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

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.