MS Seminar (Mathematics - String Theory)

Speaker: Kazunobu Maruyoshi (SISSA)
Title: Quantized integrable systems, matrix models and AGT correspondence
Date: Tue, Apr 26, 2011, 13:15 - 14:45
Place: Seminar Room A
Related File: 428.pdf
Abstract: We study the relation between four-dimensional N=2 gauge theories in the omega-background, where one deformation parameter is taken to zero, and quantized Hitchin systems. We consider this by using the AGT correspondence and its matrix model description. The wave-function of the Hitchin system can be identified with the conformal block where degenerate fields are additionally inserted, which is shown to satisfy the same differential equation as that of the corresponding integrable system. We show that the differential equation and the wave-function agree, respectively, with the loop equation and the integral of the resovlent of the matrix model. We will see this in the cases associated to a punctured sphere and torus.