Coadjoint Orbits of Central Extensions of Gauge Groups

We study geometrically the coadjoint orbits of the central extensions of gauge groups over arbitrary manifolds. We show that these orbits are classified by a dimension one foliation with a transverse measure, together with a leafwise connection. For the case of a two-dimensional torus with standard trivial foliation, we show that the holonomies along the leaves give a complete invariant for the regular coadjoint orbits. We investigate in detail the Kronecker foliation of a torus using a new construction which we call asymptotic holonomy.