Abstract
In order to investigate possible topological vortex structures in generalized models, we developed a perturbative generation approach for scalar-vector theories. We demonstrate explicitly that the dielectric permeability functions must have a nonpolynomial shape, i. e., the form of the logarithmic function. Basing on this result, we built models in $(2+1)D$ with logarithmic dielectric permeability in order to investigate the presence of topological vortex structures in a Maxwell model. This type of scalar-vector models is important because they can generate stationary field solutions in theories describing the dynamics of the scalar field. As examples, we chose models of the complex scalar field coupled to the Maxwell field. Subsequently, we investigated the model's Bogomol'nyi equations to describe the field configurations. Then, we demonstrate numerically, for an ansatz with rotational symmetry, that the solutions of the complex scalar field generating minimum energy configurations are topological structures depending on the parameters obtained in the perturbative generation of the vector-scalar theory.
Highlights
We demonstrate numerically, for an ansatz with rotational symmetry, that the solutions of the complex scalar field generating minimum energy configurations are topological structures depending on the parameters obtained in the perturbative generation of the vector-scalar theory
Topological vortex studies have attracted the interest of many researchers, see, for example, Refs. [1,2,3,4,5], due to the possibility of their application in condensed matter physics [6]
The Bogomol’nyi-Prasad-Sommerfield (BPS) topological vortices arising within field theory context are similar to the known Abrikosov vortices known as characteristic phenomena in condensed matter physics [8,9]
Summary
Topological vortex studies have attracted the interest of many researchers, see, for example, Refs. [1,2,3,4,5], due to the possibility of their application in condensed matter physics [6]. From the qualitative viewpoint, such topological structures are formed during a phase transition related to the breaking of some symmetry [7] In this way, the Bogomol’nyi-Prasad-Sommerfield (BPS) topological vortices arising within field theory context are similar to the known Abrikosov vortices known as characteristic phenomena in condensed matter physics [8,9]. It is interesting to mention that vortices arise within the study of the dynamics of scalar field or static vector field coupled to a gauge field in three-dimensional space-time These structures find applications in several areas of physics. We propose a form for the electrical permeability function and show that the generalized models constructed with use of this function in the three-dimensional case admit topological solutions with interesting physical properties. IV, we present some results and some conclusions obtained throughout the work
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