Wednesday, July 4, 2012

1207.0787 (O. Gamayun et al.)

Conformal field theory of Painlevé VI    [PDF]

O. Gamayun, N. Iorgov, O. Lisovyy
Generic Painlev\'e VI tau function \tau(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 \tau(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 Painlev\'e VI.
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