Multilayered vortices

Abstract

Vortices are localized planar structures that attain topological stability and can be used to describe collective behavior in a diversity of situations of current interest in nonlinear science. In high energy physics, vortices engender integer winding number and appear under the presence of a local Abelian symmetry. In this work we study vortices in a Maxwell-Higgs model, in which the gauge symmetry is enhanced to accommodate additional symmetries, responsible to generate localized structures to be used to constrain the vortex structure in a given region in the plane. The main aim is to examine how the vortex profile changes when it inhabits a limited region, an issue of current interest to the study of vortices at the nanometric scale. arXiv:1908.07871v2 [hep-th]

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. 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.…”

BPS solitons with internal structure in the gauged O(3) sigma model

“…[34] to circumvent the Derrick-Hobart theorem [35,36]. Furthermore, such an approach already has been used in different contexts, e.g., Maxwell-Higgs [29,37], magnetic monopoles [38], and gauged CPð2Þ [30].…”

“…The particular case α ¼ 1 has been previously approached in different contexts as global defect structures [34], skyrmionlike configurations [39,40], massless Dirac fermions [41], magnetic monopoles [38] and vortices with internal structures [29,30]. On the other hand, arbitrary values of α were used to discuss the solutions into a multilayered structure [37]. Then, by assuming the superpotential (30), the BPS equation (27) results…”

“…In what follows, we present the numerical solution of the system formed by Eqs. (37) and (38) for some values of N and r 0 . The resulting field profiles for the gauge and sigma fields, magnetic field, and energy density ε Σ ðrÞ are shown in Figs.…”