4,956 research outputs found
Self-similarity of complex networks and hidden metric spaces
We demonstrate that the self-similarity of some scale-free networks with respect to a simple degree-thresholding renormalization scheme finds a natural interpretation in the assumption that network nodes exist in hidden metric spaces. Clustering, i.e., cycles of length three, plays a crucial role in this framework as a topological reflection of the triangle inequality in the hidden geometry. We prove that a class of hidden variable models with underlying metric spaces are able to accurately reproduce the self-similarity properties that we measured in the real networks. Our findings indicate that hidden geometries underlying these real networks are a plausible explanation for their observed topologies and, in particular, for their self-similarity with respect to the degree-based renormalization
Self-stabilization of extra dimensions
We show that the problem of stabilization of extra dimensions in Kaluza-Klein
type cosmology may be solved in a theory of gravity involving high-order
curvature invariants. The method suggested (employing a slow-change
approximation) can work with rather a general form of the gravitational action.
As examples, we consider pure gravity with Lagrangians quadratic and cubic in
the scalar curvature and some more complex ones in a simple Kaluza-Klein
framework. After a transition to the 4D Einstein conformal frame, this results
in effective scalar field theories with certain effective potentials, which in
many cases possess positive minima providing stable small-size extra
dimensions. Estimates made in the original (Jordan) conformal frame show that
the problem of a small value of the cosmological constant in the present
Universe is softened in this framework but is not solved completely.}Comment: 10 pages, 4 figures, revtex4. Version with additions and corrections,
accepted at Phys. Rev.
Five--Branes and Supersymmetry Breaking in M--Theory
Supersymmetry breaking via gaugino condensation is studied in vacua of
heterotic M-theory with five-branes. We show that supersymmetry is still broken
by a global mechanism and that the non-perturbative superpotential takes the
standard form. When expressed in terms of low energy fields, a modification
arises due to a threshold correction in the gauge kinetic function that depends
on five-brane moduli. We also determine the form of the low energy matter field
Kahler potential. These results are used to discuss the soft supersymmetry
breaking parameters, in particular the question of universality.Comment: 28 pages, Late
Chern-Simons Vortices in Supergravity
We study supersymmetric vortex solutions in three-dimensional abelian gauged
supergravity. First, we construct the general U(1)-gauged D=3, N=2 supergravity
whose scalar sector is an arbitrary Kahler manifold with U(1) isometry. This
construction clarifies the connection between local supersymmetry and the
specific forms of some scalar potentials previously found in the literature --
in particular, it provides the locally supersymmetric embedding of the abelian
Chern-Simons Higgs model. We show that the Killing spinor equations admit
rotationally symmetric vortex solutions with asymptotically conical geometry
which preserve half of the supersymmetry.Comment: 26 pages, LaTeX2
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