QM Research Seminar: Quantization of Hitchin integrable system and N=2 gauge theory with surface defects

Speaker: Saebyeok Jeong (Department of Theoretical Physics, CERN)

Abstract:

The Coulomb branch of four-dimensional N=2 supersymmetric gauge theory of class S is well-known to be identical to the moduli space of Hitchin's equations. I will consider the case of genus-0 with regular marked points, where the associated integrable system is the Gaudin model. I'll explain how the quantization of the Gaudin model can be formulated in the N=2 supersymmetric gauge theory with the help of half-BPS surface defects. We consider two types of surface defects: the "canonical" surface defect and the "regular monodromy" surface defect, inserted on top of each other. The action of the former on the latter is diagonal due to cluster decomposition, interpreted as the Hecke eigensheaf property with the eigenvalue given by the oper. In this way, we formulate the geometric Langlands correspondence in the N=2 gauge theory setting. I will also explain that the separation of variables and the bispectral duality of the quantum Hitchin integrable system can be accounted for by surface defect transitions.