arXiv subjects

R S Ward

Publications and source records attributed to R S Ward.

5 recordsLinked to original sources

arXiv2014

Geometry of Periodic Monopoles

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 fixed is a 4-dimensional manifold with a natural hyperkähler metric, and its geodesics correspond to slow-motion monopole scattering. The purpose of this paper is to study the geometry of M in terms of the Nahm/Hitchin data, i.e. in terms of structures on $\mathbb{R}\times S^1$. In particular, we identify the moduli, derive the asymptotic metric on M, and discuss several geodesic surfaces and geodesics on M. The latter include novel examples of monopole dynamics.

hep-th↗

arXiv2002

Stabilizing textures with magnetic fields

The best-known way of stabilizing textures is by Skyrme-like terms, but another possibility is to use gauge fields. The semilocal vortex may be viewed as an example of this, in two spatial dimensions. In three dimensions, however, the idea (in its simplest form) does not work -- the link between the gauge field and the scalar field is not strong enough to prevent the texture from collapsing. Modifying the |D Phi|^2 term in the Lagrangian (essentially by changing the metric on the Phi-space) can strengthen this link, and lead to stability. Furthermore, there is a limit in which the gauge field is entirely determined in terms of the scalar field, and the system reduces to a pure Skyrme-like one. This is described for gauge group U(1), in dimensions two and three. The non-abelian version is discussed briefly, but as yet no examples of texture stabilization are known in this case.

hep-th↗

arXiv2000

Integrable Yang-Mills-Higgs Equations in 3-Dimensional De Sitter Space-Time

This paper describes an integrable Yang-Mills-Higgs system on (2+1)-dimensional de Sitter space-time. It is the curved-space-time analogue of the Bogomolnyi equations for monopoles on R^3. A number of solutions, of various types, are constructed.

nlin.SI↗

arXiv1998

Hopf Solitons on S^3 and R^3

The Skyrme-Faddeev system, a modified O(3) sigma model in three space dimensions, admits topological solitons with nonzero Hopf number. One may learn something about these solitons by considering the system on the 3-sphere of radius R. In particular, the Hopf map is a solution which is unstable for R > \sqrt{2}.

hep-th↗

arXiv1998

Two Integrable Systems Related to Hyperbolic Monopoles

Monopoles on hyperbolic 3-space were introduced by Atiyah in 1984. This article describes two integrable systems which are closely related to hyperbolic monopoles: a one-dimensional lattice equation (the Braam-Austin or discrete Nahm equation), and a soliton system in (2+1)-dimensional anti-deSitter space-time.

solv-int↗