1,351 research outputs found
The dynamics of vortices on S^2 near the Bradlow limit
The explicit solutions of the Bogomolny equations for N vortices on a sphere
of radius R^2 > N are not known. In particular, this has prevented the use of
the geodesic approximation to describe the low energy vortex dynamics. In this
paper we introduce an approximate general solution of the equations, valid for
R^2 close to N, which has many properties of the true solutions, including the
same moduli space CP^N. Within the framework of the geodesic approximation, the
metric on the moduli space is then computed to be proportional to the Fubini-
Study metric, which leads to a complete description of the particle dynamics.Comment: 17 pages, 9 figure
Symetric Monopoles
We discuss Bogomolny monopoles of arbitrary charge invariant
under various symmetry groups. The analysis is largely in terms of the spectral
curves, the rational maps, and the Nahm equations associated with monopoles. We
consider monopoles invariant under inversion in a plane, monopoles with cyclic
symmetry, and monopoles having the symmetry of a regular solid. We introduce
the notion of a strongly centred monopole and show that the space of such
monopoles is a geodesic submanifold of the monopole moduli space.
By solving Nahm's equations we prove the existence of a tetrahedrally
symmetric monopole of charge and an octahedrally symmetric monopole of
charge , and determine their spectral curves. Using the geodesic
approximation to analyse the scattering of monopoles with cyclic symmetry, we
discover a novel type of non-planar -monopole scattering process
Sigma Model BPS Lumps on Torus
We study doubly periodic Bogomol'nyi-Prasad-Sommerfield (BPS) lumps in
supersymmetric CP^{N-1} non-linear sigma models on a torus T^2. Following the
philosophy of the Harrington-Shepard construction of calorons in Yang-Mills
theory, we obtain the n-lump solutions on compact spaces by suitably arranging
the n-lumps on R^2 at equal intervals. We examine the modular invariance of the
solutions and find that there are no modular invariant solutions for n=1,2 in
this construction.Comment: 15 pages, 3 figures, published versio
Statistical Mechanics of Charged Particles in Einstein-Maxwell-Scalar Theory
We consider an -body system of charged particle coupled to gravitational,
electromagnetic, and scalar fields. The metric on moduli space for the system
can be considered if a relation among the charges and mass is satisfied, which
includes the BPS relation for monopoles and the extreme condition for charged
black holes. Using the metric on moduli space in the long distance
approximation, we study the statistical mechanics of the charged particles at
low velocities. The partition function is evaluated as the leading order of the
large expansion, where is the spatial dimension of the system and will
be substituted finally as .Comment: 11 pages, RevTeX3.
Massless monopoles and the moduli space approximation
We investigate the applicability of the moduli space approximation in
theories with unbroken non-Abelian gauge symmetries. Such theories have
massless magnetic monopoles that are manifested at the classical level as
clouds of non-Abelian field surrounding one or more massive monopoles. Using an
SO(5) example with one massive and one massless monopole, we compare the
predictions of the moduli space approximation with the results of a numerical
solution of the full field equations. We find that the two diverge when the
cloud velocity becomes of order unity. After this time the cloud profile
approximates a spherical wavefront moving at the speed of light. In the region
well behind this wavefront the moduli space approximation continues to give a
good approximation to the fields. We therefore expect it to provide a good
description of the motion of the massive monopoles and of the transfer of
energy between the massive and massless monopoles.Comment: 18 pages, 5 figure
A note on the (1, 1,..., 1) monopole metric
Recently K. Lee, E.J. Weinberg and P. Yi in CU-TP-739, hep-th/9602167,
calculated the asymptotic metric on the moduli space of (1, 1, ..., 1) BPS
monopoles and conjectured that it was globally exact. I lend support to this
conjecture by showing that the metric on the corresponding space of Nahm data
is the same as the metric they calculate.Comment: 12 pages, latex, no figures, uses amsmath, amsthm, amsfont
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