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2-parameter $\tau$-function for the first Painlev\'e equation -Topological recursion and direct monodromy problem via exact WKB analysis-
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abstract
We show that a 2-parameter family of $\tau$-functions for the first Painlev\'e 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.
Forward citations
Cited by 2 Pith papers
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Many-faced Painlev\'e I: irregular conformal blocks, topological recursion, and holomorphic anomaly approaches
The paper proves the conifold gap property for Weierstrass elliptic topological recursion and gives an algebraic construction of the rank 5/2 Virasoro Whittaker state, linking the Painlevé I tau function to CFT and ho...
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Universal Correlators on Exponentially Ramified Spectral Curves
Generalized topological recursion extends to spectral curves with essential singularities by replacing residues at the essential point with residues at ordinary meromorphic points.
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