Symplectic cuts and open/closed strings II

TL;DR

This paper links symplectic cuts of Calabi-Yau manifolds to open and closed string theories, extending previous work to higher-dimensional Calabi-Yau geometries and deriving related Picard-Fuchs equations.

Contribution

It establishes a connection between equivariant disk potentials and periods of higher-dimensional Calabi-Yau manifolds, extending the framework to include moduli spaces of multiple symplectic cuts.

Findings

Equivariant disk potential as a period of Calabi-Yau fourfolds and fivefolds.

Derived extended Picard-Fuchs equations for toric branes.

Connected symplectic cuts to higher-dimensional Calabi-Yau geometries.

Abstract

In arXiv:2306.07329 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 arXiv:alg-geom/9712024. 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.