Non-Abelian strings and domain walls in two Higgs doublet models

TL;DR

This paper explores topologically stable vortex strings and domain walls in two Higgs doublet models, revealing new stable configurations and their properties through numerical analysis, including non-Abelian moduli and effects of parameter deformations.

Contribution

It demonstrates the existence of stable topological strings and domain walls in two Higgs doublet models, including non-Abelian strings with moduli, and analyzes their tensions and stability under various parameters.

Findings

Existence of topological $Z$-strings and domain walls confirmed numerically.

Gauging $U(1)_Y$ lowers $Z$-string tension but not $W$-string tension.

Parameter regions where $W$-strings are most stable identified.

Abstract

Contrary to the standard model that does not admit topologically nontrivial solitons, two Higgs doublet models admit topologically stable vortex strings and domain walls. We numerically confirm the existence of a topological $Z$-string confining fractional $Z$-flux inside. We show that topological strings at $\sin\theta_W = 0$ limit reduce to non-Abelian strings which possess non-Abelian moduli $S^2$ associated with spontaneous breakdown of the $SU(2)$ custodial symmetry. We numerically solve the equations of motion for various parameter choices. It is found that a gauging $U(1)_Y$ always lowers the tension of the $Z$-string while it keeps that of the $W$-string. On the other hand, a deformation of the Higgs potential is either raising or lowering the tensions of the $Z$-string and $W$-string. We numerically obtain an effective potential for the non-Abelian moduli $S^2$ for various parameter deformations under the restriction $\tan\beta=1$. It is the first time to show that there exists a certain parameter region where the topological $W$-string can be the most stable topological excitation, contrary to conventional wisdom of electroweak theories. We also obtain numerical solutions of composites of the string and domain walls in a certain condition.