Voros Coefficients and the Topological Recursion for a Class of the Hypergeometric Differential Equations associated with the Degeneration of the 2-dimensional Garnier System

2020/05/17 by Yumiko Takei, Takei, Yumiko
Mathematics · Physics and Astronomy · #34M60 (Primary) #81T45 (Secondary) #Algebraic structures and combinatorial models #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.2005.08957

openalex publication_date 2020/05/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In my joint papers with Iwaki and Koike ([IKoT1, IKoT2]) we found an intriguing relation between the Voros coefficients in the exact WKB analysis and the free energy in the topological recursion introduced by Eynard and Orantin in the case of the confluent family of the Gauss hypergeometric differential equations. In this paper we discuss its generalization to the case of the hypergeometric differential equations associated with 2-dimensional degenerate Garnier systems.

Citations

• About the x-y symmetry of the F_g algebraic invariants

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