On axially symmetrical solitons in Abelian-Higgs models
  A numerical search for bosonic superconducting static vortex rings in a $U(1)_{A}\times U(1)_{W}$ model is presented. The fate of these rings without current, is to shrink due to their tension until extinction. The superconductivity of the loop does not seem to prevent shrinking. Current quenching takes place before stabilization. 
C.G.Doudoulakis