Actions on the quiver: discrete quotients on the Coulomb branch

This paper introduces two operations in quiver gauge theories. The first operation, collapse, takes a quiver with a permutation symmetry S_n and gives a quiver with adjoint loops. The corresponding 3d $\mathcal{N}$ \( \mathcal{N} \) = 4 Coulomb branches are related by an orbifold of S_n. The second operation, multi-lacing, 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 ${\mathbb{Z}}_q^{n-1}$ \( {\mathbb{Z}}_q^{n-1} \) . Collapse generalises known cases that appeared in the literature [1–3]. These two operations can be combined to generate new relations between moduli spaces that are constructed using the magnetic construction.