Relations among topological solitons

Abstract

We clarify relations among topological solitons in various dimensions: a domain wall, non-Abelian vortex, magnetic monopole and Yang-Mills instanton, together with a (non-Abelian) sine-Gordon soliton, baby Skyrmion (lump) and Skyrmion. We construct a composite configuration consisting of a domain wall, vortex, magnetic monopole and Yang-Mills instanton (wall-vortex-monopole-instanton) using the effective theory technique or moduli approximation. Removing some solitons from such a composite, we obtain all possible composite solitons in the form of solitons within a soliton, including all the previously known configurations, yielding relations among topological solitons.

42 pages, 4 figures, published version

References in corpus (69)

• Generalized Global Symmetries
• Skyrmion fractionalization and merons in chiral magnets with easy-plane anisotropy
• Magnetic bion condensation: A new mechanism of confinement and mass gap in four dimensions
• Stationary ring solitons in field theory - knots and vortons
• Skyrmion Lattice in Two-Dimensional Chiral Magnet
• All Exact Solutions of a 1/4 Bogomol'nyi-Prasad-Sommerfield Equation
• Instantons in the Higgs Phase
• Magnetic Monopole Dynamics, Supersymmetry, and Duality
• Construction of Non-Abelian Walls and Their Complete Moduli Space
• Non-Abelian Walls in Supersymmetric Gauge Theories
• Universal Reconnection of Non-Abelian Cosmic Strings
• On the moduli space of semilocal strings and lumps
• Manifestly Supersymmetric Effective Lagrangians on BPS Solitons
• Higher-form symmetries and 3-group in axion electrodynamics
• Non-Abelian duality from vortex moduli: a dual model of color-confinement
• Neutral bions in the $\mathbb{C}{P}^{N-1}$ model
• D-brane Construction for Non-Abelian Walls
• Skyrmions from Instantons inside Domain Walls
• Josephson vortices and the Atiyah-Manton construction
• Constructing Non-Abelian Vortices with Arbitrary Gauge Groups
• Correspondence between Skyrmions in 2+1 and 3+1 Dimensions
• Instanton constituents in the O(3) model at finite temperature
• Cosmic Strings
• Domain wall Skyrmions
• Matryoshka Skyrmions
• Classifying bions in Grassmann sigma models and non-Abelian gauge theories by D-branes
• Global Structure of Moduli Space for BPS Walls
• Incarnations of Skyrmions
• Domain Walls with Non-Abelian Clouds
• Statistical Mechanics of Vortices from D-branes and T-duality
• Intersecting Solitons, Amoeba and Tropical Geometry
• Non-Abelian Vortices in SO(N) and USp(N) Gauge Theories
• Non-Abelian Sine-Gordon Solitons
• Fermion structure of non-Abelian vortices in high density QCD
• Confined Monopoles Induced by Quantum Effects in Dense QCD
• Interactions of Non-Abelian Global Strings
• Non-Abelian Sine-Gordon Solitons: Correspondence between $SU(N)$ Skyrmions and $\mathbb{C}{P}^{N-1}$ Lumps
• Non-Abelian Monopoles in the Higgs Phase
• Confined Magnetic Monopoles in Dense QCD
• Emergence of Transient Domain Wall Skyrmions after Ultrafast Demagnetisation
• Fractional Skyrmions and their molecules
• Higher Derivative Corrections to Non-Abelian Vortex Effective Theory
• Topological Excitations in Spinor Bose-Einstein Condensates
• Dynamics of Strings between Walls
• Non-Abelian Global Vortices
• Non-Abelian Global Strings at Chiral Phase Transition
• Chains of Skyrmions
• Wigner solids of domain wall skyrmions
• Emergent discrete 3-form symmetry and domain walls
• The Moduli Space Metric for Well-Separated Non-Abelian Vortices
• Group Theory of Non-Abelian Vortices
• Neutral bions in the CP^{N-1} model for resurgence
• Skyrmions confined as beads on a vortex ring
• Nonlinear sigma models at nonzero chemical potential: breaking up instantons and the phase diagram
• Walls and chains of planar skyrmions
• Effective field theories on solitons of generic shapes
• Vortex counting from field theory
• Instantons confined by monopole strings
• D-brane solitons in various dimensions
• Monopole-vortex complex at large distances and nonAbelian duality
• Lattice $\mathbb{C}{P}^{N-1}$ model with ${\mathbb{Z}}_N$ twisted boundary condition: bions, adiabatic continuity and pseudo-entropy
• Walls of massive Kähler sigma models on SO(2N)/U(N) and Sp(N)/U(N)
• Formation of Non-Abelian Monopoles Connected by Strings
• Dyonic Non-Abelian Vortices
• Vacua and walls of mass-deformed Kähler nonlinear sigma models on $SO(2N)/U(N)$
• Brane Realization of Nambu Monopoles and Electroweak Strings
• Stabilizing semilocal strings by polarization
• Solvable Models of Magnetic Skyrmions
• Dyonic non-Abelian vortex strings in supersymmetric and non-supersymmetric theories: tensions and higher derivative corrections