A SU(5) × Z₂ kink solution and its local stability

A non-abelian kink inducing asymptotically the breaking pattern SU(5)×Z₂ → SU(4)×U(1)/Z₄ is obtained. We consider a fourth order Higgs potential in a 1 + 1 theory where the scalar field is in the adjoint representation of SU(5). The perturbative stability of the kink is also evaluated. A Schrödinger-like equation for the excitations along each SU(5) generator is determined, and in none of the cases negative eigenvalues compromising the stability of solution are found. In particular, several bounded scalar states are determined, being one of them the translational zero mode of the flat space SU(5) × Z₂ kink.