12,072 research outputs found
A complete family of separability criteria
We introduce a new family of separability criteria that are based on the
existence of extensions of a bipartite quantum state to a larger number
of parties satisfying certain symmetry properties. It can be easily shown that
all separable states have the required extensions, so the non-existence of such
an extension for a particular state implies that the state is entangled. One of
the main advantages of this approach is that searching for the extension can be
cast as a convex optimization problem known as a semidefinite program (SDP).
Whenever an extension does not exist, the dual optimization constructs an
explicit entanglement witness for the particular state. These separability
tests can be ordered in a hierarchical structure whose first step corresponds
to the well-known Positive Partial Transpose (Peres-Horodecki) criterion, and
each test in the hierarchy is at least as powerful as the preceding one. This
hierarchy is complete, in the sense that any entangled state is guaranteed to
fail a test at some finite point in the hierarchy, thus showing it is
entangled. The entanglement witnesses corresponding to each step of the
hierarchy have well-defined and very interesting algebraic properties that in
turn allow for a characterization of the interior of the set of positive maps.
Coupled with some recent results on the computational complexity of the
separability problem, which has been shown to be NP-hard, this hierarchy of
tests gives a complete and also computationally and theoretically appealing
characterization of mixed bipartite entangled states.Comment: 21 pages. Expanded introduction. References added, typos corrected.
Accepted for publication in Physical Review
A Brane World Perspective on the Cosmological Constant and the Hierarchy Problems
We elaborate on the recently proposed static brane world scenario, where the
effective 4-D cosmological constant is exponentially small when parallel
3-branes are far apart. We extend this result to a compactified model with two
positive tension branes. Besides an exponentially small effective 4-D
cosmological constant, this model incorporates a Randall-Sundrum-like solution
to the hierarchy problem. Furthermore, the exponential factors for the
hierarchy problem and the cosmological constant problem obey an inequality that
is satisfied in nature. This inequality implies that the cosmological constant
problem can be explained if the hierarchy problem is understood. The basic idea
generalizes to the multibrane world scenario. We discuss models with piecewise
adjustable bulk cosmological constants (to be determined by the 5-dimensional
Einstein equation), a key element of the scenario. We also discuss the global
structure of this scenario and clarify the physical properties of the particle
(Rindler) horizons that are present. Finally, we derive a 4-D effective theory
in which all observers on all branes not separated by particle horizons measure
the same Newton's constant and 4-D cosmological constant.Comment: revtex, 63 pages, 8 figures, one table, revised version, more
discussions on the global structure, references adde
Convex cocompactness and stability in mapping class groups
We introduce a strong notion of quasiconvexity in finitely generated groups,
which we call stability. Stability agrees with quasiconvexity in hyperbolic
groups and is preserved under quasi-isometry for finitely generated groups. We
show that the stable subgroups of mapping class groups are precisely the convex
cocompact subgroups. This generalizes a well-known result of Behrstock and is
related to questions asked by Farb-Mosher and Farb.Comment: 15 pages, 1 figur
Lectures on walking technicolor, holography and gauge/gravity dualities
Dynamical electro-weak symmetry breaking is an appealing, strongly-coupled
alternative to the weakly-coupled models based on an elementary scalar field
developing a vacuum expectation value. In the first two sections of this set of
lectures, I summarize the arguments, based on low-energy phenomenology,
supporting walking technicolor as a realistic realization of this idea. This
pedagogical introduction to walking technicolor, and more generally to the
physics of extensions of the standard model, makes extensive use of effective
field theory arguments, symmetries and counting rules. The strongly-coupled
nature of the underlying interactions, and the peculiar quasi-conformal
behavior of the theory, require to use non-perturbative methods in order to
address many fundamental questions within this framework. The recent
development of gauge/gravity dualities provides an ideal set of such
non-perturbative instruments. The remaining two sections illustrate the
potential of these techniques with two technical examples, one within the
bottom-up phenomenological approach to holography in five-dimensions, the other
within a more systematic top-down construction derived from ten-dimensional
type-IIB supergravity.Comment: 67 pages, 16 figures
On the Integrability of Supersymmetric Versions of the Structural Equations for Conformally Parametrized Surfaces
The paper presents the bosonic and fermionic supersymmetric extensions of the
structural equations describing conformally parametrized surfaces immersed in a
Grasmann superspace, based on the authors' earlier results. A detailed analysis
of the symmetry properties of both the classical and supersymmetric versions of
the Gauss-Weingarten equations is performed. A supersymmetric generalization of
the conjecture establishing the necessary conditions for a system to be
integrable in the sense of soliton theory is formulated and illustrated by the
examples of supersymmetric versions of the sine-Gordon equation and the
Gauss-Codazzi equations
The Big Constant Out, The Small Constant In
Some time ago, Tseytlin has made an original and unusual proposal for an
action that eliminates an arbitrary cosmological constant. The form of the
proposed action, however, is strongly modified by gravity loop effects, ruining
its benefit. Here I discuss an embedding of Tseytlin's action into a broader
context, that enables to control the loop effects. The broader context is
another universe, with its own metric and dynamics, but only globally connected
to ours. One possible Lagrangian for the other universe is that of unbroken AdS
supergravity. A vacuum energy in our universe does not produce any curvature
for us, but instead increases or decreases the AdS curvature in the other
universe. I comment on how to introduce the accelerated expansion in this
framework in a technically natural way, and consider the case where this is
done by the self-accelerated solutions of massive gravity and its extensions.Comment: 14 pages; a brief paragraph unfolded; 3 refs added; minor
improvement
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