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Airy equation for the topological string partition function in a scaling limit

Murad Alim Shing-Tung Yau Jie Zhou

Mathematical Physics mathscidoc:1912.43633

Letters in Mathematical Physics, 106, (6), 719-729, 2016.6
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 CalabiYau 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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@inproceedings{murad2016airy,
  title={Airy equation for the topological string partition function in a scaling limit},
  author={Murad Alim, Shing-Tung Yau, and Jie Zhou},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224204601736091197},
  booktitle={Letters in Mathematical Physics},
  volume={106},
  number={6},
  pages={719-729},
  year={2016},
}
Murad Alim, Shing-Tung Yau, and Jie Zhou. Airy equation for the topological string partition function in a scaling limit. 2016. Vol. 106. In Letters in Mathematical Physics. pp.719-729. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224204601736091197.
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