On $q$-Isomonodromic Deformations and $q$-Nekrasov Functions

Abstract

We construct a fundamental system of a $q$-difference Lax pair of rank $N$ in terms of 5d Nekrasov functions with $q=t$. Our fundamental system degenerates by the limit $q\to 1$ to a fundamental system of a differential Lax pair, which yields the Fuji-Suzuki-Tsuda system. We introduce tau functions of our system as Fourier transforms of 5d Nekrasov functions. Using asymptotic expansions of the fundamental system at $0$ and $\infty$, we obtain several determinantal identities of the tau functions.

References in corpus (22)

• Liouville Correlation Functions from Four-dimensional Gauge Theories
• Instanton counting on blowup. I. 4-dimensional pure gauge theory
• Dispersive estimates for Schrodinger operators in dimensions one and three
• Quantum Algebraic Approach to Refined Topological Vertex
• Isomonodromic tau-functions from Liouville conformal blocks
• On Painlevé/gauge theory correspondence
• Vertices, Vortices & Interacting Surface Operators
• 3d & 5d gauge theory partition functions as q-deformed CFT correlators
• Irregular conformal blocks and connection formulae for Painlevé V functions
• The Liouville side of the Vortex
• Analyticity of Nekrasov Partition Functions
• Cluster Toda chains and Nekrasov functions
• Variations of $q$-Garnier system
• CFT approach to the $q$-Painlevé VI equation
• Combinatorial expressions for the tau functions of $q$-Painlevé V and III equations
• A class of higher order Painleve systems arising from integrable hierarchies of type A
• Remarks on irregular conformal blocks and Painlevé III and II tau functions
• Study of $q$-Garnier system by Padé method
• On solutions of the Fuji-Suzuki-Tsuda system
• A Variation of the $q$-Painlevé System with Affine Weyl Group Symmetry of Type $E_7^{(1)}$
• Drinfeld-Sokolov hierarchies of type A and fourth order Painleve systems
• Affine Weyl group symmetry of the Garnier system