Potential energy of Yang-Mills vortices in three and four dimensions

Abstract

We calculate the energy of a Yang-Mills vortex as function of its magnetic flux or, else, of the Wilson loop surrounding the vortex center. The calculation is performed in the 1-loop approximation. A parallel with a potential as function of the Polyakov line at nonzero temperatures is drawn. We find that quantized Z(2) vortices are dynamically preferred though vortices with arbitrary fluxes cannot be ruled out.