Space of kink solutions in SU(N)\times Z_2

TL;DR

This paper classifies and constructs multiple classes of kink solutions in an SU(N)×Z_2 field theory, revealing their stability properties, degeneracy manifolds, and potential in three-dimensional structures, with explicit SU(5) examples.

Contribution

It introduces a classification of kink solutions into (N+1)/2 classes in SU(N)×Z_2 theories, detailing their stability, degeneracy spaces, and explicit constructions for SU(5).

Findings

Identified (N+1)/2 classes of kink solutions in SU(N)×Z_2.

Found degeneracy manifolds containing incontractable spheres.

Constructed explicit solutions for SU(5) model.

Abstract

We find $(N+1)/2$ distinct classes (``generations'') of kink solutions in an $SU(N)\times Z_2$ field theory. The classes are labeled by an integer $q$. The members of one class of kinks will be globally stable while those of the other classes may be locally stable or unstable. The kink solutions in the $q^{th}$ class have a continuous degeneracy given by the manifold $\Sigma_q=H/K_q$, where $H$ is the unbroken symmetry group and $K_q$ is the group under which the kink solution remains invariant. The space $\Sigma_q$ is found to contain incontractable two spheres for some values of $q$, indicating the possible existence of certain incontractable spherical structures in three dimensions. We explicitly construct the three classes of kinks in an SU(5) model with quartic potential and discuss the extension of these ideas to magnetic monopole solutions in the model.