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.

arXiv comment26 pages

References in corpus (4)

• Five-dimensional AGT Conjecture and the Deformed Virasoro Algebra
• Quantum Algebraic Approach to Refined Topological Vertex
• On Painlevé/gauge theory correspondence
• Fredholm determinant and Nekrasov sum representations of isomonodromic tau functions

Cited by in corpus (13)

• Cluster integrable systems, q-Painleve equations and their quantization
• A slow review of the AGT correspondence
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• Orthogonal Polynomials in Mathematical Physics
• q-Painleve equation from Virasoro constraints
• Combinatorial expressions for the tau functions of $q$-Painlevé V and III equations
• Cluster integrable systems and spin chains
• Quantum Representation of Affine Weyl Groups and Associated Quantum Curves
• Twisted Representations of Algebra of $q$-Difference Operators, Twisted $q$-$W$ Algebras and Conformal Blocks
• Circular quiver gauge theories, isomonodromic deformations and $W_N$ fermions on the torus
• On $q$-Isomonodromic Deformations and $q$-Nekrasov Functions
• Folding transformations for q-Painleve equations
• Blowup relations on ${\mathbb{C}}^2/{\mathbb{Z}}_2$ from Nakajima-Yoshioka blowup relations