Three-dimensional Quiver Gauge Theories Research Articles

Bosonizing three-dimensional quiver gauge theories

We start with the recently conjectured 3d bosonization dualities and gauge global symmetries to generate an infinite sequence of new dualities. These equate theories with non-Abelian product gauge groups and bifundamental matter. We uncover examples of Bose/Bose and Fermi/Fermi dualities, as well as a sequence of dualities between theories with scalar matter in two-index representations. Our conjectures are consistent with level/rank duality in massive phases.

On three-dimensional quiver gauge theories of type B

We study three-dimensional supersymmetric quiver gauge theories with a nonsimply laced global symmetry primarily focusing on framed affine BN quiver theories. Using a supersymmetric partition function on a three sphere, and its transformation under S-duality, we study the three-dimensional ADHM quiver for SO(2N + 1) instantons with a half-integer Chern-Simons coupling. The theory after S-duality has no Lagrangian, and can not be represented by a single quiver, however its partition function can be conveniently described by a collection of framed affine BN quivers. This correspondence can be conjectured to generalize three-dimensional mirror symmetry to theories with nontrivial Chern-Simons terms. In addition, we propose a formula for the superconformal index of a theory described by a framed affine BN quiver.

The ADHM-like constructions for instantons on [formula omitted] and three-dimensional gauge theories

We study the moduli spaces of self-dual instantons on CP2 in a simple group G. When G is a classical group, these instanton solutions can be realized using ADHM-like constructions which can be naturally embedded into certain three-dimensional quiver gauge theories with four supercharges. The topological data for such instanton bundles and their relations to the quiver gauge theories are described. Based on such gauge theory constructions, we compute the Hilbert series of the moduli spaces of instantons that correspond to various configurations. The results turn out to be equal to the Hilbert series of their counterparts on C2 upon an appropriate mapping. We check the former against the Hilbert series derived from the blowup formula for the Hirzebruch surface F1 and find an agreement. The connection between the moduli spaces of instantons on such two spaces is explained in detail.

Mirror symmetry in three dimensions via gauged linear quivers

Starting from mirror pairs consisting only of linear (framed A-type) quivers, we demonstrate that a wide class of three-dimensional quiver gauge theories with N=4 supersymmetry and their mirror duals can be obtained by suitably gauging flavor symmetries. Infinite families of mirror pairs including various quivers of D and E-type and their affine extensions, star-shaped quivers, and quivers with symplectic gauge groups may be generated in this fashion. We present two different computational strategies to perform the aforementioned gauging procedure - one of them involves N=2* classical parameter space description, while the other one uses partition functions of the N=4 theories on S^3. The partition function, in particular, turns out to be an extremely efficient tool for implementing this gauging procedure as it readily generalizes to arbitrary size of the quiver and arbitrary rank of the gauge group at each node. For most examples of mirror pairs obtained via this procedure, we perform additional checks of mirror symmetry using the Hilbert series.

Supersymmetric quiver gauge theories on the lattice

Abstract In this paper we detail the lattice constructions of several classes of supersymmetric quiver gauge theories in two and three Euclidean spacetime dimensions possessing exact supersymmetry at finite lattice spacing. Such constructions are obtained through the methods of topological twisting and geometric discretization of Euclidean Yang-Mills theories with eight and sixteen supercharges in two and three dimensions. We detail the lattice constructions of two-dimensional quiver gauge theories possessing four and eight supercharges and three-dimensional quiver gauge theories possessing eight supercharges.