Kinks in massive non-linear ${\mathbb S}^1\times{\mathbb S}^1$-Sigma models

TL;DR

This paper analytically characterizes all kink solutions in massive non-linear Sigma models with a torus target space, revealing stability properties influenced by the target space topology.

Contribution

It provides the first analytical solutions for kink varieties in these models, including non-topological kinks stabilized by topology.

Findings

Analytical solutions for all kink types in the models.

Non-topological kinks can be globally stable due to topology.

Complete linear stability analysis for basic kinks.

Abstract

In this paper the whole kink varieties arising in several massive non-linear Sigma models whose target space is the torus ${\mathbb S}^1\times{\mathbb S}^1$ are analytically calculated. This possibility underlies the construction of first-order differential equations by adapting the Bogomolny procedure to non-Euclidean spaces. Among the families of solutions non-topological kinks connecting the same vacuum are found. This class of solutions are usually considered to be not globally stable. However, in this context the topological constraints obtained by the non-simply connectedness of the target space turn these non-topological kinks into globally stable solutions. The analytical resolution of the equations allows the complete study of the linear stability for some basic kinks.