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

TL;DR

This paper develops a universal recursion formula for elliptic genera of certain 6d SCFTs with exceptional gauge groups, unifying various computational approaches and revealing new relations to Schur indices.

Contribution

It introduces a universal recursion formula for elliptic genera of 6d (1,0) SCFTs with exceptional gauge groups, extending previous methods and uncovering new theoretical connections.

Findings

Explicit computation of elliptic genera and BPS invariants.

Recovery of results from topological string theory and other frameworks.

Discovery of a relation between k-string elliptic genus and Schur indices.

Abstract

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. We also observe an intriguing relation between the $k$-string elliptic genus and the Schur indices of rank $k$ $H_{G}$ SCFTs, as a generalization of Lockhart-Zotto's conjecture at the rank one cases. In a subsequent paper, we deal with all other non-Higgsable clusters with matters.

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