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Mathematical aspects of two-dimensional Yang-Mills theory : an introduction

Banff International Research Station for Mathematical Innovation and Discovery

In the fifties, Chen Ning Yang and Robert Mills made a major breakthrough in quantum field theory by extending the concept of gauge theory to non-abelian groups. The mathematical and physical consequences of going from a commutative to a non-commutative theory are major and since then, the mathematics of Yang-Mills theory has been a very active field of research. In this talk, meant to be an introductory as possible, I will focus on the last two-decade developments of Yang-Mills theory on two-dimensional manifolds with gauge group U(N) or SU(N). I will rely on the fascinating properties of the heat kernel (ie the Brownian motion and bridge) on these groups. I will in particular explain the construction of the master field, arising in the large-N limit for these models, in relation with free probability theory.

Mathematics; Probability Theory And Stochastic Processes; Global Analysis; Analysis On Manifolds

video/mp4

Author affiliation: Université de Lille, France

2021-09-05

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/79655

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/