Stationary ring solitons in field theory - knots and vortons

Abstract

We review the current status of the problem of constructing classical field theory solutions describing stationary vortex rings in Minkowski space in 3+1 dimensions. We describe the known up to date solutions of this type, such as the static knot solitons stabilized by the topological Hopf charge, the attempts to gauge them, the anomalous solitons stabilized by the Chern-Simons number, as well as the non-Abelian monopole and sphaleron rings. Passing to the rotating solutions, we first discuss the conditions insuring that they do not radiate, and then describe the spinning $Q$-balls, their twisted and gauged generalizations reported here for the first time, spinning skyrmions, and rotating monopole-antimonopole pairs. We then present the first explicit construction of global vortons as solutions of the elliptic boundary value problem, which demonstrates their non-radiating character. Finally, we describe the analogs of vortons in the Bose-Einstein condensates, analogs of spinning $Q$-balls in the non-linear optics, and also moving vortex rings in superfluid helium and in ferromagnetics.

103 pages, 31 figures. Numerous modifications in the text, a strongly expanded description of Faddeev-Skyrme knots, a new section on spinning Q-balls as light bullets, many new references. To appear in Physics Reports

References in corpus (19)

• CMB power spectrum contribution from cosmic strings using field-evolution simulations of the Abelian Higgs model
• Rotating Boson Stars and Q-Balls II: Negative Parity and Ergoregions
• Spin-Charge Separation, Conformal Covariance and the SU(2) Yang-Mills Theory
• Knots in the Skyrme-Faddeev model
• Spinning Gravitating Skyrmions
• Twisted Superconducting Semilocal Strings
• Vortex rings in ferromagnets
• Anomalous Abelian solitons
• Investigation of the Nicole model
• Superconducting Electroweak Strings
• Sphalerons, Antisphalerons and Vortex Rings
• Investigation of the stability of Hopfions in the two-component Ginzburg-Landau model
• Stability Analysis of The Twisted Superconducting Semilocal Strings
• The logarithmic equation of state for superconducting cosmic strings
• Inner topological structure of Hopf invariant
• Kinky Vortons
• Spontaneous Breaking of Rotational Symmetry in Rotating Solitons - a Toy Model of Excited Nucleons with High Angular Momentum
• On vortices and rings in extended Abelian models
• Nucleation of solitary wave complexes in two-component mixture Bose-Einstein condensates

Cited by in corpus (62)

• Particle-like topologies in light
• Kerr-Newman scalar clouds
• Twisted toroidal vortex-solitons in inhomogeneous media with repulsive nonlinearity
• Non-linear Q-clouds around Kerr black holes
• Creating vortons and three-dimensional skyrmions from domain wall annihilation with stretched vortices in Bose-Einstein condensates
• Incarnations of Skyrmions
• Three-dimensional hybrid vortex solitons
• Non-Meissner electrodynamics and knotted solitons in two-component superconductors
• Optical excitations of Skyrmions, knotted solitons, and defects in atoms
• Delicate topology protected by rotation symmetry: Crystalline Hopf insulators and beyond
• Q-balls in flat potentials
• Fractional instantons and bions in the O(N) model with twisted boundary conditions
• Crystals of superconducting Baryonic tubes in the low energy limit of QCD at finite density
• Relations among topological solitons
• Spinning Supersymmetric Q-balls
• Pulsating and persistent vector solitons in a Bose-Einstein condensate in a lattice upon phase separation instability
• On the Structure of Rotating Charged Boson Stars
• Vorton construction and dynamics
• Baryonic torii: Toroidal baryons in a generalized Skyrme model
• Spinning Electroweak Sphalerons
• $U(1)$ gauged boson stars in the Einstein-Friedberg-Lee-Sirlin model
• Electric charge on the brane?
• Affleck-Dine dynamics, Q-ball formation and thermalisation
• Effective field theories on solitons of generic shapes
• Topological optical skyrmion transfer to matter
• Skyrmions and Hopfions in 3D Frustrated Magnets
• Non Abelian Chern-Simons-Higgs solutions in (2+1) dimensions
• Spatiotemporal solitons in dispersion-managed multimode fibers
• Chains of rotating boson stars
• A two-dimensional soliton system in the Maxwell-Chern-Simons gauge model
• Kinky Vortons
• Q-ball stress stability criterion in the $U(1)$ gauged scalar theories
• A detailed study of the stability of vortons
• Formation and evolution of kinky vortons
• Quantum current dissipation in superconducting strings and vortons
• Perturbations of Q-balls: from spectral structure to radiation pressure
• Exact \textit{pp}-waves, (A)dS waves and Kundt spaces in the Abelian-Higgs model
• Excited oscillons: cascading levels and higher multipoles
• Slowly rotating Q-balls
• Gauged Hopfions
• Tachyon Condensation and Brane Annihilation in Bose-Einstein Condensates: Spontaneous Symmetry Breaking in Restricted Lower-dimensional Subspace
• Q-chains in the $U(1)$ gauged Friedberg-Lee-Sirlin model
• The Physics of Q-balls
• Investigation of Q-tubes stability using the piecewise parabolic potential
• A one-dimensional soliton system of gauged Q-ball and anti-Q-ball
• Probing the Ellis-Bronnikov wormhole geometry with a scalar field: clouds, waves and Q-balls
• Stable knots in the trapped Bose-Einstein condensates
• Properties of Charged Rotating Electroweak Sphaleron-Antisphaleron Systems
• Relativistic head-on collisions of $U(1)$ gauged Q-balls
• Black holes with Skyrmion-anti-Skyrmion hairs
• Dynamics of slender monopoles and anti-monopoles in non-Abelian superconductor
• 3D Vortices and rotating solitons in ultralight dark matter
• Spinning solutions for the bosonic M2-brane with $C_{\pm }$ fluxes
• CFT-approach to Rotating Field Lumps in Attractive Potential
• Scattering of fermions on a one-dimensional Q-ball
• On a classical solution to the Abelian Higgs model
• Knot solitons in modified Ginzburg-Landau model
• A nontopological soliton in an $\mathcal{N}=1$ supersymmetric gauge Abelian model
• Stable cosmic vortons in bosonic field theory
• New Frontiers in Multidimensional Self-Trapping of Nonlinear Fields and Matter
• Understanding the Quantized Angular Momentum of Rotating Q-balls
• Gravitational Wave Mountains: current-carrying domain walls