1,168 research outputs found
A Skyrme lattice with hexagonal symmetry
Recently it has been found that the structure of Skyrmions has a close
analogy to that of fullerene shells in carbon chemistry. In this letter we show
that this analogy continues further, by presenting a Skyrme field that
describes a lattice of Skyrmions with hexagonal symmetry. This configuration, a
novel `domain wall' in the Skyrme model, has low energy per baryon (about 6%
above the Faddeev-Bogomolny bound) and in many ways is analogous to graphite.
By comparison to the energy per baryon of other known Skyrmions and also the
Skyrme crystal, we discuss the possibility of finding Skyrmion shells of higher
charge.Comment: 12 pages, 1 figure. To appear in Phys. Lett.
Monopoles and Harmonic Maps
Recently Jarvis has proved a correspondence between SU(N) monopoles and
rational maps of the Riemann sphere into flag manifolds. Furthermore, he has
outlined a construction to obtain the monopole fields from the rational map. In
this paper we examine this construction in some detail and provide explicit
examples for spherically symmetric SU(N) monopoles with various symmetry
breakings. In particular we show how to obtain these monopoles from harmonic
maps into complex projective spaces. The approach extends in a natural way to
monopoles in hyperbolic space and we use it to construct new spherically
symmetric SU(N) hyperbolic monopoles.Comment: Version to appear in J. Math. Phy
Non-BPS String Junctions and Dyons in N=4 Super-Yang-Mills
We construct non-BPS dyon solutions of N=4 SU(n) supersymmetric Yang-Mills
theory. These solutions are the worldvolume solitons which describe non-BPS
Type IIB non-planar string junctions connecting n parallel D3-branes. The
solutions are smooth deformations of the 1/4 BPS states which describe planar
string junctions.Comment: 10 pages plus 3 figure
SU(N) Monopoles and Platonic Symmetry
We discuss the ADHMN construction for SU(N) monopoles and show that a
particular simplification arises in studying charge N-1 monopoles with minimal
symmetry breaking. Using this we construct families of tetrahedrally symmetric
SU(4) and SU(5) monopoles. In the moduli space approximation, the SU(4)
one-parameter family describes a novel dynamics where the monopoles never
separate, but rather, a tetrahedron deforms to its dual. We find a
two-parameter family of SU(5) tetrahedral monopoles and compute some geodesics
in this submanifold numerically. The dynamics is rich, with the monopoles
scattering either once or twice through octahedrally symmetric configurations.Comment: 14pp, RevTex, two figures made of six Postscript files. To appear in
the Journal of Mathematical Physic
Octahedral and Dodecahedral Monopoles
It is shown that there exists a charge five monopole with octahedral symmetry
and a charge seven monopole with icosahedral symmetry. A numerical
implementation of the ADHMN construction is used to calculate the energy
density of these monopoles and surfaces of constant energy density are
displayed. The charge five and charge seven monopoles look like an octahedron
and a dodecahedron respectively. A scattering geodesic for each of these
monopoles is presented and discussed using rational maps. This is done with the
aid of a new formula for the cluster decomposition of monopoles when the poles
of the rational map are close together.Comment: uuencoded latex, 20 pages, 2 figures To appear in Nonlinearit
Non-Bogomolny SU(N) BPS Monopoles
For N>2 we present static monopole solutions of the second order SU(N) BPS
Yang-Mills-Higgs equations which are not solutions of the first order Bogomolny
equations. These spherically symmetric solutions may be interpreted as monopole
anti-monopole configurations and their construction involves harmonic maps into
complex projective spaces.Comment: 14 pages, 1 figur
Rational Maps, Monopoles and Skyrmions
We discuss the similarities between BPS monopoles and Skyrmions, and point to
an underlying connection in terms of rational maps between Riemann spheres.
This involves the introduction of a new ansatz for Skyrme fields. We use this
to construct good approximations to several known Skyrmions, including all the
minimal energy configurations up to baryon number nine, and some new solutions
such as a baryon number seventeen Skyrme field with the truncated icosahedron
structure of a buckyball.
The new approach is also used to understand the low-lying vibrational modes
of Skyrmions, which are required for quantization. Along the way we discover an
interesting Morse function on the space of rational maps which may be of use in
understanding the Sen forms on the monopole moduli spaces.Comment: 35pp including four figures, typos corrected, appearing in Nuclear
Physics
Monopoles from Rational Maps
The moduli space of charge k SU(2) BPS monopoles is diffeomorphic to the
moduli space of degree k rational maps between Riemann spheres. In this note we
describe a numerical algorithm to compute the monopole fields and energy
density from the rational map. The results for some symmetric examples are
presented.Comment: 8 pages, 2 figures. To appear in Phys. Lett.
Non-BPS Dirac-Born-Infeld Solitons
We show that CPn sigma model solitons solve the field equations of a
Dirac-Born-Infeld (DBI) action and, furthermore, we prove that the non-BPS
soliton/anti-soliton solutions of the sigma model also solve the DBI equations.
Using the moduli space approximation we compare the dynamics of the BPS sigma
model solitons with that of the associated DBI solitons. We find that for the
CP1 case the metric on the moduli space of sigma model solitons is identical to
that of the moduli space of DBI solitons, but for CPn with n>1 we show that the
two metrics are not equal. We also consider the possibility of similar non-BPS
solitons in other DBI theories.Comment: Major changes; sections removed and title changed. Version published
in JHE
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