Borel singularities and Stokes constants of the topological string free energy on one-parameter Calabi-Yau threefolds

TL;DR

This paper analyzes the Borel plane of topological string free energy on hypergeometric Calabi-Yau models, revealing connections between Borel singularities, Stokes constants, and D-brane charges near singular points.

Contribution

It uncovers the relationship between Borel singularities, Stokes constants, and D-brane charges in hypergeometric Calabi-Yau models, especially near singular points.

Findings

Borel singularities align with D-brane central charges.

Stokes constants match generalized Donaldson-Thomas invariants.

Massless D-branes influence the Borel plane structure.

Abstract

We study the Borel plane of the topological string free energy on all hypergeometric one-parameter Calabi-Yau models close to singular points in moduli space, focusing on the location of Borel singularities and the value of the associated Stokes constants. We find in particular that in models which exhibit massless D-branes at a singular point, the central charge of the D-brane close to the singular point coincides with the location of the leading Borel singularity, and the generalized Donaldson-Thomas invariant associated to the charge of the D-brane, in as far as its value is known, coincides with the Stokes constant associated to the Borel singularity.