First order framework for gauge k-vortices

TL;DR

This paper introduces a first order framework for gauge k-vortices in generalized Maxwell-Higgs models, providing analytical solutions, a decoupling method for equations, and discovering a compact vortex with energy localized in a circle.

Contribution

It develops a novel first order formalism for gauge k-vortices, enabling analytical solutions and a method to construct models with energy depending solely on boundary conditions.

Findings

Analytical solutions for gauge k-vortices are obtained.

A decoupling method for first order equations is introduced.

A compact vortex configuration with localized energy density is found.

Abstract

We study vortices in generalized Maxwell-Higgs models, with the inclusion of a quadratic kinetic term with the covariant derivative of the scalar field in the Lagrangian density. We discuss the stressless condition and show that the presence of analytical solutions help us to define the model compatible with the existence of first order equations. A method to decouple the first order equations and to construct the model is then introduced and, as a bonus, we get the energy depending exclusively on a function of the fields calculated from the boundary conditions. We investigate some specific possibilities and find, in particular, a compact vortex configuration in which the energy density is all concentrated in a unit circle.