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

作者：Alim Murad^*; Yau Shing Tung^*; Zhou Jie^*

来源：Letters in Mathematical Physics, 2016, 106(6): 719-729.

DOI：10.1007/s11005-016-0840-z

• topological string theory
• mirror symmetry

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.

• 出版日期2016-6