43,863 research outputs found
Exact self-duality in a modified Skyrme model
We propose a modification of the Skyrme model that supports a self-dual
sector possessing exact non-trivial finite energy solutions. The action of such
a theory possesses the usual quadratic and quartic terms in field derivatives,
but the couplings of the components of the Maurer-Cartan form of the Skyrme
model is made by a non-constant symmetric matrix, instead of the usual Killing
form of the SU(2) Lie algebra. The introduction of such a matrix make the
self-duality equations conformally invariant in three space dimensions, even
though it may break the global internal symmetries of the original Skyrme
model. For the case where that matrix is proportional to the identity we show
that the theory possesses exact self-dual Skyrmions of unity topological
charges.Comment: 12 pages, no figure
Hopf solitons and area preserving diffeomorphisms of the sphere
We consider a (3+1)-dimensional local field theory defined on the sphere. The
model possesses exact soliton solutions with non trivial Hopf topological
charges, and infinite number of local conserved currents. We show that the
Poisson bracket algebra of the corresponding charges is isomorphic to that of
the area preserving diffeomorphisms of the sphere. We also show that the
conserved currents under consideration are the Noether currents associated to
the invariance of the Lagrangian under that infinite group of diffeomorphisms.
We indicate possible generalizations of the model.Comment: 6 pages, LaTe
Exact Self-Dual Skyrmions
We introduce a Skyrme type model with the target space being the 3-sphere S^3
and with an action possessing, as usual, quadratic and quartic terms in field
derivatives. The novel character of the model is that the strength of the
couplings of those two terms are allowed to depend upon the space-time
coordinates. The model should therefore be interpreted as an effective theory,
such that those couplings correspond in fact to low energy expectation values
of fields belonging to a more fundamental theory at high energies. The theory
possesses a self-dual sector that saturates the Bogomolny bound leading to an
energy depending linearly on the topological charge. The self-duality equations
are conformally invariant in three space dimensions leading to a toroidal
ansatz and exact self-dual Skyrmion solutions. Those solutions are labelled by
two integers and, despite their toroidal character, the energy density is
spherically symmetric when those integers are equal and oblate or prolate
otherwise.Comment: 14 pages, 3 figures, a reference adde
Self-dual Hopfions
We construct static and time-dependent exact soliton solutions with
non-trivial Hopf topological charge for a field theory in 3+1 dimensions with
the target space being the two dimensional sphere S**2. The model considered is
a reduction of the so-called extended Skyrme-Faddeev theory by the removal of
the quadratic term in derivatives of the fields. The solutions are constructed
using an ansatz based on the conformal and target space symmetries. The
solutions are said self-dual because they solve first order differential
equations which together with some conditions on the coupling constants, imply
the second order equations of motion. The solutions belong to a sub-sector of
the theory with an infinite number of local conserved currents. The equation
for the profile function of the ansatz corresponds to the Bogomolny equation
for the sine-Gordon model.Comment: plain latex, no figures, 23 page
On the connections between Skyrme and Yang Mills theories
Skyrme theories on S^3 and S^2, are analyzed using the generalized zero
curvature in any dimensions. In the first case, new symmetries and integrable
sectors, including the B =1 skyrmions, are unraveled. In S^2 the relation to
QCD suggested by Faddeev is discussedComment: Talk at the Workshop on integrable theories, solitons and duality.
IFT Sao Paulo July 200
Exact static soliton solutions of 3+1 dimensional integrable theory with nonzero Hopf numbers
In this paper we construct explicitly an infinite number of Hopfions (static,
soliton solutions with non-zero Hopf topological charges) within the recently
proposed 3+1-dimensional, integrable and relativistically invariant field
theory. Two integers label the family of Hopfions we have found. Their product
is equal to the Hopf charge which provides a lower bound to the soliton's
finite energy. The Hopfions are constructed explicitly in terms of the toroidal
coordinates and shown to have a form of linked closed vortices.Comment: LaTeX, 7 pg
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