2-Parameter τ-Function for the First Painlevé Equation: Topological Recursion and Direct Monodromy Problem via Exact WKB Analysis

We show that a 2-parameter family of τ -functions for the first Painlevé equation can be constructed by the discrete Fourier transform of the topological recursion partition function for a family of elliptic curves. We also perform an exact WKB theoretic computation of the Stokes multipliers of asso...

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Bibliographic Details
Published inCommunications in mathematical physics Vol. 377; no. 2; pp. 1047 - 1098
Main Author Iwaki, Kohei
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.07.2020
Springer Nature B.V
Subjects
Classical and Quantum Gravitation
Complex Systems
Curves
Fourier transforms
Mathematical and Computational Physics
Mathematical Physics
Parameters
Partitions (mathematics)
Physics
Physics and Astronomy
Quantum Physics
Relativity Theory
Theoretical
Topology
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Summary:We show that a 2-parameter family of τ -functions for the first Painlevé equation can be constructed by the discrete Fourier transform of the topological recursion partition function for a family of elliptic curves. We also perform an exact WKB theoretic computation of the Stokes multipliers of associated isomonodromy system assuming certain conjectures.
ISSN:0010-3616
1432-0916
DOI:10.1007/s00220-020-03769-2