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Painlevé equations and Hitchin systems in four-dimensional N = 2 theories

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Painlevé equations can be obtained both from time-dependent classical Hamiltonian systems and from isomonodromic deformation problems. These realizations lead to a precise matching between Painlevé equations and Hitchin systems associated to four-dimensional N=2 SQCD as well as Argyres-Douglas theories. Long-time analysis of the Painlevé Hamiltonians dynamics allows to extract the unrefined "instanton" partition function for these theories at all strong-coupling points