2022/07/14 by Fabrizio Del Monte, Del Monte, Fabrizio, Pietro Longhi +1 · 3 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics
paper · pdf · doi:10.48550/arxiv.2207.07135
openalex publication_date 2022/07/14 · openalex created_date 2022/07/19 · openalex updated_date 2026/07/28
We show that TBA equations defined by the BPS spectrum of 5d N=1 SU(2) Yang-Mills on S1× ℝ4 encode the q-Painlevé III3 equation. We find a fine-tuned stratum in the physical moduli space of the theory where solutions to TBA equations can be obtained exactly, and verify that they agree with the algebraic solutions to q-Painlevé. Switching from the physical moduli space to that of stability conditions, we identify a one-parameter deformation of the fine-tuned stratum, where the general solution of the q-Painlevé equation in terms of dual instanton partition functions continues to provide explicit TBA solutions. Motivated by these observations, we propose a further extensions of the range of validity of this correspondence, under a suitable identification of moduli. As further checks of our proposal, we study the behavior of exact WKB quantum periods for the quantum curve of local ℙ1×ℙ1.