The master field on the plane

Title The master field on the plane

 

SpeakerThierry Levy, Université Pierre et Marie Curie

 

Time4:00-5:00 pm; March 21; 2013

 

PlaceConference Room A304, Department of Mathematical Sciences

 

Abstract: The Yang-Mills field on the plane is a collection of random matrices indexed by the set of loops based at the origin on the plane. These matrices belong to a fixed compact group, for example the unitary group U(N), and the Yang-Mills field can be thought of as a random unitary representation of the group of rectifiable loops on the plane, the group operation being concatenation. I will describe the large N limit of this random reprensentation, in particular the fact that it converges almost surely towards a deterministic limit. This limit, which is an instance of what physicists call the master field, takes the form of a plain deterministic real-valued function on the set of loops. This function can be computed by a recursive algorithm based on the so-called Makeenko-Migdal equations, which are a graphical translation of the algebraic structure of freeness.

 

ContactJun Ye