Cosmic String in Abelian-Higgs Model with Enhanced Symmetry -- Implication to the Axion Domain-Wall Problem --

TL;DR

This study investigates cosmic string solutions in an Abelian-Higgs model with enhanced symmetry, demonstrating that the evolution of string networks in 3+1 dimensions can suppress problematic strings, potentially resolving the axion domain-wall problem.

Contribution

The paper extends previous 2+1D simulations to 3+1D, showing that uncompensated strings are suppressed over time, offering a new approach to avoid the axion domain-wall issue.

Findings

Uncompensated strings are highly suppressed at late times in 3+1D simulations.

The complex evolution of string networks differs significantly from 2+1D cases.

The setup can potentially solve the axion domain-wall problem.

Abstract

In our previous work, we found new types of the cosmic string solutions in the Abelian-Higgs model with an enhanced $U(1)$ global symmetry. We dubbed those solutions as the compensated/uncompensated strings. The compensated string is similar to the conventional cosmic string in the Abrikosov-Nielsen-Olesen (ANO) string, around which only the would-be Nambu-Goldstone (NG) boson winds. Around the uncompensated string, on the other hand, the physical NG boson also winds, where the physical NG boson is associated with the spontaneous breaking of the enhanced symmetry. Our previous simulation in the 2+1 dimensional spacetime confirmed that both the compensated/uncompensated strings are formed at the phase transition of the symmetry breaking. Non-trivial winding of the physical NG boson around the strings potentially causes the so-called axion domain-wall problem when the model is applied to the axion model. In this paper, we perform simulation in the 3+1 dimensional spacetime to discuss the fate of the uncompensated strings. We observe that the evolution of the string-network is highly complicated in the 3+1 dimensional simulation compared with that seen in the previous simulation. Despite such complications, we find that the number of the uncompensated strings which could cause can be highly suppressed at late times. Our observation suggests that the present setup can be applied to the axion model without suffering from the axion domain-wall problem.