CFT approach to the $q$-Painlevé VI equation

Abstract

Iorgov, Lisovyy, and Teschner established a connection between isomonodromic deformation of linear differential equations and Liouville conformal field theory at $c=1$. In this paper we present a $q$ analog of their construction. We show that the general solution of the $q$-Painlevé VI equation is a ratio of four tau functions, each of which is given by a combinatorial series arising in the AGT correspondence. We also propose conjectural bilinear equations for the tau functions.

26 pages

Cited by in corpus (3)

• On determinant representation and integrability of Nekrasov functions
• Folding transformations for q-Painleve equations
• Blowup relations on ${\mathbb{C}}^2/{\mathbb{Z}}_2$ from Nakajima-Yoshioka blowup relations