2,203 research outputs found
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
Calogero-Moser Models V: Supersymmetry and Quantum Lax Pair
It is shown that the Calogero-Moser models based on all root systems of the
finite reflection groups (both the crystallographic and non-crystallographic
cases) with the rational (with/without a harmonic confining potential),
trigonometric and hyperbolic potentials can be simply supersymmetrised in terms
of superpotentials. There is a universal formula for the supersymmetric ground
state wavefunction. Since the bosonic part of each supersymmetric model is the
usual quantum Calogero-Moser model, this gives a universal formula for its
ground state wavefunction and energy, which is determined purely algebraically.
Quantum Lax pair operators and conserved quantities for all the above
Calogero-Moser models are established.Comment: LaTeX2e, 31 pages, no figure
Thermodynamics of Vortices in the Plane
The thermodynamics of vortices in the critically coupled abelian Higgs model,
defined on the plane, are investigated by placing vortices in a region of
the plane with periodic boundary conditions: a torus. It is noted that the
moduli space for vortices, which is the same as that of
indistinguishable points on a torus, fibrates into a bundle over the
Jacobi manifold of the torus. The volume of the moduli space is a product of
the area of the base of this bundle and the volume of the fibre. These two
values are determined by considering two 2-surfaces in the bundle corresponding
to a rigid motion of a vortex configuration, and a motion around a fixed centre
of mass. The partition function for the vortices is proportional to the volume
of the moduli space, and the equation of state for the vortices is in the thermodynamic limit, where is the pressure, the area of
the region of the plane occupied by the vortices, and the temperature.
There is no phase transition.Comment: 17 pages, DAMTP 93-3
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
Skyrmions, Rational Maps & Scaling Identities
Starting from approximate Skyrmion solutions obtained using the rational map
ansatz, improved approximate Skyrmions are constructed using scaling arguments.
Although the energy improvement is small, the change of shape clarifies whether
the true Skyrmions are more oblate or prolate.Comment: 13 pages, 3 figure
New results on twinlike models
In this work we study the presence of kinks in models described by a single
real scalar field in bidimensional spacetime. We work within the first-order
framework, and we show how to write first-order differential equations that
solve the equations of motion. The first-order equations strongly simplify the
study of linear stability, which is implemented on general grounds. They also
lead to a direct investigation of twinlike theories, which is used to introduce
a family of models that support the same defect structure, with the very same
energy density and linear stability.Comment: 6 pages, 1 figur
The K\"ahler Potential of Abelian Higgs Vortices
We calculate the K\"ahler potential for the Samols metric on the moduli space
of Abelian Higgs vortices on \mathbbm{R}^{2}, in two different ways. The
first uses a scaling argument. The second is related to the Polyakov conjecture
in Liouville field theory. The K\"ahler potential on the moduli space of
vortices on \mathbbm{H}^{2} is also derived, and we are led to a geometrical
reinterpretation of these vortices. Finally, we attempt to find the K\"ahler
potential for vortices on \mathbbm{R}^{2} in a third way by relating the
vortices to SU(2) Yang-Mills instantons on \mathbbm{R}^{2}\times S^{2}. This
approach does not give the correct result, and we offer a possible explanation
for this.Comment: 25 page
Reparametrising the Skyrme Model using the Lithium-6 Nucleus
The minimal energy B=6 solution of the Skyrme model is a static soliton with
symmetry. The symmetries of the solution imply that the quantum
numbers of the ground state are the same as those of the Lithium-6 nucleus.
This identification is considered further by obtaining expressions for the mean
charge radius and quadrupole moment, dependent only on the Skyrme model
parameters (a dimensionless constant) and (the pion decay
constant). The optimal values of these parameters have often been deliberated
upon, and we propose, for , changing them from those which are most
commonly accepted. We obtain specific values for these parameters for B=6, by
matching with properties of the Lithium-6 nucleus. We find further support for
the new values by reconsidering the -particle and deuteron as quantized
B=4 and B=2 Skyrmions.Comment: 18 page
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