Stable finite energy global vortices and asymptotic freedom

This work deals with global vortices in the three-dimensional spacetime. We study the case of a simple model with $U(1)$ symmetry and find a way to describe stable, finite energy global vortices. The price we pay to stabilize the solution is the presence of scale invariance, but we have found a way to trade it with an electric charge in a medium with generalized permittivity, which is further used to capture the basic feature of asymptotic freedom.