Formal series expansions of accessory parameters in confluent Heun equations are obtained from Voros periods and matched to classical irregular conformal blocks by choosing appropriate cycles on the spectral curve.
Voros Coefficients for the Hypergeometric Differential Equations and Eynard-Orantin's Topological Recursion - Part II : For the Confluent Family of Hypergeometric Equations
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abstract
We show that the each member of the confluent family of the Gauss hypergeometric equations is realized as quantum curves for appropriate spectral curves. As an application, relations between the Voros coefficients of those equations and the free energy of their classical limit computed by the topological recursion are established. We will also find explicit expressions of the free energy and the Voros coefficients in terms of the Bernoulli numbers and Bernoulli polynomials.
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Lecture notes review exact WKB analysis for ODEs and its combination with topological recursion and isomonodromy to compute monodromy and resurgent structures for Painlevé equations.
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Accessory Parameter of Confluent Heun Equations, Voros Periods and classical irregular conformal blocks
Formal series expansions of accessory parameters in confluent Heun equations are obtained from Voros periods and matched to classical irregular conformal blocks by choosing appropriate cycles on the spectral curve.
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Les Houches Lectures on Exact WKB Analysis and Painlev\'e Equations
Lecture notes review exact WKB analysis for ODEs and its combination with topological recursion and isomonodromy to compute monodromy and resurgent structures for Painlevé equations.