Combinatorial aspects of 2-dimensional Yang-Mills theory (Thierry Lévy, Paris)

19.05.2017 14:00

I will discuss connections between 2-dimensional Yang-Mills theory and `string theory’, that is, ensembles of ramified coverings of surfaces and slightly more exotic topological objects. These connections were investigated at least by Kostov and Gross -- Taylor but they are still not completely understood. In particular, pioneering work of Kazakov and Kostov suggested that a relatively simple combinatorial formula should exist for the master field (the large N limit of the U(N) Wilson loop expectations), but a clear understanding of the formulas that they proposed still eludes me.
The mathematical background of this stringy interpretation of Yang-Mills theory is the Schur-Weyl duality, which yields combinatorial interpretations of many quantities arising from harmonic analysis on the unitary group.

Lieu

Bâtiment: Battelle

Séminaire "Groupes de Lie et espaces des modules"

entrée libre