Collapsing domain walls beyond $Z_2$

TL;DR

This paper investigates domain walls from breaking larger discrete symmetries like Z_N, focusing on Z_3, analyzing their properties, dynamics, and gravitational wave signatures beyond the well-studied Z_2 case.

Contribution

It provides a detailed study of Z_N domain walls, especially Z_3, including semi-analytical tension and thickness calculations, and explores their unique collapse dynamics and gravitational wave signals.

Findings

Z_3 domain walls have distinct tension and thickness properties.

Explicit symmetry breaking causes more complex collapse dynamics.

Gravitational wave signals differ from Z_2 domain walls.

Abstract

Discrete symmetries are widely imposed in particle theories. It is well-known that the spontaneous breaking of discrete symmetries leads to domain walls. Current studies of domain walls have focused on those from the spontaneous breaking of a $Z_2$ symmetry. Larger discrete symmetries have multiple degenerate vacua, leading to the domain walls in principle different from the simplest $Z_2$ domain wall. We take domain walls from $Z_N$ symmetry breaking as an illustrative study, and study in detail the $Z_3$ case, in which semi-analytical results for the tension and thickness of domain walls are derived. Explicit symmetry breaking terms lead to the dynamics of domain walls collapsing more complicated than the $Z_2$ case. Gravitational wave signals deviate from those from $Z_2$ domain walls.