More on Classical Stability of Hopf-like Solitons of the Toroidal-Twisted type

TL;DR

This paper numerically confirms that large Hopf-like solitons, modeled as twisted toroidal structures, exist as local energy minima in the full QED theory, supporting Faddeev-Noemi's conjecture.

Contribution

It provides a numerical validation of the existence of large Hopf-like solitons as local minima in the full QED model, extending previous qualitative arguments.

Findings

Large-size Hopf-like solitons are confirmed as local energy minima.

Numerical analysis supports the Faddeev-Noemi conjecture.

Solitons can be viewed as twisted toroidal structures in QED.

Abstract

The Faddeev-Hopf model [1] supporting Hopfions was shown to emerge in the low-energy limit of four-dimensional scalar quantum electrodynamics (QED) with two charged scalar fields [2, 3]. Faddeev and Noemi conjectured that the Hopfions and Hopf-like solitons -- vortons -- can be based on a twisted toroidal structure inherent to QED [4-6]. This conjecture was discussed in detail in [2] in the approximation of negligibly small extrinsic curvature. Qualitative and semi-quantitative arguments were used to demonstrate the validity of the Faddeev-Noemi hypothesis. Here we further enhance the proof by applying a numerical analysis which confirms that large-size Hopf-like solitons exist as local energy minima in the full QED theory (in the Faddeev-Skyrme model they become topological solitons representing the global minima in the given topological sector).