Stable finite energy global vortices and asymptotic freedom

Abstract

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.

Electrically charged localized structures

“…The use of a field-dependent function coupled with the gauge field dynamical term has also been recently considered in [14] in the electric context, that is, in the presence of an electric charge fixed at the origin; there, we showed that the electric field has a behavior that captures the basic feature of asymptotic freedom, an effect that is usually associated to quarks and gluons. It was also considered, for instance, in [15][16][17][18][19] to describe vortex configurations with internal structures in the plane in the magnetic context.…”

“…Inspired by the results of [14], in the present work we first consider the field-dependent function as a dielectric function to be governed by a single scalar field. In the sequence, we add an extra scalar field, that modifies both the dielectric function and the dynamical term of the first scalar field in the Lagrange density.…”

“…Equations with the above form, with the 1/r factor, were considered before in Refs. [14,34], and they engender scale invariance. Moreover, the above first-order equations have two signs; they are related by the change r → 1/r , so we only deal with the positive sign from now on.…”

“…The field-dependent function can be used to modify the magnetic properties of the medium to study vortices, as in [7][8][9][15][16][17][18][19], but it can also be considered to modify electrical properties of the medium, as in [3,4] and in [14], for instance.…”

Vortices in Maxwell-Chern-Simons-Higgs models with nonminimal coupling

“…In a similar context, in the recent work in Ref. [34], it has been used to trade scale invariance with an electric charge that capture the basic feature of asymptotic freedom. It has also been added in Refs.…”