Analytic topologically non-trivial solutions of the (3+1)-dimensional $U(1)$ gauged Skyrme model and extended duality

Abstract

We construct the first analytic examples of topologically non-trivial solutions of the (3+1)-dimensional $U(1)$ gauged Skyrme model within a finite box in (3+1)-dimensional flat space-time. There are two types of gauged solitons. The first type corresponds to gauged Skyrmions living within a finite volume. The second corresponds to gauged time-crystals (smooth solutions of the $U(1)$ gauged Skyrme model whose periodic time-dependence is protected by a winding number). The notion of electromagnetic duality can be extended for these two types of configurations in the sense that the electric and one of the magnetic components can be interchanged. These analytic solutions show very explicitly the Callan-Witten mechanism (according to which magnetic monopoles may "swallow" part of the topological charge of the Skyrmion) since the electromagnetic field contribute directly to the conserved topological charge of the gauged Skyrmions. As it happens in superconductors, the magnetic field is suppressed in the core of the gauged Skyrmions. On the other hand, the electric field is strongly suppresed in the core of gauged time crystals.

arXiv comment19 pages, 2 figures, version accepted for publication in Physical Review D

References in corpus (44)

• Observation of a Discrete Time Crystal
• Observation of discrete time-crystalline order in a disordered dipolar many-body system
• Floquet Time Crystals
• On the phase structure of driven quantum systems
• Quantum Time Crystals
• Skyrmion Lattice in a Doped Semiconductor
• Discrete time crystals: rigidity, criticality, and realizations
• Absence of Quantum Time Crystals
• Classical Time Crystals
• Modeling spontaneous breaking of time-translation symmetry
• Impossibility of Spontaneously Rotating Time-Crystals: A No-Go Theorem
• Observation of Topologically Stable 2D Skyrmions in an Antiferromagnetic Spinor Bose-Einstein Condensate
• Comment on "Quantum Time Crystals": a new paradigm or just another proposal of perpetuum mobile?
• Analytic self-gravitating Skyrmions, cosmological bounces and AdS wormholes
• Superfluidity and Space-Time Translation Symmetry Breaking
• Skyrmions with low binding energies
• Hedgehog ansatz and its generalization for self-gravitating Skyrmions
• Non-linear superposition law and Skyrme crystals
• Comment on "Space-Time Crystals of Trapped Ions": And Yet it Moves Not !
• Incarnations of Skyrmions
• Static solutions in the U(1) gauged Skyrme model
• Exact multi-soliton solutions in the four dimensional Skyrme model
• Integrability and chemical potential in the (3+1)-dimensional Skyrme model
• Spinning Gravitating Skyrmions
• Skyrmions and Semilocal Strings in Cosmology
• Spinning U(1) gauged Skyrmions
• Non-Abelian Sine-Gordon Solitons
• Skyrme models and nuclear matter equation of state
• Non-Abelian Sine-Gordon Solitons: Correspondence between $SU(N)$ Skyrmions and $\mathbb{C}{P}^{N-1}$ Lumps
• Black Hole Skyrmions with Negative Cosmological Constant
• Skyrmion Black Hole Hair: Conservation of Baryon Number by Black Holes and Observable Manifestations
• Exact Kink Solitons in Skyrme Crystals
• Kantowski-Sachs Universes sourced by a Skyrme fluid
• Black hole Skyrmion in a generalized Skyrme model
• Scattering of Skyrmions
• Cosmological dynamics of gravitating hadron matter
• Gravitational catalysis of merons in Einstein-Yang-Mills theory
• Multi-Skyrmions with orientational moduli
• Skyrme model and Isospin Chemical Potential
• On the possibility of spinorial quantization in the Skyrme model
• Skyrmions in the presence of isospin chemical potential
• Constraining Monopoles by Topology: an Autonomous System
• $SU(N)$ BPS Monopoles in ${\mathcal{M}}^2\times S^2$
• Nontopological structures in the baby-Skyrme model

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• Analytic self-gravitating $4$-Baryons, traversable NUT-AdS wormholes, flat space-time multi-Skyrmions at finite volume and a novel transition in the $SU(3)$-Skyrme model
• Analytic crystals of solitons in the four dimensional gauged non-linear sigma model
• Analytic (3+1)-dimensional gauged Skyrmions, Heun and Whittaker-Hill equations and resurgence
• Pion crystals hosting topologically stable baryons
• Black hole and BTZ-black string in the Einstein-SU(2) Skyrme model
• Analytic Studies of Static and Transport Properties of (Gauged) Skyrmions
• Analytic SU(N) Skyrmions at finite Baryon density
• Spherical Skyrmion black holes as gravitational lenses
• Analytic multi-Baryonic solutions in the SU(N)-Skyrme model at finite density
• Gravitating superconducting solitons in the (3+1)-dimensional Einstein gauged non-linear sigma-model
• Exact \textit{pp}-waves, (A)dS waves and Kundt spaces in the Abelian-Higgs model
• Crystals of gauged solitons, force free plasma and resurgence
• Analytic meronic black holes, gravitating solitons and higher spins in the Einstein $SU(N)$-Yang-Mills theory
• Thermodynamics and Phase Transition in Shapere-Wilczek {\it fgh} model: Cosmological Time Crystal in Quadratic Gravity
• Bianchi IX cosmologies in the Einstein-Skyrme system in a sector with non-trivial topological charge
• Analytic non-homogeneous condensates in the $(2+1)$-dimensional Yang-Mills-Higgs-Chern-Simons theory at finite density
• Analytic Baby Skyrmions at Finite Density
• Backreacted Coulomb energy in the Skyrme model
• Existence of a supersymmetric extension of the gauged non-linear $\Sigma$-model and the transition from integrability to chaos