# Note on a solution to domain wall problem with the Lazarides-Shafi mechanism in axion dark matter models

## TL;DR

This paper investigates the Lazarides-Shafi mechanism in axion dark matter models, showing how non-Abelian symmetries lead to stable string-wall configurations that eventually collapse, emitting axions and avoiding cosmological issues.

## Contribution

It provides a detailed analysis of string and wall configurations in the Lazarides-Shafi mechanism, highlighting the splitting of Abelian strings into Alice strings and their subsequent collapse.

## Key findings

- Abelian axion strings with high domain wall number split into Alice strings.
- Alice strings can be attached by a single wall due to non-Abelian rotations.
- Walls collapse by tension, emitting axions, preventing stable networks.

## Abstract

Axion is a promising candidate of dark matter. After the Peccei-Quinn symmetry breaking, axion strings are formed and attached by domain walls when the temperature of the universe becomes comparable to the QCD scale. Such objects can cause cosmological disasters if they are long-lived. As a solution for it, the Lazarides-Shafi mechanism is often discussed through introduction of a new non-Abelian (gauge) symmetry. We study this mechanism in detail and show configuration of strings and walls. Even if Abelian axion strings with a domain wall number greater than one are formed in the early universe, each of them is split into multiple Alice axion strings due to a repulsive force between the Alice strings even without domain wall. When domain walls are formed as the universe cools down, a single Alice string can be attached by a single wall because a vacuum is connected by a non-Abelian rotation without changing energy. Even if an Abelian axion string attached by domain walls are created due to the Kibble Zurek mechanism at the chiral phase transition, such strings are also similarly split into multiple Alice strings attached by walls in the presence of the domain wall tension. Such walls do not form stable networks since they collapse by the tension of the walls, emitting axions.