Percolation of Domain Walls in the Two-Higgs Doublet Model

TL;DR

This paper investigates the dynamics of domain walls in the Two-Higgs Doublet Model, revealing slower percolation due to long-lived loops and potential formation of stationary configurations called Kinky Vortons.

Contribution

It provides the first numerical simulation of domain wall percolation in the 2HDM, highlighting differences from simpler models and suggesting new stable configurations.

Findings

Percolation process is slower in 2HDM due to long-lived loops.

Long-lived loops may lead to stationary Kinky Vorton configurations.

Long-time limit of domain wall density is similar to simpler models.

Abstract

Domain walls formed during a phase transition in a simple field theory model with $\mathbb{Z}_2$ symmetry in a periodic box have been demonstrated to annihilate as fast as causality allows and their area density scales $\propto t^{-1}$. We have performed numerical simulations of the dynamics of domain walls in the Two-Higgs Doublet Model (2HDM) where the potential has $\mathbb{Z}_2$ symmetry in two spatial dimensions. We observed significant differences with the standard case. Although the extreme long-time limit is the same for the $\approx 10^{5}$ sets of random initial configurations analysed, the percolation process is much slower due to the formation of long-lived loops. We suggest that this is due to the build up of superconducting currents on the walls which could lead ultimately to stationary configurations known as Kinky Vortons. We discuss the relevance of these findings for the production of Vortons in three spatial dimensions.