A relation between the exact WKB analysis and the topological recursion - in the case of the Gauss hypergeometric differential equation

摘要

In my joint papers with Iwaki et al. (arXiv:1805.10945, arXiv:1810.02946), we show that there is a relation between the Voros coefficients in the exact WKB analysis and the free energy in the topological recursion introduced by Eynard and Orantin (Commun Number Theory Phys 2007;1:347-452). As an introduction to these papers, we explain this relation in the case of the Gauss hypergeometric differential equation without proofs in this paper.