Twisted Skyrmion String

TL;DR

This paper investigates the properties of twisted Skyrmion strings within the nonlinear sigma model, revealing their stability conditions, energy characteristics, and numerical energy estimates, contributing to understanding topological solitons.

Contribution

It introduces the concept of twist in Skyrmion strings, analyzes their stability, and provides numerical estimates of their energy per unit length.

Findings

Twisted Skyrmion strings are neutrally stable to scale changes.

The minimum energy per unit length is approximately 20.37×10^60 eV/m.

Stability conditions relate to the energy being minimum and scale-free.

Abstract

We study nonlinear sigma model, especially Skyrme model without twist and Skyrme model with twist: twisted Skyrmion string. Twist term, $mkz$, is indicated in vortex solution. Necessary condition for stability of vortex solution has consequence that energy of vortex is minimum and scale-free (vortex solution is neutrally stable to changes in scale). We find numerically that the value of vortex minimum energy per unit length for twisted Skyrmion string is $20.37\times 10^{60}~\text{eV/m}$.