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

Understand

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.