Branes, Quivers, and the Affine Grassmannian

TL;DR

This paper explores the connection between brane systems in string theory and the affine Grassmannian, introducing a quiver addition algorithm to generate and study its geometric structure.

Contribution

It presents a novel framework linking brane systems with the affine Grassmannian and introduces a quiver addition algorithm for its construction.

Findings

Explicit quivers for the affine Grassmannian are provided.

A new quiver addition algorithm is developed.

Quivers for new elementary slices are identified.

Abstract

Brane systems provide a large class of gauge theories that arise in string theory. This paper demonstrates how such brane systems fit with a somewhat exotic geometric object, called the affine Grassmannian. This gives a strong motivation to study physical aspects of the affine Grassmannian. Explicit quivers are presented throughout the paper, and a quiver addition algorithm to generate the affine Grassmannian is introduced. An important outcome of this study is a set of quivers for new elementary slices.