Transference of kinks between $\mathbb{S}^2$ and $\mathbb{R}^2$ Sigma models

TL;DR

This paper generalizes deformation methods for scalar field theories to Sigma models, specifically exploring how kinks transfer between models on the sphere and the plane, and analyzing changes in kink structures and energies.

Contribution

It introduces a generalized deformation approach for Sigma models, enabling the transfer of kink solutions between different target spaces such as  and , and studies the resulting structural and energetic modifications.

Findings

Kink structures are successfully transferred between  and  Sigma models.

Deformations lead to significant changes in the kink energy and structure.

Three specific examples illustrate the deformation process and its effects.

Abstract

In this paper methods for deforming scalar field theories on Euclidean target spaces, in which new field theories are constructed so that solutions are known, are generalized to the context of Sigma models. In particular, deformations between Sigma models on the plane and on the sphere are considered. Three different examples are presented, where the change in the structure of the kink variety and the energy of the deformed kinks during this procedure are studied.