E 8 instantons on type-A ALE spaces and supersymmetric field theories

Abstract

We consider the 6d superconformal field theory realized on M5-branes probing the E8 end-of-the-world brane on the deformed and resolved ℂ2/ℤk 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 T2 compactification, and the star-shaped quiver obtained as the mirror of the T3 compactification.