Knots and Particles

Abstract

Using methods of high performance computing, we have found indications that knotlike structures appear as stable finite energy solitons in a realistic 3+1 dimensional model. We have explicitly simulated the unknot and trefoil configurations, and our results suggest that all torus knots appear as solitons. Our observations open new theoretical possibilities in scenarios where stringlike structures appear, including physics of fundamental interactions and early universe cosmology. In nematic liquid crystals and 3He superfluids such knotted solitons might actually be observed.

9 pages, 4 color eps figures and one b/w because of size limit (color version available from authors)

References in corpus (2)

• Big bang simulation in superfluid 3He-B -- Vortex nucleation in neutron-irradiated superflow
• The Cosmological Kibble Mechanism in the Laboratory: String Formation in Liquid Crystals

Cited by in corpus (346)

• Spinor Bose-Einstein condensates
• Reconfigurable knots and links in chiral nematic colloids
• Vortices with fractional flux in two-gap superconductors and in extended Faddeev model
• Partially Dual variables in SU(2) Yang-Mills Theory
• Topological quantum matter with cold atoms
• To be or knot to be?
• Hidden symmetry and knot solitons in a charged two-condensate Bose system
• Vortex knots in light
• Stationary ring solitons in field theory - knots and vortons
• Particle-like topologies in light
• Tying knots in light fields
• Solitons, Links and Knots
• Exceptional Links and Twisted Fermi Ribbons in non-Hermitian Systems
• Faddeev-Hopf knots: Dynamics of linked un-knots
• Knots in a Spinor Bose-Einstein Condensate
• Skyrmion knots in frustrated magnets
• Binding a Hopfion in Chiral Magnet Nanodisk
• Hopfions in chiral magnets
• Boson Stars: Alternatives to primordial black holes?
• Current-Driven Dynamics of Magnetic Hopfions
• Hopfions emerge in ferroelectrics
• Static Hopf Solitons and Knotted Emergent Fields in Solid-State Noncentrosymmetric Magnetic Nanostructures
• An effective action for monopoles and knot solitons in Yang-Mills theory
• Partial duality in SU(N) Yang-Mills theory
• Three-dimensional crystals of adaptive knots
• Energetically stable particle-like Skyrmions in a trapped Bose-Einstein condensate
• Diversity of knot solitons in liquid crystals manifested by linking of preimages in torons and hopfions
• Dual neutral variables and knot solitons in triplet superconductors
• Topological Transformation and Free-Space Transport of Photonic Hopfions
• Helicity conservation by flow across scales in reconnecting vortex links and knots
• Exact static soliton solutions of 3+1 dimensional integrable theory with nonzero Hopf numbers
• Yang-Mills theory as an Abelian theory without gauge fixing
• Twisted toroidal vortex-solitons in inhomogeneous media with repulsive nonlinearity
• Phase diagram of planar U(1)xU(1) superconductors: condensation of vortices with fractional flux and a superfluid state
• Three-dimensional dynamics of magnetic hopfion driven by spin transfer torque
• Review: Topology of solitons and singular defects in chiral liquid crystals
• Aspects of Electric and Magnetic Variables in SU(2) Yang-Mills Theory
• Vortex knots in a Bose-Einstein condensate
• Soliton gyroscopes in media with spatially growing repulsive nonlinearity
• Quark confinement: dual superconductor picture based on a non-Abelian Stokes theorem and reformulations of Yang-Mills theory
• Knots in the Skyrme-Faddeev model
• Nematics, Knots and Non-orientable Surfaces
• Spin-Charge Separation, Conformal Covariance and the SU(2) Yang-Mills Theory
• Decomposing the Yang-Mills Field
• Monopoles and Knots in Skyrme Theory
• High capacity topological coding based on nested vortex knots and links
• ``Smoke Rings'' in Ferromagnets
• QCD versus Skyrme-Faddeev Theory
• Hopf solitons in helical and conical backgrounds of chiral magnetic solids
• Glueballs, closed fluxtubes and eta(1440)
• Correspondence between Skyrmions in 2+1 and 3+1 Dimensions
• Topological superconducting phases from inversion symmetry breaking order in spin-orbit-coupled systems
• Non-linear superposition law and Skyrme crystals
• Color Reflection Invariance and Monopole Condensation in QCD
• Monopoles, Antimonopoles and Vortex Rings
• Toroidal solitons in 3+1 dimensional integrable theories
• Towards a string representation of infrared SU(2) Yang-Mills theory
