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.
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Alim, M., Yau, ST. & Zhou, J. Airy Equation for the Topological String Partition Function in a Scaling Limit. Lett Math Phys 106, 719–729 (2016). https://doi.org/10.1007/s11005-016-0840-z
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DOI: https://doi.org/10.1007/s11005-016-0840-z