Fusion of surface defects, Hecke operator, and quantum Lax equation

Abstract: I will consider a correlation function of two half-BPS surface defects in 4d N=2 gauge theory of class S, which have different 6d origins. I will explain their meaning after the reduction to the sigma model on a corner with the Hitchin moduli space target. By localization computation, we confirm that the introduction of the second surface defect induces an action on the parameter space of the first surface defect, which is shown to be that of the Hecke operator on the conformal block of the vertex algebra at the junction of the corner. Furthermore, the correlation function is shown to satisfy the 'quantum' Lax equation, leading to all the mutually commuting quantum Hamiltonian realized as differential operators acting on the vev of the first surface defect.

MathematicsPhysics

Audience: researchers in the topic

SNU String Seminar