of balanced nodes which are in the shape of a B-type Dynkin diagram
Summary
The study of the vacuum structure of SQED and SQCD with eight supercharges [1,2,3,4,5] constitutes a prodigious bridge between physics and mathematics. Where the round and square nodes denote gauge and flavor groups, respectively.8 This Coulomb branch is minimally generated by operators Oi satisfying ∆(Oi) = 1, and transforming under the adjoint representation of SU(10). We perform this computation for all different choices of the position of the non-zero component of w In this way, we obtain all possible minimally unbalanced quivers with a balanced subset of nodes corresponding to a certain Dynkin diagram. We begin our classification of minimally unbalanced quiver gauge theories with Coulomb branch isometry G that corresponds to a laced Dynkin diagram and the unbalanced node is connected by a laced edge.
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