• Magnetic Geometry and the Confinement of Electrically Conducting Plasmas
• Weaving knotted vector fields with tunable helicity
• Faddeev-Niemi Conjecture and Effective Action of QCD
• Incarnations of Skyrmions
• BRST symmetry of SU(2) Yang-Mills theory in Cho--Faddeev--Niemi decomposition
• Torus knots as Hopfions
• Collective behavior of active topological solitons, knotted streamlines, and transport of cargo in liquid crystals
• Observation of acoustic spatiotemporal vortices
• Non-Meissner electrodynamics and knotted solitons in two-component superconductors
• Classical Gauge Vacua as Knots
• BPS States in Supersymmetric Chiral Models with Higher Derivative Terms
• Classification of Electromagnetic and Gravitational Hopfions by Algebraic Type
• Solitonic symmetry beyond homotopy: Invertibility from bordism and noninvertibility from topological quantum field theory
• Optical excitations of Skyrmions, knotted solitons, and defects in atoms
• Topological interface engineering and defect crossing in ultracold atomic gases
• A supersymmetric Skyrme model
• The Interaction of Two Hopf Solitons
• Fractional instantons and bions in the O(N) model with twisted boundary conditions
• Generalized Hedgehog ansatz and Gribov copies in regions with non trivial topologies
• Emergent Magneto-multipoles and Nonlinear Responses of a Magnetic Hopfion
• Exact vortex solutions in an extended Skyrme-Faddeev model
• Andreev-Bashkin effect and knot solitons in interacting mixture of a charged and a neutral superfuids with possible releveance for neutron stars
• Relations among topological solitons
• Supersymmetric K field theories and defect structures
• Observation of topological links associated with Hopf insulators in a solid-state quantum simulator
• A model of glueballs
• Knot Topology of QCD Vacuum
• Localizing modes of massive fermions and a U(1) gauge field in the inflating baby-skyrmion branes
• Simulated Annealing for Topological Solitons
• The Supersymmetric Extension of the Faddeev model
• Geometric transformation and three-dimensional hopping of Hopf solitons
• The Hopf Skyrmion in QCD with Adjoint Quarks
• Exact vortex solutions in a CP^N Skyrme-Faddeev type model
• Anomalous Abelian solitons
• Static Einstein-Maxwell black holes with no spatial isometries in AdS space
• Topological Excitations in Spinor Bose-Einstein Condensates
• Untangling knots via reaction-diffusion dynamics of vortex strings
• Relaxation of twisted vortices in the Faddeev-Skyrme model
• Magnonic Hall Effect and Magnonic Holography of Hopfions
• Baryonic torii: Toroidal baryons in a generalized Skyrme model
• Knots as possible excitations of the quantum Yang-Mills fields
• Fermionic quantization of Hopf solitons
• Excitation of knotted vortex lines in matter waves
• The volume of a soliton
• Investigation of the Nicole model
• On Energy Functions for String-Like Continuous Curves, Discrete Chains, and Space-Filling One Dimensional Structures
• Magnetic monopoles vs. Hopf defects in the Laplacian (Abelian) gauge
• Estimation of the Lin-Yang bound of the least static energy of the Faddeev model
• Glueball phenomenology and the relativistic flux tube model
• Unwinding in Hopfion vortex bunches
• Topological interface physics of defects and textures in spinor Bose-Einstein condensates
• Winding Hopfions on R^2 x S^1
• Nonabelian Faddeev-Niemi Decomposition of the SU(3) Yang-Mills Theory
• Isospinning hopfions
• Glueball mass from quantized knot solitons and gauge-invariant gluon mass
• Infinite symmetries in the Skyrme model
• Exact Self-Dual Skyrmions
• Q Rings
• Inflating baby-Skyrme branes in six dimensions
• Classically Isospinning Hopf Solitons
• Linked and Knotted Gravitational Radiation
• Investigation of the stability of Hopfions in the two-component Ginzburg-Landau model
• Reinterpretation of Faddeev-Niemi Knot in Skyrme Theory
• Non-Abrikosov Vortex and Topological Knot in Two-gap Superconductor
• Electronic scattering off a magnetic hopfion
• Fractional-flux vortices and spin superfluidity in triplet superconductors
• Knots in interaction
• New String Excitations in the Two-Higgs Standard Model
• Supersymmetric Preons and the Standard Model
• A topological mechanism of discretization for the electric charge
• A Skyrme-like model with an exact BPS bound
• Gauged Aloof Baby Skyrme Model
• Formation and Controlling of Optical Hopfions in High Harmonic Generation
