Related papers: Symetric Monopoles
We discuss the spectral curves and rational maps associated with $SU(2)$ Bogomolny monopoles of arbitrary charge $k$. We describe the effect on the rational maps of inverting monopoles in the plane with respect to which the rational maps…
By imposing certain combined inversion and rotation symmetries on the rational maps for SU(2) BPS monopoles we construct geodesics in the monopole moduli space. In the moduli space approximation these geodesics describe a novel kind of…
We study charge k SU(2) BPS monopoles which are symmetric under the cyclic group of order k. Approximate twistor data (spectral curves and Nahm data) is constructed using a new technique based upon a Painleve analysis of Nahm's equation…
We consider singly periodic solutions to the SU(2) Bogomolny equations and use the Nahm transform to generate a class of monopoles of charge k>2, thereby extending known results for lower charge chains. Some simple scattering processes are…
BPS monopoles on $\mathbb{R}^2\times S^1$ correspond, via the generalized Nahm transform, to certain solutions of the Hitchin equations on the cylinder $\mathbb{R}\times S^1$. The moduli space M of two monopoles with their centre-of-mass…
We classify all possible charge-3 monopole spectral curves with non-trivial automorphism group and within these identify those with elliptic quotients. By focussing on elliptic quotients the transcendental constraints for a monopole…
A self-contained study of monopole configurations of pure Yang-Mills theories and a discussion of their charges is carried out in the language of principal bundles. A n-dimensional monopole over the sphere S^n is a particular type of…
Monopoles are solutions of an SU(2) gauge theory in $\mathbb{R}^{3}$ satisfying a lower bound for energy and certain asymptotic conditions, which translate as topological properties encoded in their charge. Using methods from integrable…
The dynamics of n slowly moving fundamental monopoles in the SU(n+1) BPS Yang-Mills-Higgs theory can be approximated by geodesic motion on the 4n-dimensional hyperkahler Lee-Weinberg-Yi manifold. In this paper we apply a variational method…
I survey the theory of Bogomolny monopoles and the various approaches to their study. These include the spectral curve, Nahm correspondence and rational maps.
We determine the spectral curve of charge 3 BPS su(2) monopoles with C_3 cyclic symmetry. The symmetry means that the genus 4 spectral curve covers a (Toda) spectral curve of genus 2. A well adapted homology basis is presented enabling the…
BPS monopoles which are periodic in one of the spatial directions correspond, via a generalized Nahm transform, to solutions of the Hitchin equations on a cylinder. A one-parameter family of solutions of these equations, representing a…
The moduli space of centred Bogomolny-Prasad-Sommmerfield 2-monopole fields is a 4-dimensional manifold M with a natural metric, and the geodesics on M correspond to slow-motion monopole dynamics. The best-known case is that of monopoles on…
This paper deals with static BPS monopoles in three dimensions which are periodic either in one direction (monopole chains) or two directions (monopole sheets). The Nahm construction of the simplest monopole chain is implemented…
Using a numerical implementation of the ADHMN construction, we compute the fields and energy densities of a charge three monopole with tetrahedral symmetry and a charge four monopole with octahedral symmetry. We then construct a one…
It is shown that there exists a charge five monopole with octahedral symmetry and a charge seven monopole with icosahedral symmetry. A numerical implementation of the ADHMN construction is used to calculate the energy density of these…
We develop the Atiyah-Drinfeld-Manin-Hitchin-Nahm construction to study SU(2) non-abelian charge 3 monopoles within the algebro-geometric method. The method starts with finding an algebraic curve, the monopole spectral curve, subject to…
We study Bogomolny equations on $R^2\times S^1$. Although they do not admit nontrivial finite-energy solutions, we show that there are interesting infinite-energy solutions with Higgs field growing logarithmically at infinity. We call these…
We present explicit expressions for the fields of a charge one BPS monopole with two Dirac singularities. These are solutions of the nonlinear Bogomolny equations with the gauge group U(2) or SO(3). We derive these expressions by applying…
We consider 3-monopoles symmetric under inversion symmetry. We show that the moduli space of these monopoles is an Atiyah-Hitchin submanifold of the 3-monopole moduli space. This allows what is known about 2-monopole dynamics to be…