More on Classical Stability of Hopf-like Solitons of the Toroidal-Twisted type
Chao-Hsiang Sheu, Mikhail Shifman
TLDR
Numerical analysis confirms the existence and classical stability of large-size, toroidal-twisted Hopf-like solitons in full QED theory.
Key contributions
- Enhances the proof for Faddeev-Noemi's twisted toroidal structure hypothesis for Hopfions.
- Applies numerical analysis to confirm the existence of Hopf-like solitons.
- Demonstrates large-size Hopf-like solitons are local energy minima in full QED theory.
Why it matters
This paper provides strong numerical evidence for the existence and stability of complex topological structures (Hopf-like solitons) in fundamental physics theories like QED. It moves beyond qualitative arguments, solidifying a long-standing conjecture, and deepening our understanding of particle-like excitations.
Original 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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