Symplectic Cuts and Open/Closed Strings II

Abstract In Cassia et al. (Commun Math Phys 406(1):15, 2025), we established a connection between symplectic cuts of Calabi–Yau threefolds and open topological strings, and used this to introduce an equivariant deformation of the disk potential of toric branes. In this paper, we establish a connection to higher-dimensional Calabi–Yau geometries by showing that the equivariant disk potential arises as an equivariant period of certain Calabi–Yau fourfolds and fivefolds, which encode moduli spaces of one and two symplectic cuts (the maximal case) by a construction of Braverman (J für die Reine und Angew Math 1999 (508):85–98, 1999). Extended Picard–Fuchs equations for toric branes, capturing dependence on both open and closed string moduli, are derived from a suitable limit of the equivariant quantum cohomology rings of the higher Calabi–Yau geometries.