Global monopoles in the two-Higgs-doublet-model

TL;DR

This paper investigates the formation, structure, and properties of global monopoles arising from spontaneous symmetry breaking in the two-Higgs-doublet model, revealing their relation to Nambu monopoles and their scaling behavior.

Contribution

It introduces a detailed description of global monopoles in the two-Higgs-doublet model, including their formation, structure, and relation to Nambu monopoles, with analysis of their density scaling.

Findings

Monopoles form with a charged vacuum at the center.

A spherical symmetric solution with uniform winding is found.

Monopole density scales despite complex structure.

Abstract

We discuss monopoles formed due to the spontaneous breakdown of a global $SO(3)_{\rm HF}$ symmetry within the global two-Higgs doublet model. We explain that the Higgs sector dynamics can be described in terms of two vectors one of which is null, $R^A=(R^0,R^a,R^4,R^5)$ for $a=1,2,3$, with 5 independent components describing the Higgs family symmetry and another, $n^a$, with 3 independent components related to the ``would-be'' Goldstone bosons. When formed from random initial conditions we find that monopoles are formed with a charged vacuum in the centre which couples the two fields together. We find a spherical symmetric solution which is an approximately uniform, unit winding of the sphere in both the $R^a$ and $n^a$ vectors. These global monopoles are closely related to the Nambu monopole. The additional complexity and structure contained in these monopoles does not appear to prevent the scaling of their density.