# A $SU(5)\times Z_2$ kink solution and its local stability

## TL;DR

This paper constructs a non-abelian $SU(5) imes Z_2$ kink solution in a 1+1 dimensional scalar field theory with a fourth order Higgs potential, analyzing its stability and identifying scalar excitations.

## Contribution

It introduces a new $SU(5) imes Z_2$ kink solution with a specific symmetry breaking pattern and evaluates its perturbative stability through a Schrödinger-like analysis.

## Key findings

- The kink solution is perturbatively stable with no negative eigenvalues.
- Several bounded scalar states are identified, including a translational zero mode.
- The stability analysis confirms the robustness of the kink configuration.

## Abstract

A non-abelian kink inducing asymptotically the breaking pattern $SU(5)\times Z_2\rightarrow SU(4)\times U(1)/Z_4$ 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 Schr\"odinger-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 found, being one of them the translational zero mode of the flat space $SU(5)\times Z_2$ kink.