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 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.
- Publication:
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Journal of High Energy Physics
- Pub Date:
- July 2014
- DOI:
- 10.1007/JHEP07(2014)144
- arXiv:
- arXiv:1309.4700
- Bibcode:
- 2014JHEP...07..144L
- Keywords:
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- Integrable Hierarchies;
- Integrable Field Theories;
- Differential and Algebraic Geometry;
- High Energy Physics - Theory;
- Mathematical Physics
- E-Print:
- 19 pages, 5 figures