Remarks on irregular conformal blocks and Painlev\'e III and II tau functions
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We prove a conjecture on uniqueness and existence of the irregular vertex operators of rank $r$ introduced in our previous paper. We also introduce ramified irregular vertex operators of the Virasoro algebra. As applications, we give conjectural formulas for series expansions of Painlev\'e III and II tau functions in terms of our ramified irregular conformal blocks.
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Cited by 2 Pith papers
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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.
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