Kinks, chains, and loop groups in the CP^n sigma models

Abstract

We consider topological solitons in the CP^n sigma models in two space dimensions. In particular, we study "kinks", which are independent of one coordinate up to a rotation of the target space, and "chains", which are periodic in one coordinate up to a rotation of the target space. Kinks and chains both exhibit constituents, similar to monopoles and calorons in SU(n) Yang-Mills-Higgs and Yang-Mills theories. We examine the constituent structure using Lie algebras.

19 pages, 3 figures v2: Discussions improved, examples added, references added, typos corrected

References in corpus (6)

• Non-Abelian Vortices on Cylinder -- Duality between vortices and walls
• Instanton constituents in the O(3) model at finite temperature
• Instanton constituents and fermionic zero modes in twisted CP(n) models
• Periodic Monopoles
• Large scale and large period limits of symmetric calorons
• Calorons, Nahm's equations on S^1 and bundles over P^1xP^1

Cited by in corpus (21)

• Resurgence and Trans-series in Quantum Field Theory: The CP(N-1) Model
• Resurgence in QFT: Unitons, Fractons and Renormalons in the Principal Chiral Model
• Neutral bions in the $\mathbb{C}{P}^{N-1}$ model
• From 4d Yang-Mills to 2d ${\mathbb{CP}}^{N-1}$ model: IR problem and confinement at weak coupling
• Resurgence in sine-Gordon quantum mechanics: Exact agreement between multi-instantons and uniform WKB
• Classifying bions in Grassmann sigma models and non-Abelian gauge theories by D-branes
• O(3) nonlinear sigma model in 1+1 dimensions with matrix product states
• Dual lattice representations for O(N) and CP(N-1) models with a chemical potential
• Fractional instantons and bions in the O(N) model with twisted boundary conditions
• Relations among topological solitons
• Non-BPS exact solutions and their relation to bions in $\mathbb{C}{P}^{N-1}$ models
• Fractional instantons and bions in the principal chiral model on ${\mathbb{R}}^2\times S^1$ with twisted boundary conditions
• Neutral bions in the CP^{N-1} model for resurgence
• A low-dimensional analogue of holographic baryons
• Josephson instantons and Josephson monopoles in a non-Abelian Josephson junction
• Nonlinear sigma models at nonzero chemical potential: breaking up instantons and the phase diagram
• Revisiting the Faddeev-Skyrme Model and Hopf Solitons
• Clustering and decomposition for non BPS solutions of the ${\mathbb{CP}}^{N-1}$ models
• On Supersymmetric Interface Defects, Brane Parallel Transport, Order-Disorder Transition and Homological Mirror Symmetry
• Complex instantons in sigma models with chemical potential
• Near integrability of kink lattice with higher order interactions