Knot Solitons

The existence of ring-like and knotted solitons in O(3) non-linear sigma model is analysed. The role of isotopy of knots/links in classifying such solitons is pointed out. Appearance of torus knot solitons is seen.Comment: Latex 9 pages + 2 eps figure

Knots in interaction

We study the geometry of interacting knotted solitons. The interaction is local and advances either as a three-body or as a four-body process, depending on the relative orientation and a degeneracy of the solitons involved. The splitting and adjoining is governed by a four-point vertex in combination with duality transformations. The total linking number is preserved during the interaction. It receives contributions both from the twist and the writhe, which are variable. Therefore solitons can twine and coil and links can be formed.Comment: figures now in GIF forma

Maxwell--Chern-Simons gauged non-relativistic O(3) model with self-dual vortices

A non-relativistic version of the 2+1 dimensional gauged Chern-Simons O(3) sigma model, augmented by a Maxwell term, is presented and shown to support topologically stable static self-dual vortices. Exactly like their counterparts of the ungauged model, these vortices are shown to exhibit Hall behaviour in their dynamics.Comment: 12 pages, LateX, to appear in Mod. Phys. Lett. 199

Comment on ``Reduction of static field equation of Faddeev model to first order PDE'', arXiv:0707.2207

The authors of the article Phys. Lett. B 652 (2007) 384, (arXiv:0707.2207), propose an interesting method to solve the Faddeev model by reducing it to a set of first order PDEs. They first construct a vectorial quantity $\bm \alpha$, depending on the original field and its first derivatives, in terms of which the field equations reduce to a linear first order equation. Then they find vectors $\bm \alpha_1$ and $\bm \alpha_2$ which identically obey this linear first order equation. The last step consists in the identification of the $\bm \alpha_i$ with the original $\bm \alpha$ as a function of the original field. Unfortunately, the derivation of this last step in the paper cited above contains an error which invalidates most of its results

Knots, Braids and Hedgehogs from the Eikonal Equation

The complex eikonal equation in the three space dimensions is considered. We show that apart from the recently found torus knots this equation can also generate other topological configurations with a non-trivial value of the $\pi_2(S^2)$ index: braided open strings as well as hedgehogs. In particular, cylindric strings i.e. string solutions located on a cylinder with a constant radius are found. Moreover, solutions describing strings lying on an arbitrary surface topologically equivalent to cylinder are presented. We discus them in the context of the eikonal knots. The physical importance of the results originates in the fact that the eikonal knots have been recently used to approximate the Faddeev-Niemi hopfions.Comment: 15 pages, 5 figure

Magnetic Geometry and the Confinement of Electrically Conducting Plasmas

We develop an effective field theory approach to inspect the electromagnetic interactions in an electrically neutral plasma, with an equal number of negative and positive charge carriers. We argue that the static equilibrium configurations within the plasma are topologically stable solitons, that describe knotted and linked fluxtubes of helical magnetic fields.Comment: 9 pages 1 ps-figur

Symmetries of generalized soliton models and submodels on target space S2S^2

Some physically relevant non-linear models with solitons, which have target space $S^2$, are known to have submodels with infinitly many conservation laws defined by the eikonal equation. Here we calculate all the symmetries of these models and their submodels by the prolongation method. We find that for some models, like the Baby Skyrme model, the submodels have additional symmetries, whereas for others, like the Faddeev--Niemi model, they do not.Comment: 18 pages, one Latex fil

Solitons in 1+1 Dimensional Gauged Sigma Models

We study soliton solutions in 1+1 dimensional gauged sigma models, obtained by dimensional reduction from its 2+1 dimensional counterparts. We show that the Bogomol'nyi bound of these models can be expressed in terms of two conserved charges in a similar way to that of the BPS dyons in 3+1 dimensions. Purely magnetic vortices of the 2+1 dimensional completely gauged sigma model appear as charged solitons in the corresponding 1+1 dimensional theory. The scale invariance of these solitons is also broken because of the dimensional reduction. We obtain exact static soliton solutions of these models saturating the Bogomol'nyi bound.Comment: 21 pages, RevTeX, minor changes, version to appear in Physical Review

Soliton solutions in an effective action for SU(2) Yang-Mills theory: including effects of higher-derivative term

The Skyrme-Faddeev-Niemi (SFN) model which is an O(3) $\sigma$ model in three dimensional space upto fourth-order in the first derivative is regarded as a low-energy effective theory of SU(2) Yang-Mills theory. One can show from the Wilsonian renormalization group argument that the effective action of Yang-Mills theory recovers the SFN in the infrared region. However, the thoery contains an additional fourth-order term which destabilizes the soliton solution. In this paper, we derive the second derivative term perturbatively and show that the SFN model with the second derivative term possesses soliton solutions.Comment: 7 pages, 3 figure