Topological Defects in the Georgi-Machacek Model

TL;DR

This paper investigates topological defects like domain walls and vortices in the Georgi-Machacek model, revealing stable non-Abelian structures and their potential cosmological implications.

Contribution

It demonstrates the existence of topologically stable non-Abelian defects in the model and analyzes their properties under different symmetry-breaking conditions.

Findings

Existence of non-Abelian domain walls and vortices in the model.

Vortices become topologically stable Z-strings when U(1)_Y coupling is included.

Domain walls can decay via quantum tunneling, producing detectable gravitational waves.

Abstract

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) in this model. In the limit of the vanishing $U(1)_{\rm Y}$ gauge coupling in which the custodial symmetry becomes exact, the presence of a vortex spontaneously breaks the custodial symmetry, giving rise to $S^2$ 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 $U(1)_{\rm Y}$ 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 $S^2$ NG modes. Finally, we discuss the existence of domain wall solutions bounded by flux tubes, where their $S^2$ 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