On vortices and solitons in Goldstone and abelian-Higgs models

TL;DR

This paper investigates various vortex and soliton solutions in Goldstone and abelian-Higgs models, exploring their stability and potential physical relevance, especially in high-energy physics contexts like the LHC.

Contribution

It introduces new stable solutions in a $U(1)$ model with a Ginzburg-Landau potential and analyzes the stability of vortex rings in extended models with higher derivatives.

Findings

Stable straight string solutions exist in a specific parameter region.

Vortex rings are generally unstable due to current quenching.

Adding higher derivative terms does not guarantee vortex ring stability.

Abstract

In the present work we discuss non-linear physics problems such as Nielsen-Olesen strings, superconducting bosonic straight strings and static vortex rings. We start with a toy model. We search for antiperiodic solitons of the Goldstone model on a circle. Such models provide the basis as well as useful hints for further research on three-dimensional more realistic problems. We proceed with a full research on a $U(1)$ model which admits stable straight string solutions in a small, numerically determined area. That model has a Ginzburg-Landau potential with a cubic term added to it and can be found in condensed matter problems as well. The next part of our research, has to do with a $U(1) \times U(1)$ model which is the main subject of our interest. There, we search for stable axially symmetric solutions which are solitons, which can represent particles, the mass of which is of the order of TeV. The confirmation or rejection of the existence of those defects is of great interest if we consider that LHC will work in the same energy range. In our study, we find out that due to current quenching, these vortex rings seem to be unstable. We also extend the model of vortex rings by adding higher derivative terms which are favorable for stability. After the extensive analysis we performed, we conclude that these objects don’t seem to be stable. The reasons which brought us to this conclusion are explained.