• Compact Q-balls and Q-shells in the CPN type models
• A lattice study of the Faddeev-Niemi effective action
• Toroidal Solitons in Nicole-type Models
• Topological Objects in Two-component Bose-Einstein Condensates
• Kelvin knots in superconducting state
• The tight knot spectrum in QCD
• Revisiting the Faddeev-Skyrme Model and Hopf Solitons
• Scattering of knotted vortices (Hopfions) in the Faddeev-Skyrme model
• Chromoelectric Knot in QCD
• Stability of Hopfions in Bulk Magnets with Competing Exchange Interactions
• Topological optical skyrmion transfer to matter
• Skyrmions and Hopfions in 3D Frustrated Magnets
• Hopf solitons and elastic rods
• T-Duality for Coset Models
• On the geometrized Skyrme and Faddeev models
• Ring-shaped exact Hopf solitons
• Skyrmions in Yang--Mills Theories with Massless Adjoint Quarks
• Stabilizing textures with magnetic fields
• Knots from wall--anti-wall annihilations with stretched strings
• Magnetic monopoles in a charged two-condensate Bose-Einstein system
• Generalized Eikonal Knots and New Integrable Dynamical Systems
• Effective model and Magnetic Properties of the Resistive Electron Quadrupling State
• Integrability and Hopf Solitons in Models with Explicitly Broken O(3) Symmetry
• Knotlike Cosmic Strings in The Early Universe
• Topological Q-Solitons
• A Topological Structure in the Set of Classical Free Radiation Electromagnetic Fields
• Hopf solitons and Hopf Q-balls on S^3
• Low-Energy Limit of Yang-Mills with Massless Adjoint Quarks: Chiral Lagrangian and Skyrmions
• Stable Knotted Strings
• Vortices in the extended Skyrme-Faddeev model
• Instantons, Monopoles and the Flux Quantization in the Faddeev-Niemi Decomposition
• Aspects of Duality and Confining Strings
• On the Strong Coupling Limit of the Faddeev-Hopf Model
• Generalized integrability conditions and target space geometry
• Spacetime magnetic hopfions: from internal excitations and braiding of skyrmions
• When do knots in light stay knotted?
• Hopf instantons in Chern-Simons theory
• Emergent magnetic field and vector potential of the toroidal magnetic hopfions
• Topological Dark Matter in the Little Higgs Models
• $SU(3)$ Knot Solitons: Hopfions in the $F_2$ Skyrme-Faddeev-Niemi model
• Perfect fluids from high power sigma-models
• Skyrmions and Faddeev-Hopf Solitons
• Gravitating sphalerons in the Skyrme model
• Experimental demonstration of adversarial examples in learning topological phases
• A study on relativistic lagrangian field theories with non-topological soliton solutions
• Dual Superconductors and SU(2) Yang-Mills
• Potentials and the vortex solutions in the $C{P}^N$ Skyrme-Faddeev model
• Imprinting a topological interface using Zeeman shifts in an atomic spinor Bose-Einstein condensate
• Static Hopfions in the extended Skyrme-Faddeev model
• Knot soliton in Weinberg-Salam model
• Exact time dependent Hopf solitons in 3+1 dimensions
• Energy Bounds of Linked Vortex States
• Field Decomposition and the Ground State Structure of SU(2) Yang-Mills Theory
• Analog of gravitational anomaly in topological chiral superconductors
• Colour chiral solitons in low energy QCD
• BRST Symmetry for Torus Knot
• New Interpretation of Skyrme Theory
• Numerical Calculation of the Hopf Index for 3D Magnetic Textures
• Infrared degrees of freedom of Yang-Mills theory in the Schroedinger representation
• Elliptic solutions of the Skyrme model
• Constant spacing in filament bundles
• The BPS sectors of the Skyrme model and their non-BPS extensions
• New Integrable Sectors in Skyrme and 4-dimensional CP^n Model
• Knotted Solitons in a Charged Two-Condensate Bose System
• Stationary Precession Topological Solitons with Nonzero Hopf Invariant in a Uniaxial Ferromagnet
• A study of polymer knots using a simple knot invariant written consisting of multiple contour integrals
• Dynamics of dipoles and vortices in nonlinearly-coupled three-dimensional harmonic oscillators
• Nonlinear electrodynamics is skilled with knots
• Hopf solitons in the Nicole model
• Half-knot in the spinor condensates
• Gauged Hopfions
• Confinement and duality in supersymmetric gauge theories
• Spin-Orbital momentum decomposition and helicity exchange in a set of non-null knotted electromagnetic fields
• Class of exact solutions of the Skyrme and the Faddeev model
• Some properties of (3+1) dimensional vortex solutions in the extended CP^N Skyrme-Faddeev model
