Massive Hopfions

TL;DR

This paper explores a modified Skyrme-Faddeev model with symmetry breaking potential, revealing that in the infinite mass limit, it admits compact knotted solutions with energy behaviors similar to the standard model.

Contribution

It introduces a Skyrme-Faddeev model with symmetry breaking potential and analyzes its infinite mass limit, discovering compact knotted solutions and their energy properties.

Findings

Infinite mass model has compact knotted solutions.

Charged solutions similar to the m=0 model are found.

Energy growth follows a power law similar to the standard model.

Abstract

The Skyrme-Faddeev model is a (3+1)-dimensional model which has knotted, string-like, soliton solutions. In this paper we investigate a Skyrme-Faddeev model with an SO(3) symmetry breaking potential. We then rescale this model and take the mass to infinity. This infinite mass model is found to have compact knotted solutions. In all of the investigated massive models we find similar charged solutions as in the usual, m=0, model. We also find that their energies follow a similar power growth as the m=0 model.