2017/11/30 by M. Bershtein, P. Gavrylenko, A. Marshakov · 1 citation
Physics and Astronomy · Mathematics · #math-ph #hep-th #math.MP #nlin.SI
paper · pdf · doi:10.1007/jhep02(2018)077
published as JHEP 1802:077, 2018 · 28 pages; v2 30 pages references added, misprints corrected; v3 small changes, references added, to appear in JHEP
arxiv created 2018/02/12 · arxiv updated 2018/02/19
We discuss the relation between the cluster integrable systems and q-difference Painlevé equations. The Newton polygons corresponding to these integrable systems are all 16 convex polygons with a single interior point. The Painlevé dynamics is interpreted as deautonomization of the discrete flows, generated by a sequence of the cluster quiver mutations, supplemented by permutations of quiver vertices. We also define quantum q-Painlevé systems by quantization of the corresponding cluster variety. We present formal solution of these equations for the case of pure gauge theory using q-deformed conformal blocks or 5-dimensional Nekrasov functions. We propose, that quantum cluster structure of the Painlevé system provides generalization of the isomonodromy/CFT correspondence for arbitrary central charge.