Knots from wall--anti-wall annihilations with stretched strings

A pair of a domain wall and an anti-domain wall is unstable to decay. We show that when a vortex-string is stretched between the walls, there remains a knot soliton (Hopfion) after the pair annihilation.Comment: 10 pages, 6 figures, published version. arXiv admin note: text overlap with arXiv:1205.244

Instantons confined by monopole strings

It is known that monopoles can be confined by vortex-strings in d=3+1 while vortices can be confined by domain-lines in d=2+1. Here, as a higher dimensional generalization of these, we show that Yang-Mills instantons can be confined by monopole-strings in d=4+1. We achieve this by putting the system into the Higgs phase in which the configuration can be constructed inside a non-Abelian vortex sheet.Comment: 15 pages, 2 figures, v2: published versio

Matryoshka Skyrmions

We construct a stable Skyrmion in 3+1 dimensions as a sine-Gordon kink inside a domain wall within a domain wall in an O(4) sigma model with hierarchical mass terms without the Skyrme term. We also find that higher dimensional Skyrmions can stably exist with a help of non-Abelian domain walls in an O(N) model with hierarchical mass terms without a Skyrme term, which leads a matryoshka structure of Skyrmions.Comment: 14 pages, 3+1 figures, v2: references added, published versio

Fractional instantons and bions in the principal chiral model on R2×S1{\mathbb R}^2\times S^1 with twisted boundary conditions

Bions are multiple fractional instanton configurations with zero instanton charge playing important roles in quantum field theories on a compactified space with a twisted boundary condition. We classify fractional instantons and bions in the $SU(N)$ principal chiral model on ${\mathbb R}^2 \times S^1$ with twisted boundary conditions. We find that fractional instantons are global vortices wrapping around $S^1$ with their $U(1)$ moduli twisted along $S^1$, that carry $1/N$ instanton (baryon) numbers for the ${\mathbb Z}_N$ symmetric twisted boundary condition and irrational instanton numbers for generic boundary condition. We work out neutral and charged bions for the $SU(3)$ case with the ${\mathbb Z}_3$ symmetric twisted boundary condition. We also find for generic boundary conditions that only the simplest neutral bions have zero instanton charges but instanton charges are not canceled out for charged bions. A correspondence between fractional instantons and bions in the $SU(N)$ principal chiral model and those in Yang-Mills theory is given through a non-Abelian Josephson junction.Comment: 30 pages, 2 figures. v2: published version. arXiv admin note: text overlap with arXiv:1412.768

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

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.Comment: 18 pages, 3 figures, v2: typos corrected, minor changes, references added, v3: published versio

Instantons in Lifshitz Field Theories

BPS instantons are discussed in Lifshitz-type anisotropic field theories. We consider generalizations of the sigma model/Yang-Mills instantons in renormalizable higher dimensional models with the classical Lifshitz scaling invariance. In each model, BPS instanton equation takes the form of the gradient flow equations for "the superpotential" defining "the detailed balance condition". The anisotropic Weyl rescaling and the coset space dimensional reduction are used to map rotationally symmetric instantons to vortices in two-dimensional anisotropic systems on the hyperbolic plane. As examples, we study anisotropic BPS baby Skyrmion 1+1 dimensions and BPS Skyrmion in 2+1 dimensions, for which we take Kahler 1-form and the Wess-Zumiono-Witten term as the superpotentials, respectively, and an anisotropic generalized Yang-Mills instanton in 4+1 dimensions, for which we take the Chern-Simons term as the superpotential.Comment: 32 pages, 5 figure

Vortex trimer in three-component Bose-Einstein condensates

Vortex trimer is predicted in three-component Bose-Einstein condensates with internal coherent couplings. The molecule is made by three constituent vortices which are bounded by domain walls of the relative phases. We show that the shape and the size of the molecule can be controlled by changing the internal coherent couplings.Comment: 6 pages, 5 figure