On the Brane Configuration of $N=(4,4)$ 2D supersymmetric gauge theory

TL;DR

This paper explores the brane configurations of 2D N=(4,4) supersymmetric gauge theories, analyzing their mirror duals, Higgs branches, and string theory realizations with orientifold planes.

Contribution

It provides a detailed study of brane setups for various gauge groups and matter representations, including mirror symmetry and Matrix theory realizations.

Findings

Mirror theories become equivalent at strong coupling.

Higgs branch parametrized by adjoint matter in specific cases.

Involvement of orientifold planes in certain configurations.

Abstract

We study two dimensional $N=(4,4)$ supersymmetric gauge theories with various gauge groups and various hypermultiplets in the fundamental as well as bi-fundamental and adjoint representations. They have " mirror theories " which become equivalent to them at the strong coupling. The theory with one fundamental and one adjoint has a Higgs branch which is parametrized by the adjoint matter. We also consider theories which involve an orientifold plane. The brane realization of the Matrix theory formulation of NS 5-branes in Type II string theories is also considered.