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

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

2001-05-14

arxiv.org/abs/hep-th/0105128v2

Phys.Rev. D64 (2001) 105023

Physics

High Energy Physics

High Energy Physics - Theory

11 pages, 3 figures. Several minor changes made. Matches the version accepted to PRD

Scientific paper

10.1103/PhysRevD.64.105023

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.

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