Geometric transition in Non-perturbative Topological string

TL;DR

This paper investigates the application of geometric transitions in non-perturbative topological string theory, specifically from local alB_3 to the resolved conifold, including both closed and open string cases, and identifies parameter corrections.

Contribution

It demonstrates that geometric transitions are valid in non-perturbative topological strings and computes the necessary corrections to Ke4hler parameters for these transitions.

Findings

Geometric transition applies to non-perturbative topological strings.

Corrections to Ke4hler parameters are identified.

Transitions between local alB_3 and resolved conifold are established.

Abstract

We study a geometric transition in non-perturbative topological string. We consider two cases. One is the geometric transition from the closed topological string on the local $\mathcal{B}_{3}$ to the closed topological string on the resolved conifold. The other is the geometric transition from the closed topological string on the local $\mathcal{B}_{3}$ to the open topological string on the resolved conifold with a toric A-brane. We find that, in both cases, the geometric transition can be applied for the non-perturbative topological string. We also find the corrections of the value of K\"ahler parameters at which the geometric transition occurs.