Discrete Gauging in Coulomb branches of Three Dimensional $\mathcal{N}=4$ Supersymmetric Gauge Theories

TL;DR

This paper investigates how gauging discrete non-Abelian symmetries in 3d $ ext{N}=4$ supersymmetric quiver gauge theories affects their Coulomb branches, proposing a new orbifold construction and testing it across multiple quiver families.

Contribution

It introduces and tests a conjecture relating discrete gauging of $S_n$ symmetries to Coulomb branch orbifolds in 3d $ ext{N}=4$ theories, expanding understanding of their moduli space transformations.

Findings

Confirmed the conjecture for three simply laced quiver families.

Validated the orbifold structure of Coulomb branches after discrete gauging.

Extended the analysis to a non-simply laced quiver with $C_2$ symmetry.

Abstract

This paper tests a conjecture on discrete non-Abelian gauging of 3d $\mathcal{N} = 4$ supersymmetric quiver gauge theories. Given a parent quiver with a bouquet of $n$ nodes of rank $1$, invariant under a discrete $S_n$ global symmetry, one can construct a daughter quiver where the bouquet is substituted by a single adjoint $n$ node. Based on the main conjecture in this paper, the daughter quiver corresponds to a theory where the $S_n$ discrete global symmetry is gauged and the new Coulomb branch is a non-Abelian orbifold of the parent Coulomb branch. We demonstrate and test the conjecture for three simply laced families of bouquet quivers and a non-simply laced bouquet quiver with $C_2$ factor in the global symmetry.