Actions on the quiver: discrete quotients on the Coulomb branch

Abstract

Abstract This paper introduces two operations in quiver gauge theories. The first operation, collapse, takes a quiver with a permutation symmetry Sn and gives a quiver with adjoint loops. The corresponding 3d $$ \mathcal{N} $$ N = 4 Coulomb branches are related by an orbifold of Sn. 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 $$ {\mathbb{Z}}_q^{n-1} $$ 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.