Boundaries, defects, and quantization

Abstract: An interesting aspect of four-dimensional N=2 supersymmetric field theories is their correspondence with integrable systems. At the example of class S theories and Hitchin integrable systems, I will explain how half-BPS defects in gauge theory can be utilized in the quantization problem. More specifically, the vacuum expectation values and correlation functions of these defects are exactly computed by localization, and analytic constraints make them obey certain differential equations in coupling parameters. These equations and solutions are interpreted geometrically in the Hitchin moduli space side, yielding various implications on the quantization problem. I will also discuss how these results can be reformulated in the point of view of the two-dimensional sigma model with the Hitchin target space, connecting the story to that of the N=4 theory of Kapustin-Witten.

high energy physicsmathematical physics

Audience: researchers in the topic

SNU String Seminar