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

Incarnations of Instantons

Yang-Mills instantons in a pure Yang-Mills theory in four Euclidean space can be promoted to particle-like topological solitons in d=4+1 dimensional space-time. When coupled to Higgs fields, they transform themselves in the Higgs phase into Skyrmions, lumps and sine-Gordon kinks, with trapped inside a non-Abelian domain wall, non-Abelian vortex and monopole string, respectively. Here, we point out that a closed monopole string, non-Abelian vortex sheet and non-Abelian domain wall in $S^1$, $S^2$ and $S^3$ shapes, respectively, are all Yang-Mills instantons if their $S^1$, $S^2$ and $S^3$ moduli, respectively, are twisted along their world-volumes.Comment: 17 pages, 3 figures, v2: published versio

Josephson junction of non-Abelian superconductors and non-Abelian Josephson vortices

A Josephson junction is made of two superconductors sandwiching an insulator, and a Josephson vortex is a magnetic vortex (flux tube) absorbed into the Josephson junction, whose dynamics can be described by the sine-Gordon equation. In a field theory framework, a flexible Josephson junction was proposed, in which the Josephson junction is represented by a domain wall separating two condensations and a Josephson vortex is a sine-Gordon soliton in the domain wall effective theory. In this paper, we propose a Josephson junction of non-Abelian color superconductors, that is described by a non-Abelian domain wall, and show that a non-Abelian vortex (color magnetic flux tube) absorbed into it is a non-Abelian Josephson vortex represented as a non-Abelian sine-Gordon soliton in the domain wall effective theory, that is the $U(N)$ principal chiral model.Comment: 19 pages, 3 figures, v2: published versio