Analytic crystals of solitons in the four dimensional gauged non-linear sigma model

Abstract

The first analytic topologically non-trivial solutions in the (3+1)-dimensional gauged non-linear sigma model representing multi-solitons at finite volume with manifest ordered structures generating their own electromagnetic field are presented. The complete set of seven coupled non-linear field equations of the gauged non-linear sigma model together with the corresponding Maxwell equations are reduced in a self-consistent way to just one linear Schrodinger-like equation in two dimensions. The corresponding two dimensional periodic potential can be computed explicitly in terms of the solitons profile. The present construction keeps alive the topological charge of the gauged solitons. Both the energy density and the topological charge density are periodic and the positions of their peaks show a crystalline order. These solitons describe configurations in which (most of) the topological charge and total energy are concentrated within three-dimensional tube-shaped regions. The electric and magnetic fields vanish in the center of the tubes and take their maximum values on their surface while the electromagnetic current is contained within these tube-shaped regions. Electromagnetic perturbations of these families of gauged solitons are shortly discussed.

arXiv comment18 pages, 22 figures, accepted for publication on EUROPEAN PHYSICAL JOURNAL C

References in corpus (31)

• QCD and strongly coupled gauge theories: challenges and perspectives
• Skyrme Crystal In A Two-Dimensional Electron Gas
• Disordered nuclear pasta, magnetic field decay, and crust cooling in neutron stars
• Bogomol'nyi solitons in a gauged $O(3)$ sigma model
• Analytic self-gravitating Skyrmions, cosmological bounces and AdS wormholes
• Emergence of Skyrme crystal in Gross-Neveu and 't Hooft models at finite density
• Hedgehog ansatz and its generalization for self-gravitating Skyrmions
• Parking-garage structures in astrophysics and biophysics
• Non-linear superposition law and Skyrme crystals
• Skyrme-Maxwell Solitons in (2+1) Dimensions
• Static solutions in the U(1) gauged Skyrme model
• Exact multi-soliton solutions in the four dimensional Skyrme model
• Ordered arrays of Baryonic tubes in the Skyrme model in (3+1) dimensions at finite density
• Integrability and chemical potential in the (3+1)-dimensional Skyrme model
• Spinning U(1) gauged Skyrmions
• SO(3) Gauged Soliton of an O(4) Sigma Model on $R_3$
• Skyrme Crystal from a Twisted Instanton on a Four-Torus
• Analytic (3+1)-dimensional gauged Skyrmions, Heun and Whittaker-Hill equations and resurgence
• Exact Kink Solitons in Skyrme Crystals
• Analytic topologically non-trivial solutions of the (3+1)-dimensional $U(1)$ gauged Skyrme model and extended duality
• SU(N) Multi-Skyrmions at Finite Volume
• Black hole and BTZ-black string in the Einstein-SU(2) Skyrme model
• Analytic Studies of Static and Transport Properties of (Gauged) Skyrmions
• Two Species of Vortices in a massive Gauged Non-linear Sigma Model
• Cosmological Einstein-Skyrme solutions with non-vanishing topological charge
• Magnetothermodynamics of BPS baby skyrmions
• Solitons in a cavity for the Einstein-SU(2) Non-linear Sigma Model and Skyrme model
• A two-dimensional soliton system in the Maxwell-Chern-Simons gauge model
• Quantisation of Global Isospin in the Skyrme Crystal
• Rolling Skyrmions and the Nuclear Spin-Orbit Force
• Supersymmetric solutions of the cosmological, gauged, C magic model

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