Discrete and continuous Yang-Mills measure for non-trivial bundles over compact surfaces

Thierry Lévy (1)

1 DMA - Département de Mathématiques et Applications - ENS Paris

We construct one Yang-Mills measure on a compact surface for each isomorphism class of principal bundles over this surface. For this, we define a new discrete gauge theory which is essentially a covering of the usual one. We prove that the measures correponding to different isomorphism classes of bundles or to different total areas of the surface are mutually singular. We give also a combinatorial computation of the partition functions based on the formalism of fat graphs.

Mots clés: Yang-Mills measure; non-trivial bundles; singular measures; partition functions; fat graphs

Domaines: Physique mathématique [math-ph]; Probabilités [math.PR]

Thierry Lévy. Discrete and continuous Yang-Mills measure for non-trivial bundles over compact surfaces. 2005. ⟨hal-00003808⟩