To be or knot to be?

Abstract

It has been suggested recently that knots might exist as stable soliton solutions in a simple three-dimensional classical field theory, opening up a wide range of possible applications in physics and beyond. We have re-examined and extended this work in some detail using a combination of analytic approximations and sophisticated numerical algorithms. For charges between one and eight, we find solutions which exhibit a rich and spectacular variety of phenomena, including stable toroidal solitons with twists, linked loops and also knots. The physical process which allows for this variety is the reconnection of string-like segments.

7 pages plus 1 figure included in GIF format

Cited by in corpus (154)

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• Topological Objects in Two-component Bose-Einstein Condensates
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• Scattering of knotted vortices (Hopfions) in the Faddeev-Skyrme model
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• Revisiting the Faddeev-Skyrme Model and Hopf Solitons
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• Generalized Eikonal Knots and New Integrable Dynamical Systems
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• Integrability and Hopf Solitons in Models with Explicitly Broken O(3) Symmetry
• Vortices in the extended Skyrme-Faddeev model
• Instantons, Monopoles and the Flux Quantization in the Faddeev-Niemi Decomposition
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• Effective sigma models and lattice Ward identities
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• Strongly coupled Skyrme-Faddeev-Niemi hopfions
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• New Faddeev-Niemi type variables for static SU(3) Yang-Mills theory
• Some vortex solutions in the extended Skyrme-Faddeev model
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• Solitonic solutions of Faddeev model