Partial vorticity in classical Yang-Mills solutions

The classical SU(2) Yang-Mills equation is solved numerically in 2+1 dimensions with a static central point source. We study the static potentials whose rotational symmetry in two-space is manifest, i.e., does not require a gauge transformation for its realization. In the radial gauge, such a potential typically consists of two functions of the radial coordinate: a highly oscillatory tangential component Aφ and a timelike component A0 which is essentially monotonic. These two components point in two perpendicular SU(2) directions. The interest of these solutions lies in the following features. First, the asymptotic behavior of A0 at large distances is linear and hence more confining than the logarithmic, Coulomb-type behavior resulting from Aφ==0. Second, in a suitably defined strong-coupling limit, the vorticity oscillates so tightly as to disappear, while A0 remains linear instead of approaching the Coulomb form. Therefore the strong-coupling behavior could be relevant to 3+1 dimensions with spherical symmetry. A third feature is that, in the strong-coupling limit, the source becomes renormalized to an infinitesimal bare charge