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

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.

22 pages, 2 figures

References in corpus (9)

• Lectures on non-perturbative effects in large N gauge theories, matrix models and strings
• Open string amplitudes and large order behavior in topological string theory
• The Annular Report on Non-Critical String Theory
• Resurgent Transseries and the Holomorphic Anomaly: Nonperturbative Closed Strings in Local CP2
• Polynomial Structure of the (Open) Topological String Partition Function
• Large D-instanton effects in string theory
• Topological Strings and (Almost) Modular Forms
• Lectures on Mirror Symmetry and Topological String Theory
• Airy Equation for the Topological String Partition Function in a Scaling Limit

Cited by in corpus (4)

• A Primer on Resurgent Transseries and Their Asymptotics
• Resurgence in Extended Hydrodynamics
• Resurgence Matches Quantization
• High order perturbation theory for difference equations and Borel summability of quantum mirror curves