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Irregular conformal blocks and connection formulae for Painlevé V functions

Abstract : We prove a Fredholm determinant and short-distance series representation of the Painlevé V tau function τt associated with generic monodromy data. Using a relation of τt 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∞ are conjectured. Explicit evaluations of the connection constants relating the tau function asymptotics as t → 0, +∞, i∞ 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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https://hal.archives-ouvertes.fr/hal-01833756
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Submitted on : Tuesday, July 10, 2018 - 1:05:00 AM
Last modification on : Wednesday, May 27, 2020 - 7:40:23 PM

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O. Lisovyy, H. Nagoya, J. Roussillon. Irregular conformal blocks and connection formulae for Painlevé V functions. J.Math.Phys., 2018, 59 (9), pp.091409. ⟨10.1063/1.5031841⟩. ⟨hal-01833756⟩

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