Open Gromov-Witten invariants and SYZ under local conifold transitions

TL;DR

This paper computes open Gromov-Witten invariants for local Calabi-Yau manifolds obtained from toric Gorenstein singularities and constructs their SYZ mirrors, revealing relations through conifold transitions.

Contribution

It provides explicit calculations of open Gromov-Witten invariants and establishes a connection between invariants before and after conifold transitions.

Findings

Explicit open Gromov-Witten invariants for local Calabi-Yau manifolds

Construction of SYZ mirrors for these manifolds

Relation between generating functions across conifold transitions

Abstract

For a local Calabi-Yau manifold which is a smoothing of toric Gorenstein singularity, this paper computes the open Gromov-Witten invariants of a generic fiber of the special Lagrangian fibration constructed by Gross and thereby constructs its SYZ mirror. Moreover it derives a relation for the generating function of open Gromov-Witten invariants of the local Calabi-Yau manifold and that of its conifold transition.