Topological defects in the georgi-machacek model

We study topological defects in the Georgi-Machacek model in a hierarchical symmetry breaking in which extra triplets acquire vacuum expectation values before the doublet. We find a possibility of topologically stable non-Abelian domain walls and non-Abelian ux tubes (vortices) in this model. In the limit of the vanishing U(1)Y gauge coupling in which the custodial symmetry becomes exact, the presence of a vortex spontaneously breaks the custodial symmetry, giving rise to S2 Nambu-Goldstone (NG) modes localized around the vortex corresponding to non-Abelian uxes. Vortices are continuously degenerated by these degrees of freedom, thereby called non-Abelian. By taking into account the U(1)Y gauge coupling, the custodial symmetry is explicitly broken, the NG modes are lifted, and all non-Abelian vortices fall into a topologically stable Z-string. This is in contrast to the SM in which Z-strings are non-topological and are unstable in the realistic parameter region. Non-Abelian domain walls also break the custodial symmetry and are accompanied by localized S2 NG modes. Finally, we discuss the existence of domain wall solutions bounded by ux tubes, where their S2 NG modes match. The domain walls may quantum mechanically decay by creating a hole bounded by a ux tube loop, and would be cosmologically safe. Gravitational waves produced from unstable domain walls could be detected by future experiments.