Classical Conformal Blocks and Painleve VI
High Energy Physics - Theory
2015-06-17 v2 Mathematical Physics
math.MP
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.
Cite
@article{arxiv.1309.4700,
title = {Classical Conformal Blocks and Painleve VI},
author = {Alexey Litvinov and Sergei Lukyanov and Nikita Nekrasov and Alexander Zamolodchikov},
journal= {arXiv preprint arXiv:1309.4700},
year = {2015}
}
Comments
19 pages, 5 figures; references added