Actions on the quiver -- Discrete quotients on the Coulomb branch

This paper introduces two operations in quiver gauge theories. The first operation takes a quiver with a permutation symmetry $S_n$ and gives a quiver with adjoint loops. The corresponding 3d $\mathcal{N}=4$ Coulomb branches are related by an orbifold of $S_n$. The second operation takes a quiver with $n$ nodes connected by edges of multiplicity $k$ and replaces them by $n$ nodes of multiplicity $qk$. The corresponding Coulomb branch moduli spaces are related by an orbifold of type $\mathbb{Z}_q^{n-1}$. The first operation generalises known cases that appeared in the literature. These two operations can be combined to generate new relations between moduli spaces that are constructed using the magnetic construction.