Towards a Coulomb gas of instantons in the SO(4)xU(1) Higgs model on R_4

The $SO(4)\times U(1)$ Higgs model on $\R_4$ is extended by a $F^3$ term so that the action receives a nonvanishing contribution from the interactions of 2-instantons and 3-instantons, and can be expressed as the inverse of the Laplacian on $\R_4$ in terms of the mutual distances of the instantons. The one-instanton solutions of both the basic and the extended models have been studied in detail numerically.Comment: 29 pages LaTeX, 4 Figures available from authors on reques

A HIERARCHY OF GAUGED GRASSMANIAN MODELS IN 4p4p DIMENSIONS WITH SELF-DUAL INSTANTONS

We present a hierarchy of gauged Grassmanian models in $4p$ dimensions, where the gauge field takes its values in the $2^{2p- 1}\times 2^{2p-1}$ chiral representation of SO(4p). The actions of all these models are absolutely minimised by a hierarchy of self-duality equations, all of which reduce to a single pair of coupled ordinary differential equations when subjected to $4p$ dimensional spherical symmetry.Comment: latex file, 13 page

Interaction Energies of Generalised Monopoles

Generalisations of the 't Hooft-Polyakov monopole which can exhibit repulsion only, attraction only, and both attraction and repulsion, between like monopoles, are studied numerically. The models supporting these solitons are SO(3) gauged Higgs models featuring Skyrme-like terms.Comment: 46 pages, including 22 postscript figures, LaTex forma

SO(3) Gauged Soliton of an O(4) Sigma Model on R3R_3

Vector $SO(3)$ gauged $O(4)$ sigma models on $\R_3$ are presented. The topological charge supplying the lower bound on the energy and rendering the soliton stable coincides with the Baryon number of the Skyrmion. These solitons have vanishing magnetic monopole flux. To exhibit the existence of such solitons, the equations of motion of one of these models is integrated numerically. The structure of the conserved Baryon current is briefly discussed.Comment: 14 pages, latex, 3 figures available from the authors on reques

Sphaleron of a 4 dimensional SO(4) Higgs model

We construct the finite energy path between topologically distinct vacua of a 4 dimensional SO(4) Higgs model which is known to support an instanton, and show that there is a sphaleron with Chern-Simons number N_CS=1/2 at the top of the energy barrier. This is carried out using the original geometric loop construction of Manton.Comment: 9 pages, 2 figures, LaTex format, minor text corrections. To be published in Phys. Lett.

Localisation of Fermions to brane: Codimension d≥2d \geq 2

We investigate $4+d$ dimensional fermionic models in which the system in codimension-$d$ supports a topologically stable solution, and in which the fermion may be localised to the brane, with power law in 'instanton' backgrounds and exponentially in 'soliton' backgrounds. When the fermions are isoscalars, the mechanism fails, while for isospinor fermions it is successful. As backgrounds we consider instantons of Yang--Mills and sigma models in even codimensions, solitons of sigma models in odd codimensions, as well as solitons of Higgs and Goldstone models in all codimensions.Comment: 20 pages latex; expande

Self-dual instanton and nonself-dual instanton-antiinstanton solutions in d=4d=4 Yang-Mills theory

Subjecting the SU(2) Yang--Mills system to azimuthal symmetries in both the $x-y$ and the $z-t$ planes results in a residual subsystem described by a U(1) Higgs like model with two complex scalar fields on the quarter plane. The resulting instantons are labeled by integers $(m,n_1,n_2)$ with topological charges $q=\frac12 [1-(-1)^m]n_1n_2$. Solutions are constructed numerically for $m=1,2,3$ and a range of $n_1=n_2=n$. It is found that only the $m=1$ instantons are self-dual, the $m>1$ configurations describing composite instanton-antiinstanton lumps.Comment: 12 pages, 5 Figure

Conformal coupling of the scalar field with gravity in higher dimensions and invariant powers of the Laplacian

The hierarchy of conformally coupled scalars with the increasing scaling dimensions $\Delta_{k}=k-d/2$, $k=1,2,3,...$ connected with the $k$-th Euler density in the corresponding space-time dimensions $d\geq 2k$ is proposed. The corresponding conformal invariant Lagrangian with the $k$-th power of Laplacian for the already known cases $k=1,2$ is reviewed, and the subsequent case of $k=3$ is completely constructed and analyzed.Comment: Latex, 11 pages, v.2, two misprints correcte

Higher order curvature generalisations of Bartnick-McKinnon and coloured black hole solutions in d=5d=5

We construct globally regular as well as non-abelian black hole solutions of a higher order curvature Einstein-Yang-Mills (EYM) model in $d=5$ dimensions. This model consists of the superposition of the first two members of the gravitational hierarchy (Einstein plus first Gauss-Bonnet(GB)) interacting with the superposition of the first two members of the $SO(d)$ Yang--Mills hierarchy.Comment: 13 Revtex pages, 5 PS figures; discussions extended, reference adde

Spinning U(1) gauged Skyrmions

We construct axially symmetric solutions of U(1) gauged Skyrme model. Possessing a nonvanishing magnetic moment, these solitons have also a nonzero angular momentum proportional to the electric charge.Comment: v2: 7 pages, 4 eps figures; some clarifications and references added on the existence of solutions; typos correcte