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

  title={2-Parameter \$\$\tau \$\$-Function for the First Painlev{\'e} Equation: Topological Recursion and Direct Monodromy Problem via Exact WKB Analysis},
  author={Kohei Iwaki},
  journal={Communications in Mathematical Physics},
  • Kohei Iwaki
  • Published 18 February 2019
  • Mathematics
  • Communications in Mathematical Physics
We show that a 2-parameter family of $$\tau $$ -functions for the first Painleve 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. 
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