$E_8$ instantons on type-A ALE spaces and supersymmetric field theories

TL;DR

This paper explores the relationship between E8 instantons on type-A ALE spaces and supersymmetric field theories by explicitly deriving gauge theories and dual descriptions from M5-brane configurations.

Contribution

It provides an explicit algorithm to determine 6d quiver gauge theories, class S descriptions, and mirror quivers for E8 instantons on type-A ALE spaces with arbitrary holonomy.

Findings

Derived 6d quiver gauge theories for E8 instantons.

Established class S descriptions of the compactified theories.

Constructed mirror quivers for T^3 compactifications.

Abstract

We consider the 6d superconformal field theory realized on M5-branes probing the $E_8$ end-of-the-world brane on the deformed and resolved $\mathbb{C}^2/\mathbb{Z}_k$ singularity. We give an explicit algorithm which determines, for arbitrary holonomy at infinity, the 6d quiver gauge theory on the tensor branch, the type-A class S description of the $T^2$ compactification, and the star-shaped quiver obtained as the mirror of the $T^3$ compactification.