On Painleve/gauge theory correspondence

We elucidate the relation between Painleve equations and four-dimensional rank one N = 2 theories by identifying the connection associated with Painleve isomonodromic problems with the oper limit of the flat connection of the Hitchin system associated with gauge theories and by studying the corresponding renormalization group flow. Based on this correspondence, we provide long-distance expansions at various canonical rays for all Painleve tau-functions in terms of magnetic and dyonic Nekrasov partition functions for N = 2 SQCD and Argyres-Douglas theories at self-dual Omega background epsilon(1) + epsilon(2) = 0 or equivalently in terms of c = 1 irregular conformal blocks.