This seminar will be presented in hybrid mode. The speaker will deliver his talk in person.
Title: The planar master field and the Yang-Mills measure on surfaces
Abstract: The Yang-Mills measure is one of the building blocks of the standard model of particle physics. It can be formally understood as an infinite dimensional measure on a space of matrix-valued one-forms over a manifold. While a rigorous mathematical definition is missing in the physically relevant setting of a four dimensional manifold, a satisfying definition exists in dimension 2, and progress towards a definition has been made very recently in dimension 3 using regularity structures. Since the work of G. ’t Hooft on the strong interaction in the 70’s, a lot of activity in physics motivated the study of a regime, called large N limit, where the size of matrices goes to infinity. I will report here on results obtained for the large N limit in dimension 2, discussing the role of the topology of the manifold in this limit. Part of this talk is based on two joint works with Thibaut Lemoine.
The talk will be followed by refreshments in the Huxley Common Room at 4pm.