BPS Maxwell-Chern-Simons vortices with internal structures: the Abelian Higgs and the gauged $CP(2)$ cases

Abstract

We investigate the existence of first-order vortices inherent to both the Maxwell-Chern-Simons-Higgs and the Maxwell-Chern-Simons-CP (2) models extended via the inclusion of an extra scalar sector which plays the role of a source field. For both cases, we focus our attention on the timeindependent configurations with radial symmetry which can be obtained through the implementation of the so-called Bogomol'nyi-Prasad-Sommerfield (BPS) prescription. In this sense, in order to solve the corresponding first-order differential equations, we introduce some particular scenarios which are driven by the source field whose presence, we expect, must change the way the resulting vortices behave. After solving the effective first-order system through a finite-difference algorithm, we comment about the main new effects induced by the presence of the source field in the shape of the final configurations.

Electrically charged localized structures

“…Regarding the function A 0 , it has the very same expression displayed in Eq. (18), so E c = 4π|W (φ(r = 0))|. Considering the function in Eq.…”

“…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 cap-tures 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. Moreover, very recently, in [20] the authors studied the dielectric Skyrme model, that is, the Skyrme model where both the kinetic and Skyrme terms are multiplied by field-dependent functions, leading to new results of current interest.…”

“…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. 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.…”