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arXiv · 1207.0787

Conformal field theory of Painlevé VI

O. Gamayun·N. Iorgov·O. Lisovyy
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Abstract

Generic Painlevé VI tau function τ(t) can be interpreted as four-point correlator of primary fields of arbitrary dimensions in 2D CFT with c=1. Using AGT combinatorial representation of conformal blocks and determining the corresponding structure constants, we obtain full and completely explicit expansion of τ(t) near the singular points. After a check of this expansion, we discuss examples of conformal blocks arising from Riccati, Picard, Chazy and algebraic solutions of Painlevé VI.

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O. Gamayun, N. Iorgov, O. Lisovyy. 2012-10-03. Conformal field theory of Painlevé VI. https://doi.org/10.1007/jhep10(2012)038

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