Fractional instantons and bions in the O(N) model with twisted boundary conditions

Abstract

Recently, multiple fractional instanton configurations with zero instanton charge, called bions, have been revealed to play important roles in quantum field theories on compactified spacetime. In two dimensions, fractional instantons and bions have been extensively studied in the $\mathbb{C}{P}^{N-1}$ model and the Grassmann sigma model on ${\mathbb{R}}^1\times S^1$ with the ${\mathbb{Z}}_N$ symmetric twisted boundary condition. Fractional instantons in these models are domain walls with a localized $U(1)$ modulus twisted half along their world volume. In this paper, we classify fractional instantons and bions in the $O(N)$ nonlinear sigma model on ${\mathbb{R}}^{N-2}\times S^1$ with more general twisted boundary conditions in which arbitrary number of fields change sign. We find that fractional instantons have more general composite structures, that is, a global vortex with an Ising spin (or a half-lump vortex), a half sine-Gordon kink on a domain wall, or a half lump on a "space-filling brane" in the $O(3)$ model ($\mathbb{C}{P}^1$ model) on ${\mathbb{R}}^1\times S^1$, and a global monopole with an Ising spin (or a half-Skyrmion monopole), a half sine-Gordon kink on a global vortex, a half lump on a domain wall, or a half Skyrmion on a "space-filling brane" in the $O(4)$ model (principal chiral model or Skyrme model) on ${\mathbb{R}}^2\times S^1$. We also construct bion configurations in these models.

arXiv comment43 pages, 16 figures, v2: a reference added, published version

References in corpus (123)

