Presented by:
Thierry Levy
Date:
Wednesday 21st November 2018 - 15:00 to 16:30
Venue:
INI Seminar Room 2
Abstract:
The
partition function of the 2d Yang—Mills model is the natural mass of the
Yang—Mills measure, and there is at least one reasonable way of defining it.
For each oriented compact surface, it is a function on the set of all possible
boundary conditions for the Yang—Mills field, which in the 2d case is
finite-dimensional. This function plays for the 2d Yang—Mills field the role
usually played by the transition kernel of a Markov process.
The
case of the sphere is unique among closed oriented surfaces in that, in the
large N limit, the U(N) Yang—Mills model exhibits a third order phase
transition, the Douglas—Kazakov phase transition, with respect to the total
area of the sphere. This transition can be understood in terms of
non-intersecting Brownian motions on a circle, as Karl Liechty and Dong Wang
did, or in terms of a discrete Coulomb gas, as we did with Mylène Maïda.