Coulomb branch of a multiloop quiver gauge theory

TL;DR

This paper computes the Coulomb branch of a specific multiloop quiver gauge theory, revealing its structure as a Slodowy slice in a nilpotent cone, and identifies its symplectic resolution and flavor deformation.

Contribution

It explicitly describes the Coulomb branch for a multiloop quiver with one-dimensional framing and connects it to Slodowy slices in Lie algebra theory.

Findings

Coulomb branch identified with a Slodowy slice in the nilpotent cone.

Symplectic resolution with 2r fixed points under Hamiltonian torus action.

Flavor deformation corresponds to a base change of the Slodowy slice.

Abstract

We compute the Coulomb branch of a multiloop quiver gauge theory for the quiver with a single vertex, $r$ loops, one-dimensional framing, and $\dim V=2$. We identify it with a Slodowy slice in the nilpotent cone of the symplectic Lie algebra of rank $r$. Hence it possesses a symplectic resolution with $2r$ fixed points with respect to a Hamiltonian torus action. We also idenfity its flavor deformation with a base change of the full Slodowy slice.