Extended skyrme models in even dimensions and higher-dimensional solitons II: Wess-Zumino terms in two and higher dimensions

We investigate Wess-Zumino terms in higher-dimensional nonlinear sigma models using the higher-dimensional hedgehog ansatz proposed by us. The gauged Wess-Zumino terms are also calculated from a fermion determinant, and we comment on extended objects or a dibaryon ansatz.Partially supported by the Grant-in-Aid for Scientific Research, No. 61460005.     

Skyrme solitons with vector mesons

We investigate the Skyrme type soliton with vector mesons (ρ, A₁ and ω), first in the massive Yang-Mills approach and then using the hidden local symmetry Lagrangian. It is demonstrated that the two schemes give identical results for the soliton properties. A comparison is made with alternative approaches in which the A₁ degrees of freedom is eliminated.     

拓展的Skyrme模型中的Skyrmion与其量子化

考察了包含手征流非对易项的拓展Skyrme模型。 在推导出相应Skyrme模型运动方程的基础上对模型中的球对称Skyrmion孤子进行了数值模拟。 对模型进行零模(Zero-mode)量子化之后, 计算核子的若干静态性质, 并讨论了拓展Skyrme模型中手征流非对易项与QCD之间的联系。 This paper considers the extended Skyrme model with the anti commutator of the chiral current. By deducing the equations of motion of extended Skyrme model, the spherically symmetric Skyrmion was numerically simulated. After the Zero-mode quantization of the model, the static properties of nucleons were calculated and the connection of the anti commutator of the chiral current with QCD was discussed.     

Extended particles and solitons

A variational method is introduced for approximating the eigenstates of the Hamiltonian in relativistic quantum field theory. The method has three ingredients: the coherent states, the solutions of the corresponding classical field theory, and the generator-coordinate technique of nuclear physics. It provides a quantum-mechanical interpretation for solitons, some of which resemble extended particles.     

Multistable solitons in higher-dimensional cubic-quintic nonlinear Schrödinger lattices

We study the existence, stability, and mobility of fundamental discrete solitons in two- and three-dimensional nonlinear Schrödinger lattices with a combination of cubic self-focusing and quintic self-defocusing onsite nonlinearities. Several species of stationary solutions are constructed, and bifurcations linking their families are investigated using parameter continuation starting from the anti-continuum limit, and also with the help of a variational approximation. In particular, a species of hybrid solitons, intermediate between the site- and bond-centered types of the localized states (with no counterpart in the 1D model), is analyzed in 2D and 3D lattices. We also discuss the mobility of multi-dimensional discrete solitons that can be set in motion by lending them kinetic energy exceeding the appropriately defined Peierls-Nabarro barrier; however, they eventually come to a halt, due to radiation loss.     

Odd and even two-dimensional dark spatial solitons

The formation of two-Dimensional (2D) odd dark spatial solutions is analyzed numerically at an initial helical dark-beam phase distribution. Experimental results are presented for the first time confirming the existence of two-dimensional optical even dark solitons (ring dark solitons). Several aspects of the evolution of input 1D and 2D odd/even dark beams are compared qualitatively.     

Chiral anomalies in even and odd dimensions

Odd dimensional Yang-Mills theories with an extra topological mass term, defined by the Chern-Simons secondary characteristic, are discussed. It is shown in detail how the topological mass affects the equal time charge commutation relations and how the modified commutation relations are related to non-abelian chiral anomalies in even dimensions. We also study the SU(3) chiral model (Wess-Zumino model) in four dimensions and we show how a gauge invariant interaction with an external SU(3) vector potential can be defined with the help of the Chern-Simons characteristic in five dimensions.     

Extended inflation in higher-dimensional spacetime with a Brans-Dicke scalar field

Starting from an assumption of homogeneity of matter-energy tensor and Brans-Dicke (BD) scalar field we obtain a Robertson-Walker type of metric form in five-dimensional spacetime with the essential difference that our model is spatially inhomogeneous. The model exhibits an interesting feature in that as we approach the centre of symmetry the compact dimension becomes very large, with the implication that the Kaluza-Klein excitations become very light when located there and that the origin may represent a singular concentration of matter with motion in the extra dimension. Following Wesson the effective 4D properties of matter from the 5D vacuum solutions are also briefly discussed. Assuming particular functional relationships between and as also between the scale factor and scalar field, we obtain exact solutions which may be of relevance to the early universe and its extended inflation in the BD type of theory. We also discuss very briefly rollover time immediately after tunneling to the true vacuum state to explore if dimensionality has any marked influence on the situation.     

On the geometrized Skyrme and Faddeev models

The higher power derivative terms involved in both Faddeev and Skyrme energy functionals correspond to _σ2${\sigma }_2$-energy, introduced by Eells and Sampson (1964) [1]. This paper provides a detailed study of the first and second variation formulae associated to this energy. Some classes of (stable) critical points are outlined.     

Stable spinning optical solitons in three dimensions

We introduce spatiotemporal spinning solitons (vortex tori) of the three-dimensional nonlinear Schr?dinger equation with focusing cubic and defocusing quintic nonlinearities. The first ever found completely stable spatiotemporal vortex solitons are demonstrated. A general conclusion is that stable spinning solitons are possible as a result of competition between focusing and defocusing nonlinearities.     

Collision and rotation of solitons in three space-time dimensions

We investigate properties of soliton solutions in two space and one time dimension of two confining field theories, in particular rotation and Regge trajectories. Numerically we study the collision process in a two-soliton collision.     

The chiral anomaly and goldstone-wilczek current in even dimensions

The form of the non-abelian anomaly is described in arbitrary even dimension when the gauge group contains explicit U(1) factors. An effective action is constructed which when varied under the group reproduces the anomaly. It constitutes a generalization of the Wess-Zumino action.     

Toroidal solitons in Nicole-type models

A family of modified Nicole models is introduced. We show that for particular members of the family a topological soliton with a non-trivial value of the Hopf index exists. The form of the solitons as well as their energy and topological charge is explicitly found. They appear to be identical to the so-called eikonal knots. The relation between energy and topological charge of the solution is also presented. Quite interestingly it seems to differ drastically from the standard Vakulenko-Kapitansky formula.Received: 4 February 2005, Published online: 23 March 2005     

Nonlocal instantons and solitons in string models

We study a class of nonlocal systems which can be described by a local scalar field diffusing in an auxiliary radial dimension. As examples p-adic, open and boundary string field theory are considered on Minkowski, Friedmann–Robertson–Walker and Euclidean metric backgrounds. Starting from distribution-like initial field configurations which are constant almost everywhere, we construct exact and approximate nonlocal solutions. The Euclidean p-adic lump is interpreted as a solitonic brane, and the Euclidean kink of supersymmetric open string field theory as an instanton. Some relations between solutions of different string theories are highlighted also thanks to a reformulation of nonlocal systems as fixed points in a renormalization group flow.     

Vector solitons in (2 + 1) dimensions

We address the problem of the existence and stability of vector spatial solitons formed by two incoherently interacting optical beams in bulk Kerr and saturable media. We identify families of (2+1)-dimensional two-mode self-trapped beams, with and without a topological charge, and describe their properties analytically and numerically.