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

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.

arXiv comment22 pages, 6 figures

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Cited by in corpus (4)

• Families of Q-balls in a deformed $O(4)$ linear sigma model
• Localized structures in three-field models: geometrically constrained configurations and the first-order framework
• Geometric Construction of non-linear Sigma models with Q-ball/Q-kink solutions
• Topological and non-topological kink families in non-linear $({\mathbb{S}}^1\times {\mathbb{S}}^1)$-Sigma models