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arXiv · 2605.00757

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

Chao-Hsiang Sheu·Mikhail Shifman
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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).

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Chao-Hsiang Sheu, Mikhail Shifman. 2026-05-01. More on Classical Stability of Hopf-like Solitons of the Toroidal-Twisted type. https://arxiv.org/abs/2605.00757

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