Line bundles over Coulomb branches

TL;DR

This paper constructs a partial resolution of Coulomb branches for gauge theories with flavor symmetry, linking it to geometric objects like affine Grassmannian slices and Hilbert schemes.

Contribution

It introduces a new construction of partial resolutions of Coulomb branches and connects them to various geometric structures for ADE and affine type A quiver gauge theories.

Findings

Partial resolution of Coulomb branch constructed

Identification with slices in affine Grassmannian and Hilbert schemes

Applicable to ADE and affine type A quiver gauge theories

Abstract

This is the third companion paper of arXiv:1601.03586. When a gauge theory has a flavor symmetry group, we construct a partial resolution of the Coulomb branch as a variant of the definition. We identify the partial resolution with a partial resolution of a generalized slice in the affine Grassmannian, Hilbert scheme of points, and resolved Cherkis bow variety for a quiver gauge theory of type ADE or affine type A.