# Topological Nambu monopole in two Higgs doublet models

## TL;DR

This paper demonstrates the existence of a topological Nambu monopole in two Higgs doublet models, which is stabilized by discrete symmetries and attached to $Z$ strings, unlike in the standard model.

## Contribution

It introduces a new topological monopole solution in two Higgs doublet models, expanding the understanding of monopole stability beyond the standard model.

## Key findings

- Existence of a topological Nambu monopole in two Higgs doublet models.
- Explicit construction of the monopole solution through numerical simulation.
- Monopoles could be abundant and detectable in the universe.

## Abstract

We show that a topological Nambu monopole exists as a regular solution for a large range of parameters in two Higgs doublet models, contrary to the standard model admitting only non-topological Nambu monopoles. We analyze a Higgs potential with a global $U(1)$ symmetry and a discrete symmetry $\mathbb{Z}_2$. The monopole is attached by two topological $Z$ strings ($Z$ flux tubes) from both sides. Despite of a trivial second homotopy group, the discrete symmetry $\mathbb{Z}_2$ together with a non-trivial first homotopy group for $Z$ strings topologically ensures the topological stability. After analytically constructing an asymptotic form of such a configuration, we explicitly construct a solution of the equation of motion based on a 3D numerical simulation, in which magnetic fluxes spherically emanating from the monopole at large distances are deformed in the vicinity of the monopole. Since the monopoles are expected to be abundant in the present universe, they might be observed in the current monopole searches.