• BPS Sphalerons in the $F_2$ Non-Linear Sigma Model
• Particle on a torus knot: Symplectic analysis
• Leapfrogging vortex rings in the Landau-Lifshitz equation
• Exploring instantons with spin-lattice systems
• Topological aspects of dual superconductors
• Dynamics of linked filaments in excitable media
• Embedding Brans-Dicke gravity into electroweak theory
• Hopf instantons and the Liouville equation in target space
• Symmetries of generalized soliton models and submodels on target space $S^2$
• Toroidal domain walls as Hopfions
• Reflections on Topology - Viewpoints on Abelian Projections
• Gravitational Hopfions
• Deconfined quantum criticality and logarithmic violations of scaling from emergent gauge symmetry
• Infrared Yang-Mills theory as a spin system. A lattice approach
• A Class of Exact Solutions of the Faddeev Model
• Weyl symmetric structure of QCD vacuum
• Fractional Hopfions in the Faddeev-Skyrme model with a symmetry breaking potential
• On DBI Textures with Generalized Hopf Fibration
• Cabling in the Skyrme-Faddeev model
• Hopfions interaction from the viewpoint of the product ansatz
• Effective Theories of Confinement
• Knot Solitons
• Supersymmetric Q Solitons of Arbitrary Genus
• Non-Abelian Vortex-String Dynamics from Nonlinear Realization
• Linking number of vortices as baryon number
• Effective sigma models and lattice Ward identities
• Analysis of the Faddeev model
• Three-dimensional static vortex solitons in incommensurate magnetic crystals
• Topology of Knotted Optical Vortices
• Exact Hopfion Vortices in a 3D Heisenberg Ferromagnet
• Photonic Shankar skyrmion
• Knotted instantons from annihilations of monopole-instanton complex
• Hopfion canonical quantization
• Magnetic Hopfions in the Faddeev-Skyrme-Maxwell model
• Strongly coupled Skyrme-Faddeev-Niemi hopfions
• Topological atom optics and beyond with knotted quantum wavefunctions
• The Dynamics of Knotted Strings Attached to D-Branes
• Emergent Magnetic Field and Nonzero Gyrovector of the Toroidal Magnetic Hopfion
• Quantum knots in Bose-Einstein condensates created by counterdiabatic control
• Confinement, Chiral Symmetry Breaking and Faddeev-Niemi Decomposition in QCD
• Spinning Hopf solitons on S^3 x R
• Skyrmions in Orientifold and Adjoint QCD
• Self-dual Hopfions
• Hopf Soliton Solutions from Low Energy Effective Action of SU(2) Yang-Mills Theory
• Generalized Skyrme Crystals
• Twisted Vortices in a Gauge Field Theory
• Semiclassical Quantization of Hopf Solitons
• Energy minimizing Beltrami fields on Sasakian 3-manifolds
• Knotted Configurations with Arbitrary Hopf Index from the Eikonal Equation
• Stability of topological solitons in modified two-component Ginzburg-Landau model
• Homotopy classification of knotted defects in ordered media
• Euclidean 4d exact solitons in a Skyrme type model
• Topological interfaces crossed by defects and textures of continuous and discrete point group symmetries in spin-2 Bose-Einstein condensates
• Hopf Solitons in the AFZ Model
• BRST extension of the Faddeev model
• Instanton Density Operator in Lattice QCD from Higher Category Theory
• Color dielectric model with two scalar fields
• Charge Density Distributions in Doped Antiferromagnetic Insulators
• Chern-Simons Improved Hamiltonians for Strings in Three Space Dimensions
• The Bifurcation Theory of Magnetic Monopoles in a Charged Two-Condensate Bose-Einstein System
• N-Band Photonic Hopf Insulators Based on 2D Microring Lattices
• Higher Derivative Supersymmetric Nonlinear Sigma Models on Hermitian Symmetric Spaces, and BPS States Therein
• Topological invariants for superconducting cosmic strings
• Quantum lump dynamics on the two-sphere
• Converting Classical Theories to Quantum Theories by Solutions of the Hamilton-Jacobi Equation
• Stabilizing Textures in 3+1 Dimensions with Semilocality
• Collective coordinate quantization and spin statistics of the solitons in the $\mathbb{C}{P}^N$ Skyrme-Faddeev model
• Color Bosonization, Chiral Parametrization of Gluonic Field and QCD Effective Action
• Homogeneous spaces and Faddeev-Skyrme models
• Dirac Quantization of Restricted QCD
• Entangled multi-knot lattice model of anyon current
• Knotted Topological Phase Singularities of Electromagnetic Field
• Nonlinear dynamics of a charged particle in a strong non-null knot wave background
