Topological structures in a noncanonical perturbative dynamic of a cuscutonlike model

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 cuscutonlike model. The structures we study are, first, kinklike 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 one needs to introduce a standard dynamics term in the cuscutonlike 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 nontopological field solutions.

Automated summary

In this work, a possible description for the quantum dynamics of cuscuton within the sigma-model approach is presented. Perturbative corrections and divergences are studied, followed by an investigation into the existence of topological structures in the cuscutonlike model. Numerical methods are used to find kinklike configurations and vortex solutions. The study shows the existence of localized energy and quantized magnetic flux in the topological sectors.