Abstract
We study the classical c → ∞ 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 Painlevé 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 Painlevé VI equation. As a simple consequence, the monodromy problem of the Heun equation is related to the connection problem for the Painlevé VI.
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Litvinov, A., Lukyanov, S., Nekrasov, N. et al. Classical conformal blocks and Painlevé VI. J. High Energ. Phys. 2014, 144 (2014). https://doi.org/10.1007/JHEP07(2014)144
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DOI: https://doi.org/10.1007/JHEP07(2014)144