6d N=10$$ \mathcal{N}=\left(1,0\right) $$ theories on T2 and class S theories. Part I

Abstract

We show that the $$ \mathcal{N}=\left(1,0\right) $$ superconformal theory on a single M5 brane on the ALE space of type G = A n , D n , E n , when compactified on T2, becomes a class S theory of type G on a sphere with two full punctures and a simple puncture. We study this relation from various viewpoints. Along the way, we develop a new method to study the 4d SCFT arising from the T2 compactification of a class of 6d $$ \mathcal{N}=\left(1,0\right) $$ theories we call very Higgsable.