Journal
JOURNAL OF HIGH ENERGY PHYSICS
Volume -, Issue 7, Pages -Publisher
SPRINGER
DOI: 10.1007/JHEP07(2014)144
Keywords
Integrable Hierarchies; Integrable Field Theories; Differential and Algebraic Geometry
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Funding
- RFBR [12-02-00594, 12-01-00525]
- Agence Nationale de Recherche [ANR 12 BS05 003 02]
- Simons Foundation
- Stony Brook Foundation
- DOE [DE-FG02-96ER40959]
- BSF grant
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We study the classical c -> infinity 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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