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

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arxiv 1905.00864 v3 pith:NY4PCHQ2 submitted 2019-05-02 hep-th math-phmath.MP

Jie Gu , Albrecht Klemm , Kaiwen Sun , Xin Wang This is my paper · ORCID
classification hep-thmath-phmath.MP
keywords elliptictheoriesrankscftsblowupcasesequationsformula
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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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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Generalised global symmetries in 5d $\mathcal{N}=1$ theories from the blow-up equations

    hep-th 2026-07 conditional novelty 7.0 of 10

    Fractional exponents of the blow-up prefactor exp(-V_n) on 1-form backgrounds encode cubic and mixed anomalies of 5d N=1 SCFTs, deciding 2-groups versus mixed anomalies once the faithful UV symmetry is known from the index.

  2. Instantons from Blow-up

    hep-th 2019-08 conditional novelty 7.0 of 10

    The instanton partition function of many 4d N=2 and 5d N=1 gauge theories is fully determined by the perturbative part via generalized Nakajima-Yoshioka blowup equations.

  3. BPS Invariants for Generalized Toric Calabi-Yau Threefolds

    hep-th 2026-07 conditional novelty 6.0 of 10

    Gopakumar–Vafa invariants are transported across Hanany–Witten transitions after removing a universal parallel-brane sector, giving first-time high-degree invariants for local dP4.

  4. More on 5d Wilson Loops in Higher-Rank Theories and Blowup Equations

    hep-th 2026-02 conditional novelty 6.0 of 10

    For 5d N=1 pure gauge theories, Wilson-loop blowup equations can be fixed using one-form symmetry and low-instanton data, and one-instanton free energies admit a universal v=sqrt(q1q2) expansion resembling Hilbert series.

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