Vortex solutions in nonpolynomial scalar QED

TL;DR

This paper explores vortex solutions in a generalized scalar QED model with logarithmic dielectric functions, demonstrating the existence of topological vortex structures through analytical and numerical methods.

Contribution

It introduces a perturbative approach showing that dielectric functions must be nonpolynomial, specifically logarithmic, and constructs models in (2+1)D to study vortex solutions.

Findings

Logarithmic dielectric functions are essential for vortex solutions.

Numerical solutions confirm topological vortex structures.

Models exhibit minimum energy configurations with rotational symmetry.

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.