106 research outputs found
Metastable supersymmetry breaking without scales
We construct new examples of models of metastable D=4 N=1 supersymmetry
breaking in which all scales are generated dynamically. Our models rely on
Seiberg duality and on the ISS mechanism of supersymmetry breaking in massive
SQCD. Some of the electric quark superfields arise as composites of a strongly
coupled gauge sector. This allows us to start with a simple cubic
superpotential and an asymptotically free gauge group in the ultraviolet, and
end up with an infrared effective theory which breaks supersymmetry dynamically
in a metastable state.Comment: 6 pages, 1 figure; v2: journal versio
Index theory for heteroclinic orbits of Hamiltonian systems
Index theory revealed its outstanding role in the study of periodic orbits of
Hamiltonian systems and the dynamical consequences of this theory are enormous.
Although the index theory in the periodic case is well-established, very few
results are known in the case of homoclinic orbits of Hamiltonian systems.
Moreover, to the authors' knowledge, no results have been yet proved in the
case of heteroclinic and halfclinic (i.e. parametrised by a half-line) orbits.
Motivated by the importance played by these motions in understanding several
challenging problems in Classical Mechanics, we develop a new index theory and
we prove at once a general spectral flow formula for heteroclinic, homoclinic
and halfclinic trajectories. Finally we show how this index theory can be used
to recover all the (classical) existing results on orbits parametrised by
bounded intervals.Comment: 24 pages, 4 figure
On the dihedral n-body problem
Consider n=2l>=4 point particles with equal masses in space, subject to the
following symmetry constraint: at each instant they form an orbit of the
dihedral group D_l, where D_l is the group of order 2l generated by two
rotations of angle pi around two secant lines in space meeting at an angle of
pi/l. By adding a homogeneous gravitational (Newtonian) potential one finds a
special -body problem with three degrees of freedom, which is a kind of
generalisation of Devaney isosceles problem, in which all orbits have zero
angular momentum. In the paper we find all the central configurations and we
compute the dimension of the stable/unstable manifolds.Comment: Second version. In the first there was a mistake in a proof: some
section had been omitte
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