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 flux tubes (vortices or cosmic strings) 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 fluxes. 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 to become pseudo-NG modes, and all non-Abelian vortices fall into a topologically stable Z string. This is in contrast to the standard model in which Z strings are nontopological 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 flux tubes, where their S² NG modes match. The domain walls may quantum mechanically decay by creating a hole bounded by a flux tube loop, and would be cosmologically safe. Gravitational waves produced from unstable domain walls could be detected by future experiments.