Topological structures in a non-canonical perturbative dynamics of a cuscuton-like model

TL;DR

This paper explores topological structures like kinks and vortices in a cuscuton-like model, combining perturbative quantum analysis with numerical and reorganized energy methods to identify localized solutions and flux quantization.

Contribution

It introduces a novel approach to studying topological solutions in a cuscuton-like model, including the existence of kink and vortex configurations with localized energy.

Findings

Existence of kink solutions in a modified cuscuton model.

Identification of vortex solutions with quantized magnetic flux.

Non-topological solutions in the absence of spontaneous symmetry breaking.

Abstract

In this work, a possible description for quantum dynamics of the cuscuton within the sigma-model approach is presented. Lower order perturbative corrections and the structure of divergences are found. Motivated by the results generated by the perturbative approach, we investigate the existence of topological structures in the cuscuton-like model. The structures we study are, first, kink-like configurations in two dimensional spacetime, second, vortex solutions in three dimensional one with gauge field ruled by the Maxwell term. In fact, to show the existence of kink solutions it is needed to introduce a standard dynamics term in the cuscuton-like model. Then, a numerical approach (interpolation method) is used and the solution of the scalar field is presented. On the other hand, for the study of topological vortices, we reorganized the energy density to obtain, for convenience, equations similar to those canonical vortex structures, namely, the Maxwell-Higgs model. In fact, even for this particular case, we observed the existence of structures with localized energy and quantized magnetic flux in a given topological sector. We also show that when the model does not spontaneously break the symmetry, the $(2+1)D$ model only admits the so-called non-topological field solutions.