The Higgs model for anyons and Liouville action

We connect Liouville theory, anyons and Higgs model in a purely geometrical way.Comment: 9 pages Latex file, DFPD/93/TH/6

Low-Energy Dynamics of String Solitons

The dynamics of a class of fivebrane string solitons is considered in the moduli space approximation. The metric on moduli space is found to be flat. This implies that at low energies the solitons do not interact, and their scattering is trivial. The range of validity of the approximation is also briefly discussed.Comment: 8 pages, Minor typos correcte

The L^2 geometry of spaces of harmonic maps S^2 -> S^2 and RP^2 -> RP^2

Harmonic maps from S^2 to S^2 are all weakly conformal, and so are represented by rational maps. This paper presents a study of the L^2 metric gamma on M_n, the space of degree n harmonic maps S^2 -> S^2, or equivalently, the space of rational maps of degree n. It is proved that gamma is Kaehler with respect to a certain natural complex structure on M_n. The case n=1 is considered in detail: explicit formulae for gamma and its holomorphic sectional, Ricci and scalar curvatures are obtained, it is shown that the space has finite volume and diameter and codimension 2 boundary at infinity, and a certain class of Hamiltonian flows on M_1 is analyzed. It is proved that \tilde{M}_n, the space of absolute degree n (an odd positive integer) harmonic maps RP^2 -> RP^2, is a totally geodesic Lagrangian submanifold of M_n, and that for all n>1, \tilde{M}_n is geodesically incomplete. Possible generalizations and the relevance of these results to theoretical physics are briefly discussed.Comment: 27 pages, 2 figure

Low energy dynamics of U(1)^{N} Chern-Simons solitons

We apply the adiabatic approximation to investigate the low energy dynamics of vortices in the parity invariant double self-dual Higgs model with only mutual Chern-Simons interaction. When distances between solitons are large they are particles subject to the mutual interaction. The dual formulation of the model is derived to explain the sign of the statistical interaction. When vortices of different types pass one through another they behave like charged particles in magnetic field. They can form a bound state due to the mutual magnetic trapping. Vortices of the same type exhibit no statistical interaction. Their short range interactions are analysed. Possible quantum effects due to the finite width of vortices are discussed.Comment: keywords: vortex, vortices, anyons, fractional statistics, 20 pages in Latex, accepted for publication in Phys.Rev.D, ( the above keywords missing in the title were added

Conservation Laws in a First Order Dynamical System of Vortices

Gauge invariant conservation laws for the linear and angular momenta are studied in a certain 2+1 dimensional first order dynamical model of vortices in superconductivity. In analogy with fluid vortices it is possible to express the linear and angular momenta as low moments of vorticity. The conservation laws are compared with those obtained in the moduli space approximation for vortex dynamics.Comment: LaTex file, 16 page

One-vortex moduli space and Ricci flow

The metric on the moduli space of one abelian Higgs vortex on a surface has a natural geometrical evolution as the Bradlow parameter, which determines the vortex size, varies. It is shown by various arguments, and by calculations in special cases, that this geometrical flow has many similarities to Ricci flow.Comment: 20 page

Gravity thaws the frozen moduli of the CP^1 lump

The slow motion of a self-gravitating CP^1 lump is investigated in the approximation of geodesic flow on the moduli space of unit degree static solutions M_1. It is found that moduli which are frozen in the absence of gravity, parametrizing the lump's width and internal orientation, may vary once gravitational effects are included. If gravitational coupling is sufficiently strong, the presence of the lump shrinks physical space to finite volume, and the moduli determining the boundary value of the CP^1 field thaw also. Explicit formulae for the metric on M_1 are found in both the weak and strong coupling regimes. The geodesic problem for weak coupling is studied in detail, and it is shown that M_1 is geodesically incomplete. This leads to the prediction that self-gravitating lumps are unstable.Comment: 6 pages, minor error corrected (conclusions unchanged

Static intervortex forces

A point particle approximation to the classical dynamics of well separated vortices of the abelian Higgs model is developed. A static vortex is asymptotically identical to a solution of the linearized field theory (a Klein-Gordon/Proca theory) in the presence of a singular point source at the vortex centre. It is shown that this source is a composite scalar monopole and magnetic dipole, and the respective charges are determined numerically for various values of the coupling constant. The interaction potential of two well separated vortices is computed by calculating the interaction Lagrangian of two such point sources in the linear theory. The potential is used to model type II vortex scattering.Comment: Much shorter (10 pages) published version, new titl