• Knots and Particles
• Brane Dynamics and Gauge Theory
• Solitons in the Higgs phase -- the moduli matrix approach --
• Vortex Strings and Four-Dimensional Gauge Dynamics
• Non-Abelian String Junctions as Confined Monopoles
• Creating vortex rings and three-dimensional skyrmions in Bose-Einstein condensates
• Resurgence and Trans-series in Quantum Field Theory: The CP(N-1) Model
• Magnetic bion condensation: A new mechanism of confinement and mass gap in four dimensions
• Moduli Space of Non-Abelian Vortices
• Stationary ring solitons in field theory - knots and vortons
• Multisolitons in a Two-dimensional Skyrme Model
• Static solitons with non-zero Hopf number
• Dynamics of Baby Skyrmions
• A Skyrme-type proposal for baryonic matter
• The semi-classical expansion and resurgence in gauge theories: new perturbative, instanton, bion, and renormalon effects
• Stable Skyrmions in two-component Bose-Einstein condensates
• Bogomol'nyi solitons in a gauged $O(3)$ sigma model
• All Exact Solutions of a 1/4 Bogomol'nyi-Prasad-Sommerfield Equation
• Stable Skyrmions in SU(2) Gauged Bose-Einstein Condensates
• Multi-Instantons and Exact Results I: Conjectures, WKB Expansions, and Instanton Interactions
• Abelian duality, confinement, and chiral symmetry breaking in QCD(adj)
• Uniform WKB, Multi-instantons, and Resurgent Trans-Series
• Instantons in the Higgs Phase
• Continuity, Deconfinement, and (Super) Yang-Mills Theory
• A measurement of the Q^2, W and t dependences of deeply virtual Compton scattering at HERA
• Construction of Non-Abelian Walls and Their Complete Moduli Space
• Generating Non-perturbative Physics from Perturbation Theory
• A semiclassical realization of infrared renormalons
• QCD-like Theories on R_3\times S_1: a Smooth Journey from Small to Large r(S_1) with Double-Trace Deformations
• Continuity and Resurgence: towards a continuum definition of the CP(N-1) model
• Resurgence in QFT: Unitons, Fractons and Renormalons in the Principal Chiral Model
• Energetically stable particle-like Skyrmions in a trapped Bose-Einstein condensate
• Resurgence theory, ghost-instantons, and analytic continuation of path integrals
• Non-Abelian Vortices of Higher Winding Numbers
• Non-Abelian Walls in Supersymmetric Gauge Theories
• A BPS Skyrme model and baryons at large Nc
• Non-Abelian Semilocal Strings in N=2 Supersymmetric QCD
• Universal Reconnection of Non-Abelian Cosmic Strings
• On the moduli space of semilocal strings and lumps
• Conformality or confinement: (IR)relevance of topological excitations
• The baby Skyrme models and their multi-skyrmions
• Manifest Supersymmetry for BPS Walls in N=2 Nonlinear Sigma Models
• Non-Abelian Vortices on Cylinder -- Duality between vortices and walls
• Finite size phase transitions in QCD with adjoint fermions
• New Phases of SU(3) and SU(4) at Finite Temperature
• Investigation of restricted baby Skyrme models
• 1/2, 1/4 and 1/8 BPS Equations in SUSY Yang-Mills-Higgs Systems -- Field Theoretical Brane Configurations --
• Neutral bions in the $\mathbb{C}{P}^{N-1}$ model
• D-brane Construction for Non-Abelian Walls
• Skyrmions from Instantons inside Domain Walls
• Adjoint QCD on ${\mathbb{R}}^3\times S^1$ with twisted fermionic boundary conditions
• Josephson vortices and the Atiyah-Manton construction
• Correspondence between Skyrmions in 2+1 and 3+1 Dimensions
• Instanton constituents in the O(3) model at finite temperature
• Phase diagrams of SU(N) gauge theories with fermions in various representations
• Matryoshka Skyrmions
• Domain wall Skyrmions
• Stable particlelike solitons with multiply-quantized vortex lines in Bose-Einstein condensates
• Jewels on a wall ring
• Skyrmionic state and stable half-quantum vortices in chiral p-wave superconductors
• Microscopic Structure of Magnetic Bions
• Principal Chiral Field at Large N
• Polyakov loops and the Hosotani mechanism on the lattice
• The Spectrum of Bogomol'nyi Solitons in Gauged Linear Sigma Models
• Creating vortons and three-dimensional skyrmions from domain wall annihilation with stretched vortices in Bose-Einstein condensates
• Classifying bions in Grassmann sigma models and non-Abelian gauge theories by D-branes
• Instanton constituents and fermionic zero modes in twisted CP(n) models
• Incarnations of Skyrmions
• N=1 supersymmetric extension of the baby Skyrme model
• Torus knots as Hopfions
• Exact multi-soliton solutions in the four dimensional Skyrme model
• Extended Supersymmetry and BPS solutions in baby Skyrme models
• Dense Baryonic Matter in Hidden Local Symmetry Approach: Half-Skyrmions and Nucleon Mass
• Statistical Mechanics of Vortices from D-branes and T-duality
• BPS States in Supersymmetric Chiral Models with Higher Derivative Terms
• BPS Wall in N=2 SUSY Nonlinear Sigma Model with Eguchi-Hanson Manifold
• Intersecting Solitons, Amoeba and Tropical Geometry
• Non-relativistic Nambu-Goldstone modes associated with spontaneously broken space-time and internal symmetries
• Numerical Study of the stability of Skyrmions in Bose-Einstein Condensates
• Easy plane baby skyrmions
• Baby Skyrme Model, Near-BPS Approximations and Supersymmetric Extensions
• Vortex equations in abelian gauged sigma-models
• Dense baryonic matter in conformally-compensated hidden local symmetry: Vector manifestation and chiral symmetry restoration
• Stable Cosmic Vortons
• Fractional Skyrmions and their molecules
• Decomposing Instantons in Two Dimensions
• Dyon-Skyrmion Lumps
• String Tension Scaling in High-Temperature Confined SU(N) Gauge Theories
• Fractional vortex molecules and vortex polygons in a baby Skyrme model
• Chains of Skyrmions
• Relaxation of twisted vortices in the Faddeev-Skyrme model
• Two Species of Vortices in a massive Gauged Non-linear Sigma Model
• Baryonic sphere: a spherical domain wall carrying baryon number
• Baryonic torii: Toroidal baryons in a generalized Skyrme model
• Kinks, chains, and loop groups in the CP^n sigma models
• A PNJL Model for Adjoint Fermions with Periodic Boundary Conditions
• Unwinding in Hopfion vortex bunches
• Neutral bions in the CP^{N-1} model for resurgence
• Winding Hopfions on R^2 x S^1
• Vortex Rings in two Component Bose-Einstein Condensates
• Domain Lines as Fractional Strings
• Magnetothermodynamics of BPS baby skyrmions
• Phase structure and Hosotani mechanism in gauge theories with compact dimensions revisited
• Nonlinear sigma models at nonzero chemical potential: breaking up instantons and the phase diagram
• Fractionalized Non-Self-Dual Solutions in the CP(N-1) Model
• Effective field theories on solitons of generic shapes
• Vortex polygons and their stabilities in Bose-Einstein condensates and field theory
• Instantons confined by monopole strings
• Defect formation from defect--anti-defect annihilations
• Decoding perturbation theory using resurgence: Stokes phenomena, new saddle points and Lefschetz thimbles
• Knots from wall--anti-wall annihilations with stretched strings
• D-brane solitons in various dimensions
• Incarnations of Instantons
• Clustering and decomposition for non BPS solutions of the ${\mathbb{CP}}^{N-1}$ models
• Monopoles and dyons in SO(3) gauged Skyrme models
• Monopole-Skyrmions
• The absence of IR renormalons in gauge theories on ${\mathbb{R}}^3\times {\mathbb{S}}^1$ and what it means for resurgence
• Skyrmions, half-skyrmions and nucleon mass in dense baryonic matter
• Toroidal domain walls as Hopfions
• Helical buckling of Skyrme-Faddeev solitons
• Knotted instantons from annihilations of monopole-instanton complex
• The 1-soliton in the SO(3) gauged Skyrme model with mass term
• Twisted CP(N-1) instanton projectors and the N-level quantum density matrix

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• Confinement-Deconfinement Crossover in the Lattice $\mathbb{C}{P}^{N-1}$ Model
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• Instantons in Lifshitz Field Theories
• Semilocal Fractional Instantons