Blowup relations and q-Painlevé VI

2025/09/13 by Artem Stoyan, Stoyan, Artem · 1 citation
Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry and Number Theory #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.2509.10938

openalex publication_date 2025/09/13 · openalex created_date 2025/10/12 · openalex updated_date 2026/07/28

Abstract

We propose and study blowup relations obeyed by the partition functions of 5d N=1 (quiver) SYM theories with SU(2) gauge group and four flavours. By analyzing the Weyl group action on the sets of blowup relations, we identify the integer parameters of a blowup relation with the weights of a corresponding Lie algebra. We also explain how this action of the Weyl group follows from the Weyl group symmetry of the partition function. Finally, we use these relations to derive bilinear relations on the q-Painlevé VI tau functions.

Citations

• Discrete Hamiltonians of discrete Painlevé equations
• BPS/CFT correspondence V: BPZ and KZ equations from qq-characters
• CFT approach to the q-Painlevé VI equation
• Liouville Correlation Functions from Four-dimensional Gauge Theories
• Quantizing the Bäcklund transformations of Painlevé equations and the quantum discrete Painlevé VI equation
• Instanton counting on blowup. II. K-theoretic partition function

Cited by

• New recursion relations for M2-brane matrix models

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