• Skyrme and Faddeev models in the low-energy limit of 4d Yang-Mills-Higgs theories
• Chirality and fermion number in a knotted soliton background
• Steady Euler flows and the Faddeev-Skyrme model with mass term
• Effective field theory for spinor dipolar Bose Einstein condensates
• Hybrid Skyrmions in Magnetic Multilayer Thin Films are Half-Integer Hopfions
• Black magic session of concordance: Regge mass spectrum from Casson's invariant
• Particle on a Torus Knot: Anholonomy and Hannay Angle
• Center-vortex loops with one selfintersection
• Nonlinear sigma models solvable by the Aratyn-Ferreira-Zimerman ansatz
• Rogue breather modes: Topological sectors, and the `belt-trick', in a one-dimensional ferromagnetic spin chain
• Knots in Physics
• Influence of topological constraints and topological excitations: Decomposition formulas for calculating homotopy groups of symmetry-broken phases
• Finsler Geometries from Topological Electromagnetism
• Non-abelian color dielectric - towards the effective model of the low energy QCD
• Abelian Hopfions of the CP^n model on R^{2n+1} and a fractionally powered topological lower bound
• Asymptotically Free Yang-Mills Classical Mechanics with Self-Linked Orbits
• Gauge-invariant and infrared-improved variational analysis of the Yang-Mills vacuum wave functional
• Tackling tangledness of cosmic strings by knot polynomial topological invariants
• Structures of Order Parameters in Inhomogeneous Phase States of Strongly Correlated Systems
• Hopf Solitons on the Lattice
• The Curious Case of an Effective Theory
• Josephson-like oscillations in toroidal spinor Bose-Einstein condensates: a prospective symmetry probe
• Coherence simplices
• Cross-fertilization of Ferreira's Hopfions And Electromagnetic Knots
• Supersymmetric extensions of K field theories
• Knots in Condensed Matters
• Exact knot solutions in a generalized Skyrme-Faddeev model
• Waves in the Skyrme--Faddeev model and integrable reductions
• Knotted domain strings
• Skyrme-Faddeev model from 5d super-Yang-Mills
• Topological Soliton with Nonzero Hopf Invariant in Yang-Mills-Higgs Model
• The $Z_2$ Classification of Dimensional Reduced Hopf Insulators
• Nontrivial Causal Structures Engendered by Knotted Solitons
• Knot topology in QCD
• Dynamics of two topologically entangled chains
• Characteristic analysis for integrable soliton models on two-dimensional target spaces
• The topological phase of bright solitons
• Classical skyrmions in SU(N)/SO(N) cosets
• Comment on ``Reduction of static field equation of Faddeev model to first order PDE'', arXiv:0707.2207
• Topological protection breakdown: a route to frustrated ferroelectricity
• Hopf solitons on compact manifolds
• Deformation of the CP(1) model leading to fixed size solitons in 2+1 dimensions
• The RP^2 Valued Sigma and Baby Skyrme Models
• Spin-Charge Separation and the Pauli Electron
• Class of Exact Solutions of the SU(3) Skyrme Model
• Supervariable approach to particle on a torus knot: A model for Hodge theory
• The Bohr Atom of Glueballs
• New Faddeev-Niemi type variables for static SU(3) Yang-Mills theory
• Skyrme-Faddeev Lagrangian from reformulated Georgi-Glashow model
• Abelian Decomposition of Sp(2N) Yang-Mills Theory
• Confinement, Vacuum Structure: from QCD to Quantum Gravity
• Are Maxwell knots integrable?
• Twisted curve geometry underlying topological invariants
• Knot solitons in modified Ginzburg-Landau model
• Vector and Spinor Decomposition of SU(2) Gauge Potential, their quivalence and Knot Structure in SU(2) Chern-Simons Theory
• A steady Euler flow on the 3-sphere and its associated Faddeev-Skyrme solution
• Some global minimizers of a symplectic Dirichlet energy
• Extended Soliton Solutions in an Effective Action for SU(2) Yang-Mills Theory
• The gluon condensate in an effective SU(2) Yang-Mills theory
• Gauge theory of Faddeev-Skyrme functionals
• Some vortex solutions in the extended Skyrme-Faddeev model
• Radial Stabilization of Magnetic Skyrmions Under Strong External Magnetic Field
• Construction of Hopfion Crystals
• Knot Topology in Quantum Spin System
• Exact non-circular symmetric N-skyrmions in helical magnets without inversion symmetry
• Interaction of hopfions of charge 1 and 2 from product ansatz
• From Hopf fibrations to exotic causal replacements
• Soliton solutions in an effective action for SU(2) Yang-Mills theory: including effects of higher-derivative term