Cabling in the Skyrme-Faddeev model

TL;DR

This paper introduces a method to construct knotted field solutions in the Skyrme-Faddeev model, revealing the existence of hopfions with cable and hyperbolic knot structures beyond previously known torus knots.

Contribution

It presents the first construction of non-torus knot hopfions in the Skyrme-Faddeev model using cable and hyperbolic knots.

Findings

First known hopfions with cable and hyperbolic knot structures

Extension of the types of knotted solutions in the Skyrme-Faddeev model

Demonstration of energy minimization for complex knot configurations

Abstract

The Skyrme-Faddeev model is a three-dimensional non-linear field theory that has topological soliton solutions, called hopfions, which are novel string-like solutions taking the form of knots and links. Solutions found thus far take the form of torus knots and links of these, however torus knots form only a small family of known knots. It is an open question whether any non-torus knot hopfions exist. In this paper we present a construction of knotted fields with the form of cable knots to which an energy minimisation scheme can be applied. We find the first known hopfions which do not have the form of torus knots, but instead take the form of cable and hyperbolic knots.