Universality of the topological string at large radius and NS-brane resurgence

TL;DR

This paper demonstrates a universal large radius limit of topological string free energies across all Calabi-Yau geometries, revealing a milder asymptotic growth and new NS-brane instanton effects linked to the manifold's volume.

Contribution

It introduces a universal limit of topological string free energies with nonholomorphic dependence, showing a transition to NS-brane type instantons and connecting them to Calabi-Yau volume.

Findings

Universal free energy limit with nonholomorphic dependence.

Milder factorial growth leading to NS-brane instantons.

Relation between instanton action and Calabi-Yau volume.

Abstract

We show that there is a natural universal limit of the topological string free energies at the large radius point. The new free energies keep a nonholomorphic dependence on the complex structure moduli space and their functional form is the same for all Calabi-Yau geometries, compact and noncompact alike. The asymptotic nature of the free energy expansion changes in this limit due to a milder factorial growth of its coefficients, and this implies a transseries extension with instanton effects in $\exp(- 1/g_s^2)$, of NS-brane type, rather than $\exp(-1/g_s)$, of D-brane type. We show a relation between the instanton action of NS-brane type and the volume of the Calabi-Yau manifold which points to a possible interpretation in terms of NS5-branes. A similar rescaling limit has been considered recently leading to an Airy equation for the partition function which is here used to explain the resurgent properties of the rescaled transseries.