CFT approach to the $q$-Painlev\'e VI equation

Understand

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 $q$-Painlev\'e 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.