We show that the non-perturbative dynamics of $\mathcal{ N}=2$ super Yang-Mills theories in a self-dual $\Omega$-background and with an arbitrary simple gauge group is fully determined by studying renormalization group equations of vevs of surface operators generating one-form symmetries. The corresponding system of equations is a { \it non-autonomous} Toda chain, the time being the RG scale. We obtain new recurrence relations which provide a systematic algorithm computing multi-instanton corrections from the tree-level one-loop prepotential as the asymptotic boundary condition of the RGE. We exemplify by computing the $E_6$ and $G_2$ cases up to two-instantons.
Categories: hep-th math-ph math.MP nlin.SI