1,608 research outputs found
Volume of Vortex Moduli Spaces
A gas of Bogomol'nyi vortices in the Abelian Higgs model is studied on a
compact Riemann surface of genus and area . The volume of the moduli
space is computed and found to depend on and , but not on other
details of the shape of the surface. The volume is then used to find the
thermodynamic partition function and it is shown that the thermodynamical
properties of such a gas do not depend on the genus of the Riemann surface.Comment: LaTex file, 17 pages. To appear in Comm. Math. Phy
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
Monopole Planets and Galaxies
Spherical clusters of SU(2) BPS monopoles are investigated here. A large
class of monopole solutions is found using an abelian approximation, where the
clusters are spherically symmetric, although exact solutions cannot have this
symmetry precisely. Monopole clusters generalise the Bolognesi magnetic bag
solution of the same charge, but they are always larger. Selected density
profiles give structures analogous to planets of uniform density, and galaxies
with a density decaying as the inverse square of the distance from the centre.
The Bolognesi bag itself has features analogous to a black hole, and this
analogy between monopole clusters and astrophysical objects with or without
black holes in their central region is developed further. It is also shown that
certain exact, platonic monopoles of small charge have sizes and other features
consistent with what is expected for magnetic bags.Comment: 23 pages. Revised version to appear in Physical Review D. New
introduction and conclusions; analogy between monopoles and astrophysical
objects developed furthe
Vortices and Jacobian varieties
We investigate the geometry of the moduli space of N-vortices on line bundles
over a closed Riemann surface of genus g > 1, in the little explored situation
where 1 =< N < g. In the regime where the area of the surface is just large
enough to accommodate N vortices (which we call the dissolving limit), we
describe the relation between the geometry of the moduli space and the complex
geometry of the Jacobian variety of the surface. For N = 1, we show that the
metric on the moduli space converges to a natural Bergman metric on the Riemann
surface. When N > 1, the vortex metric typically degenerates as the dissolving
limit is approached, the degeneration occurring precisely on the critical locus
of the Abel-Jacobi map at degree N. We describe consequences of this phenomenon
from the point of view of multivortex dynamics.Comment: 36 pages, 2 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
The interaction energy of well-separated Skyrme solitons
We prove that the asymptotic field of a Skyrme soliton of any degree has a
non-trivial multipole expansion. It follows that every Skyrme soliton has a
well-defined leading multipole moment. We derive an expression for the linear
interaction energy of well-separated Skyrme solitons in terms of their leading
multipole moments. This expression can always be made negative by suitable
rotations of one of the Skyrme solitons in space and iso-space.We show that the
linear interaction energy dominates for large separation if the orders of the
Skyrme solitons' multipole moments differ by at most two. In that case there
are therefore always attractive forces between the Skyrme solitons.Comment: 27 pages amslate
On the constraints defining BPS monopoles
We discuss the explicit formulation of the transcendental constraints
defining spectral curves of SU(2) BPS monopoles in the twistor approach of
Hitchin, following Ercolani and Sinha. We obtain an improved version of the
Ercolani-Sinha constraints, and show that the Corrigan-Goddard conditions for
constructing monopoles of arbitrary charge can be regarded as a special case of
these. As an application, we study the spectral curve of the tetrahedrally
symmetric 3-monopole, an example where the Corrigan-Goddard conditions need to
be modified. A particular 1-cycle on the spectral curve plays an important role
in our analysis.Comment: 29 pages, 7 eps figure
Angularly localized Skyrmions
Quantized Skyrmions with baryon numbers and 4 are considered and
angularly localized wavefunctions for them are found. By combining a few low
angular momentum states, one can construct a quantum state whose spatial
density is close to that of the classical Skyrmion, and has the same
symmetries. For the B=1 case we find the best localized wavefunction among
linear combinations of and angular momentum states. For B=2, we
find that the ground state has toroidal symmetry and a somewhat reduced
localization compared to the classical solution. For B=4, where the classical
Skyrmion has cubic symmetry, we construct cubically symmetric quantum states by
combining the ground state with the lowest rotationally excited
state. We use the rational map approximation to compare the classical and
quantum baryon densities in the B=2 and B=4 cases.Comment: 22 page
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