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arXiv · 1806.08344

Irregular conformal blocks and connection formulae for Painlevé V functions

O. Lisovyy·H. Nagoya·J. Roussillon
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Abstract

We prove a Fredholm determinant and short-distance series representation of the Painlevé V tau function $τ(t)$ associated to generic monodromy data. Using a relation of $τ(t)$ to two different types of irregular $c=1$ Virasoro conformal blocks and the confluence from Painlevé VI equation, connection formulas between the parameters of asymptotic expansions at $0$ and $i\infty$ are conjectured. Explicit evaluations of the connection constants relating the tau function asymptotics as $t\to 0,+\infty,i\infty$ are obtained. We also show that irregular conformal blocks of rank 1, for arbitrary central charge, are obtained as confluent limits of the regular conformal blocks.

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O. Lisovyy, H. Nagoya, J. Roussillon. 2018-06-21. Irregular conformal blocks and connection formulae for Painlevé V functions. https://doi.org/10.1063/1.5031841

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