Dyons of One Half Monopole Charge

We would like to present some exact SU(2) Yang-Mills-Higgs dyon solutions of one half monopole charge. These static dyon solutions satisfy the first order Bogomol'nyi equations and are characterized by a parameter, $m$. They are axially symmetric. The gauge potentials and the electromagnetic fields possess a string singularity along the negative z-axis and hence they possess infinite energy density along the line singularity. However the net electric charges of these dyons which varies with the parameter $m$ are finite.Comment: 16 pages, 7 figure

Static Monopoles and Their Anti-Configurations

Recently, we have reported on the existence of some monopoles, multimonopole, and antimonopoles configurations. In this paper we would like to present more monopoles, multimonopole, and antimonopoles configurations of the magnetic ansatz of Ref.\cite{kn:9} when the parameters $p$ and $b$ of the solutions takes different serial values. These exact solutions are a different kind of BPS solution. They satisfy the first order Bogomol'nyi equation but possess infinite energy. They can have radial, axial, or rotational symmetry about the z-axis. We classified these serial solutions as (i) the multimonopole at the origin; (ii) the finitely separated 1-monopoles; (iii) the screening solutions of multimonopole and (iv) the axially symmetric monopole solutions. We also give a construction of their anti-configurations with all the magnetic charges of poles in the configurations reversed. Half-integer topological magnetic charge multimonopole also exist in some of these series of solutions.Comment: 20 pages with 4 figure

Generalized Jacobi Elliptic One-Monopole - Type A

We present new classical generalized one-monopole solution of the SU(2) Yang-Mills-Higgs theory with the Higgs field in the adjoint representation. We show that this generalized solution with $\theta$-winding number $m=1$ and $\phi$-winding number $n=1$ is an axially symmetric Jacobi elliptic generalization of the 't Hooft-Polyakov one-monopole. We construct this axially symmetric one-monopole solution by generalizing the large distance asymptotic solution of the 't Hooft-Polyakov one-monopole to the Jacobi elliptic functions and solving the second order equations of motion numerically when the Higgs potential is vanishing and non vanishing. These solutions are regular non-BPS finite energy solutions.Comment: 17 pages, 5 figure

Dynamical role of anyonic excitation statistics in rapidly rotating Bose gases

We show that for rotating harmonically trapped Bose gases in a fractional quantum Hall state, the anyonic excitation statistics in the rotating gas can effectively play a {\em dynamical} role. For particular values of the two-dimensional coupling constant $g = -2\pi \hbar^2 (2k-1)/m$, where $k$ is a positive integer, the system becomes a noninteracting gas of anyons, with exactly obtainable solutions satisfying Bogomol'nyi self-dual order parameter equations. Attractive Bose gases under rapid rotation thus can be stabilized in the thermodynamic limit due to the anyonic statistics of their quasiparticle excitations.Comment: 4 pages of RevTex4; as published in Physical Review Letter

SU(2) gauged Skyrme-monopoles in scalar-tensor gravity

Considering a Skyrme model with a peculiar gauging of the symmetry, monopole-like solutions exist through a topological lower bound. However, it was recently shown that these objects cannot form bound states in the limit of vanishing Skyrme coupling. Here we consider these monopoles in scalar-tensor gravity. A numerical study of the equations reveals that neither the coupling to gravity nor to the scalar dilaton nor to dilaton-gravity leads to bound multimonopole states.Comment: 9 Revtex pages, 2 PS-figures; formular added, typos correcte

A discrete phi^4 system without Peierls-Nabarro barrier

A discrete phi^4 system is proposed which preserves the topological lower bound on the kink energy. Existence of static kink solutions saturating this lower bound and occupying any position relative to the lattice is proved. Consequently, kinks of the model experience no Peierls-Nabarro barrier, and can move freely through the lattice without being pinned. Numerical simulations reveal that kink dynamics in this system is significantly less dissipative than that of the conventional discrete phi^4 system, so that even on extremely coarse lattices the kink behaves much like its continuum counterpart. It is argued, therefore, that this is a natural discretization for the purpose of numerically studying soliton dynamics in the continuum phi^4 model.Comment: 8 pages, LaTeX, 8 postscript figure

Half-Monopole and Multimonopole

We would like to present some exact SU(2) Yang-Mills-Higgs monopole solutions of half-integer topological charge. These solutions can be just an isolated half-monopole or a multimonopole with topological magnetic charge, ${1/2}m$, where $m$ is a natural number. These static monopole solutions satisfy the first order Bogomol'nyi equations. The axially symmetric one-half monopole gauge potentials possess a Dirac-like string singularity along the negative z-axis. The multimonopole gauge potentials are also singular along the z-axis and possess only mirror symmetries.Comment: 12 pages and 4 figures; typos corrected, reference adde

Kink dynamics in a novel discrete sine-Gordon system

A spatially-discrete sine-Gordon system with some novel features is described. There is a topological or Bogomol'nyi lower bound on the energy of a kink, and an explicit static kink which saturates this bound. There is no Peierls potential barrier, and consequently the motion of a kink is simpler, especially at low speeds. At higher speeds, it radiates and slows down.Comment: 10 pages, 7 figures, archivin

Exact String-like Solutions of the Gauged Nonlinear O(3) Model

We show that the least energy conditions in the gauged nonlinear sigma model with Chern-Simons term lead to exact soliton-like solutions which have the same features as domain walls. We will derive and discuss the corresponding solutions, and compute the total energy, charge, and spin of the resulting system.Comment: 7 pages, 5 figure

Existence of Multiple Vortices in Supersymmetric Gauge Field Theory

Two sharp existence and uniqueness theorems are presented for solutions of multiple vortices arising in a six-dimensional brane-world supersymmetric gauge field theory under the general gauge symmetry group $G=U(1)\times SU(N)$ and with $N$ Higgs scalar fields in the fundamental representation of $G$. Specifically, when the space of extra dimension is compact so that vortices are hosted in a 2-torus of volume |\Om|, the existence of a unique multiple vortex solution representing $n_1,...,n_N$ respectively prescribed vortices arising in the $N$ species of the Higgs fields is established under the explicitly stated necessary and sufficient condition \[ n_i<\frac{g^2v^2}{8\pi N}|\Om|+\frac{1}{N}(1-\frac{1}{N}[\frac{g}{e}]^2)n,\quad i=1,...,N,] where $e$ and $g$ are the U(1) electromagnetic and SU(N) chromatic coupling constants, $v$ measures the energy scale of broken symmetry, and $n=\sum_{i=1}^N n_i$ is the total vortex number; when the space of extra dimension is the full plane, the existence and uniqueness of an arbitrarily prescribed $n$-vortex solution of finite energy is always ensured. These vortices are governed by a system of nonlinear elliptic equations, which may be reformulated to allow a variational structure. Proofs of existence are then developed using the methods of calculus of variations.Comment: 23 page