Airy Equation for the Topological String Partition Function in a Scaling Limit

Abstract

We use the polynomial formulation of the holomorphic anomaly equations governing perturbative topological string theory to derive the free energies in a scaling limit to all orders in perturbation theory for any Calabi-Yau threefold. The partition function in this limit satisfies an Airy differential equation in a rescaled topological string coupling. One of the two solutions of this equation gives the perturbative expansion and the other solution provides geometric hints of the non-perturbative structure of topological string theory. Both solutions can be expanded naturally around strong coupling.

11 pages, 1 figure

References in corpus (3)

• Summing Up All Genus Free Energy of ABJM Matrix Model
• Resurgent Transseries and the Holomorphic Anomaly: Nonperturbative Closed Strings in Local CP2
• Polynomial Structure of the (Open) Topological String Partition Function

Cited by in corpus (4)

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• Universality of the topological string at large radius and NS-brane resurgence
• Holomorphic anomaly of 2d Yang-Mills theory on a torus revisited
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