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

Understand

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.