Elliptic Blowup Equations for 6d SCFTs. II: Exceptional Cases

Understand

The building blocks of 6d $(1,0)$ SCFTs include certain rank one theories with gauge group $G=SU(3),SO(8),F_4,E_{6,7,8}$.

• In this paper, we propose a universal recursion formula for the elliptic genera of all such theories.
• This formula is solved from the elliptic blowup equations introduced in our previous paper.
• We explicitly compute the elliptic genera and refined BPS invariants, which recover all previous results from topological string theory, modular bootstrap, Hilbert series, 2d quiver gauge theories and 4d $\mathcal{N}=2$ superconformal $H_{G}$ theories.