Topological energy bounds in generalized Skyrme models

The Skyrme model has a natural generalization amenable to a standard hamiltonian treatment, consisting of the standard sigma model and the Skyrme terms, a potential, and a certain term sextic in first derivatives. Here we demonstrate that, in this theory, each pair of terms in the static energy functional which may support topological solitons according to the Derrick criterion (i.e., each pair of terms with opposite Derrick scaling) separately posesses a topological energy bound. As a consequence, there exists a four-parameter family of topological bounds for the full generalized Skyrme model. The optimal bounds, i.e., the optimal values of the parameters, depend both on the form of the potential and on the relative strength of the different terms. It also follows that various submodels of the generalized Skyrme model have one-parameter families of topological energy bounds. We also consider the case of topological bounds for the generalized Skyrme model on a compact base space as well as generalizations to higher dimensions.Comment: Latex, 26 pages, version accepted for publication in PRD, presentation and motivation slightly changed, references added, results unchange

Massive and Massless Scalar Field and Confinement

Generalization of QCD motivated classical SU(2) Yang--Mills theory coupled to the scalar field is discussed. The massive scalar field, corresponding the scalar glueball, provides a confining potential for static, point-like, external sources. In case of massless scalar field screening solutions are found. However, there is a confining sector as well. Both, massive and massless confining solutions are compared with phenomenological potentials. The case of non-dynamical permittivity is also discussed.Comment: 10 pages, LaTeX, Accepted for publication in Eur. Phys. J.

Quark-antiquark potentials from a scalar field in SU(2) YM

A generalized Dick model with a potential term is discussed. The solution originating from a static, pointlike, color source is found to have a confining part. The comparison with a wide spectrum of phenomenological quark-antiquark potentials is presented.Comment: 6 pages, LaTeX; to appear in Eur. Phys. J.

Gauged BPS baby Skyrmions with quantised magnetic flux

A new type of gauged BPS baby Skyrme model is presented, where the derivative term is just the Schroers current (i.e., gauge invariant and conserved version of the topological current) squared. This class of models has a topological bound saturated for solutions of the pertinent Bogomolnyi equations supplemented by a so-called superpotential equation. In contrast to the gauged BPS baby Skyrme models considered previously, the superpotential equation is linear and, hence, completely solvable. Furthermore, the magnetic flux is quantized in units of $2\pi$, which allows, in principle, to define this theory on a compact manifold without boundary, unlike all gauged baby Skyrme models considered so far.Comment: Latex, 17 page

Non-uniqueness of the supersymmetric extension of the O(3)O(3) σ\sigma-model

We study the supersymmetric extensions of the $O(3)$ $\sigma$-model in $1+1$ and $2+1$ dimensions. We show that it is possible to construct non-equivalent supersymmetric versions of a given model sharing the same bosonic sector and free from higher-derivative terms.Comment: 19 page