Classical conformal blocks and Painlevé VI
Abstract
We study the classical c → ∞ limit of the Virasoro conformal blocks. We point out that the classical limit of the simplest nontrivial nullvector decoupling equation on a sphere leads to the Painlevé VI equation. This gives the explicit representation of generic fourpoint 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.
 Publication:

Journal of High Energy Physics
 Pub Date:
 July 2014
 DOI:
 10.1007/JHEP07(2014)144
 arXiv:
 arXiv:1309.4700
 Bibcode:
 2014JHEP...07..144L
 Keywords:

 Integrable Hierarchies;
 Integrable Field Theories;
 Differential and Algebraic Geometry;
 High Energy Physics  Theory;
 Mathematical Physics
 EPrint:
 19 pages, 5 figures