Conformal field theory of Painlevé VI
Lundi 08/10/2012, 11:00
Salle Claude Itzykson, Bât. 774, Orme des Merisiers
I will argue that generic Painlevé 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, full and completely explicit expansion of $tau(t)$ near the singular points will be obtained. After a check of this expansion, I will discuss examples of conformal blocks arising from Riccati, Picard, Chazy and algebraic solutions of Painlevé VI.