Blowup Equations for 6d SCFTs. I

Abstract

We propose novel functional equations for the BPS partition functions of 6d (1,0) SCFTs, which can be regarded as an elliptic version of Gottsche-Nakajima-Yoshioka's K-theoretic blowup equations. From the viewpoint of geometric engineering, these are the generalized blowup equations for refined topological strings on certain local elliptic Calabi-Yau threefolds. We derive recursion formulas for elliptic genera of self-dual strings on the tensor branch from these functional equations and in this way obtain a universal approach for determining refined BPS invariants. As examples, we study in detail the minimal 6d SCFTs with SU(3) and SO(8) gauge symmetry. In companion papers, we will study the elliptic blowup equations for all other non-Higgsable clusters.

arXiv comment52 pages, 3 figures

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Cited by in corpus (24)

• Revisiting the classifications of 6d SCFTs and LSTs
• Elliptic Blowup Equations for 6d SCFTs. II: Exceptional Cases
• Bootstrapping BPS spectra of 5d/6d field theories
• Elliptic Blowup Equations for 6d SCFTs. III: E-strings, M-strings and Chains
• Instantons from Blow-up
• 5d/6d Wilson loops from blowups
• More on topological vertex formalism for 5-brane webs with O5-plane
• Elliptic Blowup Equations for 6d SCFTs. IV: Matters
• Modular curves, the Tate-Shafarevich group and Gopakumar-Vafa invariants with discrete charges
• Quasi-Jacobi Forms, Elliptic Genera and Strings in Four Dimensions
• M5 branes and Theta Functions
• Twisted 6d $(2,0)$ SCFTs on a Circle
• Refined topological vertex with ON-planes
• Topological strings and Wilson loops
• Fibre-base duality of 5d KK theories
• Thermodynamic limit of Nekrasov partition function for 5-brane web with O5-plane
• Blowup Equations for Little Strings
• Weyl invariant Jacobi forms along Higgsing trees
• Quantum Periods and Spectra in Dimer Models and Calabi-Yau Geometries
• Bootstrapping ADE M-strings
• Refined BPS numbers on compact Calabi-Yau threefolds from Wilson loops
• Probing Quantum Curves and Transitions in 5d SQFTs via Defects and Blowup Equations
• State counting on fibered CY-3 folds and the non-Abelian Weak Gravity Conjecture
• More on 5d Wilson Loops in Higher-Rank Theories and Blowup Equations