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

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.

arXiv comment117 pages, 5 figures; typos corrected, new references added

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Cited by in corpus (23)

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• 5d/6d Wilson loops from blowups
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• Bootstrapping ADE M-strings
• Refined BPS numbers on compact Calabi-Yau threefolds from Wilson loops
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• Probing Quantum Curves and Transitions in 5d SQFTs via Defects and Blowup Equations
• More on 5d Wilson Loops in Higher-Rank Theories and Blowup Equations