Airy Equation for the Topological String Partition Function in a Scaling Limit
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 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 nonperturbative structure of topological string theory. Both solutions can be expanded naturally around strong coupling.
 Publication:

Letters in Mathematical Physics
 Pub Date:
 June 2016
 DOI:
 10.1007/s110050160840z
 arXiv:
 arXiv:1506.01375
 Bibcode:
 2016LMaPh.106..719A
 Keywords:

 High Energy Physics  Theory;
 Mathematical Physics;
 Mathematics  Algebraic Geometry
 EPrint:
 11 pages, 1 figure