The talk is based on . I will present a gauge theoretical derivation of the Nekrasov-Rosly-Shatashvili conjecture  (and its higher rank generalization), which identifies the generating functional of the Lagrangian variety of opers in the (generalized) NRS coordinate system with the effective twisted superpotential of a class-S theory. First, I will show that the non-perturbative Dyson-Schwinger equations obeyed by the partition function of class-S theories in the presence of a surface defect can be related to opers in the Nekrasov-Shatashvili limit. Then I will explain two different types of surface defects (vortex string and orbifold) are related by analytic continuation. I will present a higher-rank generalization of the NRS coordinate system on the moduli space of SL(N)-flat connections on a sphere, and show how the holonomies of flat connections can be expressed in these coordinates. Finally, I will show how to compute the monodromies of opers on the four-punctured sphere and compare the results with the holonomies written in the generalized NRS coordinates. The comparison explicitly shows that the generating function for the variety of opers is identified with the effective twisted superpotential.
 S. Jeong, N. Nekrasov, https://arxiv.org/abs/1806.08270
 N. Nekrasov, A. Rosly, S. Shatashvili, https://arxiv.org/abs/1103.3919