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arXiv · 1506.01375

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

Murad Alim·Shing-Tung Yau·Jie Zhou
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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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Murad Alim, Shing-Tung Yau, Jie Zhou. 2015-06-03. Airy Equation for the Topological String Partition Function in a Scaling Limit. https://doi.org/10.1007/s11005-016-0840-z

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