Monopoles and Harmonic Maps

Recently Jarvis has proved a correspondence between SU(N) monopoles and rational maps of the Riemann sphere into flag manifolds. Furthermore, he has outlined a construction to obtain the monopole fields from the rational map. In this paper we examine this construction in some detail and provide explicit examples for spherically symmetric SU(N) monopoles with various symmetry breakings. In particular we show how to obtain these monopoles from harmonic maps into complex projective spaces. The approach extends in a natural way to monopoles in hyperbolic space and we use it to construct new spherically symmetric SU(N) hyperbolic monopoles.Comment: Version to appear in J. Math. Phy

Non-BPS String Junctions and Dyons in N=4 Super-Yang-Mills

We construct non-BPS dyon solutions of N=4 SU(n) supersymmetric Yang-Mills theory. These solutions are the worldvolume solitons which describe non-BPS Type IIB non-planar string junctions connecting n parallel D3-branes. The solutions are smooth deformations of the 1/4 BPS states which describe planar string junctions.Comment: 10 pages plus 3 figure

Non-Bogomolny SU(N) BPS Monopoles

For N>2 we present static monopole solutions of the second order SU(N) BPS Yang-Mills-Higgs equations which are not solutions of the first order Bogomolny equations. These spherically symmetric solutions may be interpreted as monopole anti-monopole configurations and their construction involves harmonic maps into complex projective spaces.Comment: 14 pages, 1 figur

Classical sigma models in 2+1 dimensions

The work in this thesis is concerned with the study of dynamics, scattering and stability of solitons in planar models, i.e. where spacetime is (2+l)-dimensionaI. We consider both integrable models, where exact solutions can be written in closed form, and nonintegrable models where approximations and numerical methods must be employed. For theories that possess a topological lower bound on the energy, there is a useful approximation in which the kinetic energy is assumed to remain small. All these approaches are used at various stages of the thesis. Chapters 1 and 2 review the planar models which are the subjects of this thesis. Chapters 3 and 4 are concerned with integrable chiral equations. First we exhibit an infinite sequence of well-defined conserved quantities and then we construct exact soliton and soliton-antisoliton solutions using analytical methods. We find that there exist solitons that scatter in a different way to those previously found in integrable models. Furthermore, this soliton scattering resembles very closely that found in nonintegrable models, thereby providing a link between the two classes. Chapter 5 develops a numerical simulation based on topological arguments, which is used in a study of soliton stability in the (unmodified) 0(3) model. This confirms that the sohtons are unstable, in the sense that their size is subject to large changes. The same results are obtained by using the slow-motion approximation

Platonic Gravitating Skyrmions

We construct globally regular gravitating Skyrmions, which possess only discrete symmetries. In particular, we present tetrahedral and cubic Skyrmions. The SU(2) Skyrme field is parametrized by an improved harmonic map ansatz. Consistency then requires also a restricted ansatz for the metric. The numerical solutions obtained within this approximation are compared to those obtained in dilaton gravity.Comment: 13 pages, 4 figure

Non-BPS Dirac-Born-Infeld Solitons

We show that CPn sigma model solitons solve the field equations of a Dirac-Born-Infeld (DBI) action and, furthermore, we prove that the non-BPS soliton/anti-soliton solutions of the sigma model also solve the DBI equations. Using the moduli space approximation we compare the dynamics of the BPS sigma model solitons with that of the associated DBI solitons. We find that for the CP1 case the metric on the moduli space of sigma model solitons is identical to that of the moduli space of DBI solitons, but for CPn with n>1 we show that the two metrics are not equal. We also consider the possibility of similar non-BPS solitons in other DBI theories.Comment: Major changes; sections removed and title changed. Version published in JHE