Opers, surface defects, and Yang-Yang functional

We explore the non-perturbative Dyson-Schwinger equations obeyed by the partition functions of the Ω -deformed N = 2, d = 4 supersymmetric linear quiver gauge theories in the presence of surface defects. We demonstrate that the partition functions of different types of defects (orbifold or vortex strings) are related by analytic continuation. We introduce Darboux coordinates on a patch of the moduli space of flat SL(N)-connections on a sphere with special punctures, which generalize the NRS coordinates defined in the SL(2) case.