Classical Conformal Blocks and Painleve VI

Alexey Litvinov; Sergei Lukyanov; Nikita Nekrasov; Alexander Zamolodchikov

doi:10.1007/jhep07(2014)144

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arXiv · 1309.4700

Classical Conformal Blocks and Painleve VI

Alexey Litvinov·Sergei Lukyanov·Nikita Nekrasov·Alexander Zamolodchikov

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Abstract

We study the classical c\to \infty limit of the Virasoro conformal blocks. We point out that the classical limit of the simplest nontrivial null-vector decoupling equation on a sphere leads to the Painleve VI equation. This gives the explicit representation of generic four-point classical conformal block in terms of the regularized action evaluated on certain solution of the Painleve VI equation. As a simple consequence, the monodromy problem of the Heun equation is related to the connection problem for the Painleve VI.

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Alexey Litvinov, Sergei Lukyanov, Nikita Nekrasov, Alexander Zamolodchikov. 2013-10-13. Classical Conformal Blocks and Painleve VI. https://doi.org/10.1007/jhep07(2014)144

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