45,067 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

### 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

### 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

### Tau-functions and Dressing Transformations for Zero-Curvature Affine Integrable Equations

The solutions of a large class of hierarchies of zero-curvature equations
that includes Toda and KdV type hierarchies are investigated. All these
hierarchies are constructed from affine (twisted or untwisted) Kac-Moody
algebras~$\ggg$. Their common feature is that they have some special ``vacuum
solutions'' corresponding to Lax operators lying in some abelian (up to the
central term) subalgebra of~$\ggg$; in some interesting cases such subalgebras
are of the Heisenberg type. Using the dressing transformation method, the
solutions in the orbit of those vacuum solutions are constructed in a uniform
way. Then, the generalized tau-functions for those hierarchies are defined as
an alternative set of variables corresponding to certain matrix elements
evaluated in the integrable highest-weight representations of~$\ggg$. Such
definition of tau-functions applies for any level of the representation, and it
is independent of its realization (vertex operator or not). The particular
important cases of generalized mKdV and KdV hierarchies as well as the abelian
and non abelian affine Toda theories are discussed in detail.Comment: 27 pages, plain Te

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