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. © 2014 The Author(s).
CITATION STYLE
Litvinov, A., Lukyanov, S., Nekrasov, N., & Zamolodchikov, A. (2014). Classical conformal blocks and Painlevé VI. Journal of High Energy Physics, 2014(7). https://doi.org/10.1007/JHEP07(2014)144
Mendeley helps you to discover research relevant for your work.