Elliptic Blowup Equations for 6d SCFTs. III: E-strings, M-strings and Chains

Abstract

We establish the elliptic blowup equations for E-strings and M-strings and solve elliptic genera and refined BPS invariants from them. Such elliptic blowup equations can be derived from a path integral interpretation. We provide toric hypersurface construction for the Calabi-Yau geometries of M-strings and those of E-strings with up to three mass parameters turned on, as well as an approach to derive the perturbative prepotential directly from the local description of the Calabi-Yau threefolds. We also demonstrate how to systematically obtain blowup equations for all rank one 5d SCFTs from E-string by blow-down operations. Finally, we present blowup equations for E-M and M string chains.

arXiv comment54 pages, 10 tables, references added

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• Thermodynamic limit of Nekrasov partition function for 5-brane web with O5-plane
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• The $U$-plane of rank-one 4d $\mathcal{N}=2$ KK theories
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• Coulomb branch surgery: Holonomy saddles, S-folds and discrete symmetry gaugings
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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