A large deviation principle for the Yang-Mills measure
Résumé
We prove the first mathematical result relating the Yang-Mills measure on a compact surface and the Yang-Mills energy. We show that, at the small volume limit, the scaled Yang-Mills measures satisfy a large deviation principle with the Yang-Mills energy as rate function. This gives some rigorous content to the informal description of the Yang-Mills measure as the Gibbs measure of the Yang-Mills energy. We make the assumption that the structure group is simply connected and plan to treat the general case in a forthcoming publication.