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

TL;DR

This paper develops elliptic blowup equations for E-strings and M-strings, enabling the calculation of elliptic genera and BPS invariants, and extends these methods to chains of such strings and related 5d SCFTs.

Contribution

It introduces elliptic blowup equations for E-strings and M-strings, providing new tools for computing invariants and extending to complex string chains and 5d SCFTs.

Findings

Derived elliptic blowup equations for E-strings and M-strings.

Solved elliptic genera and refined BPS invariants using these equations.

Constructed toric hypersurfaces for relevant Calabi-Yau geometries.

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.