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

@article{Alim2015AiryEF,
  title={Airy Equation for the Topological String Partition Function in a Scaling Limit},
  author={Murad Alim and Shing-Tung Yau and Jie Zhou},
  journal={Letters in Mathematical Physics},
  year={2015},
  volume={106},
  pages={719-729}
}
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… 

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