Correspondence between Skyrmions in 2+1 and 3+1 Dimensions

Abstract

A lump (2D Skyrmion) can be constructed as a sine-Gordon kink (1D Skyrmion) inside a domain wall in the massive O(3) sigma model. In this paper, we discuss relations between Skyrmions in 2+1 and 3+1 dimensions. We first construct a Bogomol'nyi-Prasad-Sommerfield 3D Skyrmion as a lump inside a non-Abelian domain wall in an O(4) sigma model with a potential term admitting two discrete vacua. Next, we construct a conventional 3D Skyrmion as a baby Skyrmion in a non-Abelian domain wall in the Skyrme model with a modified mass term admitting two discrete vacua. We also construct a spinning 3D Skyrmion as a Q-lump in the non-Abelian domain wall.

18 pages, 3 figures, v2: typos corrected, minor changes, references added, v3: published version

References in corpus (32)

• Low energy hadron physics in holographic QCD
• More on a holographic dual of QCD
• Knots and Particles
• Vortices, Instantons and Branes
• Nonabelian Superconductors: Vortices and Confinement in $\mathcal{N}=2$ SQCD
• Solitons in the Higgs phase -- the moduli matrix approach --
• Supersymmetric Solitons and How They Help Us Understand Non-Abelian Gauge Theories
• Baryons from instantons in holographic QCD
• Moduli Space of Non-Abelian Vortices
• Multisolitons in a Two-dimensional Skyrme Model
• Dynamics of Baby Skyrmions
• Instantons in the Higgs Phase
• Non-Abelian Vortices of Higher Winding Numbers
• Localization of Non-Abelian Gauge Fields on Domain Walls at Weak Coupling (D-brane Prototypes)
• Universal Reconnection of Non-Abelian Cosmic Strings
• The baby Skyrme models and their multi-skyrmions
• Manifest Supersymmetry for BPS Walls in N=2 Nonlinear Sigma Models
• Manifestly Supersymmetric Effective Lagrangians on BPS Solitons
• 1/2, 1/4 and 1/8 BPS Equations in SUSY Yang-Mills-Higgs Systems -- Field Theoretical Brane Configurations --
• Skyrmions from Instantons inside Domain Walls
• Josephson vortices and the Atiyah-Manton construction
• Skyrmions and domain walls in (2+1) dimensions
• Domain Walls with Non-Abelian Clouds
• Ferromagnetic neutron stars: axial anomaly, dense neutron matter, and pionic wall
• Enhanced Worldvolume Supersymmetry and Intersecting Domain Walls in N=1 SQCD
• Intersecting Solitons, Amoeba and Tropical Geometry
• Decomposing Instantons in Two Dimensions
• Single State Supermultiplet in 1+1 Dimensions
• On the interactions of Skyrmions with domain walls
• Domain Lines as Fractional Strings
• Walls and chains of planar skyrmions
• Pullback of the Volume Form, Integrable Models in Higher Dimensions and Exotic Textures

Cited by in corpus (47)

• Vortices and Other Topological Solitons in Dense Quark Matter
• Scattering of the ${\phi }^8$ kinks with power-law asymptotics
• Scattering of the double sine-Gordon kinks
• Matryoshka Skyrmions
• Domain wall Skyrmions
• Jewels on a wall ring
• Incarnations of Skyrmions
• The dynamics of domain wall Skyrmions
• BPS States in Supersymmetric Chiral Models with Higher Derivative Terms
• Non-Abelian Sine-Gordon Solitons
• Fractional instantons and bions in the O(N) model with twisted boundary conditions
• Non-Abelian Sine-Gordon Solitons: Correspondence between $SU(N)$ Skyrmions and $\mathbb{C}{P}^{N-1}$ Lumps
• Loosening up the Skyrme model
• Relations among topological solitons
• Domain Wall Skyrmions in Chiral Magnets
• Fractional Skyrmions and their molecules
• Phase diagram of QCD matter with magnetic field: domain-wall Skyrmion chain in chiral soliton lattice
• Fractional vortex molecules and vortex polygons in a baby Skyrme model
• Baryonic sphere: a spherical domain wall carrying baryon number
• Scalar triplet on a domain wall: an exact solution
• Baryonic torii: Toroidal baryons in a generalized Skyrme model
• Josephson junction of non-Abelian superconductors and non-Abelian Josephson vortices
• Winding Hopfions on R^2 x S^1
• Chiral Magnets from String Theory
• Skyrmions confined as beads on a vortex ring
• Josephson instantons and Josephson monopoles in a non-Abelian Josephson junction
• Magnon dynamics in a Skyrmion-textured domain wall of antiferromagnets
• Effective field theories on solitons of generic shapes
• Quasicrystals in QCD
• Topological Defects in the Georgi-Machacek Model
• D-brane solitons in various dimensions
• Incarnations of Instantons
• Spin Statistics and Surgeries of Topological Solitons in QCD Matter in Magnetic Field
• Q-lumps on a Domain Wall with a Spin-Orbit Interaction
• Strings and skyrmions on domain walls
• Baryonic handles: Skyrmions as open vortex strings on a domain wall
• Scattering of fermionic isodoublets on the sine-Gordon kink
• An Investigation of the Casimir Energy for a Fermion Coupled to the Sine-Gordon Soliton with Parity Decomposition
• Skyrmion crystal phase on a magnetic domain wall in chiral magnets
• Domain walls in a non-linear ${\mathbb{S}}^2$-sigma model with homogeneous quartic polynomial potential
• Solitonic ground state in supersymmetric theory in background
• Creation of domain-wall Skyrmions in chiral magnets
• Domain Wall Networks as Skyrmion Crystals in Chiral Magnets
• BPS pion domain walls in the supersymmetric chiral Lagrangian
• A Unified Construction of Skyrme-type Non-linear sigma Models via The Higher Dimensional Landau Models
• Holographic QCD Matter: Chiral Soliton Lattices in Strong Magnetic Field
• Creation of domain-wall skyrmions in chiral magnets with Landau-Lifshitz-Gilbert dynamics and demagnetization