Séminaire de Physique ThéoriqueIrregular conformal blocks and Painlevé functions
Hajime Nagoya (Université Rikkyo, Tokyo, Japon)
Thursday 17 September 2015 14:00 - Tours - Salle 1180 (Bât E2)
In 2012 it was conjectured that the tau function of Painlevé VI equation admits an expansion in terms of the Virasoro conformal blocks. Since the Virasoro conformal block has an explicit formula by AGT correspondence this yields an explicit expansion of the Painlevé VI tau function. Later, by scaling limits, explicit short distance expansions of the tau functions of PV, PIII were obtained. I will present long distance expansions of irregular conformal blocks by introducing new vertex operator of the Virasoro algebra. Using them, I provide a conjectural long distance expansion formula of the tau function of Painlevé V.