393,952 research outputs found
Holographic Reconstruction and Renormalization in Asymptotically Ricci-flat Spacetimes
In this work we elaborate on an extension of the AdS/CFT framework to a
subclass of gravitational theories with vanishing cosmological constant. By
building on earlier ideas, we construct a correspondence between Ricci-flat
spacetimes admitting asymptotically hyperbolic hypersurfaces and a family of
conformal field theories on a codimension two manifold at null infinity. By
truncating the gravity theory to the pure gravitational sector, we find the
most general spacetime asymptotics, renormalize the gravitational action,
reproduce the holographic stress tensors and Ward identities of the family of
CFTs and show how the asymptotics is mapped to and reconstructed from conformal
field theory data. In even dimensions, the holographic Weyl anomalies identify
the bulk time coordinate with the spectrum of central charges with
characteristic length the bulk Planck length. Consistency with locality in the
bulk time direction requires a notion of locality in this spectrum.Comment: 44 pages, 4 figures. v2: minor changes in section
Superconformal symmetry and two-loop amplitudes in planar N=4 super Yang-Mills
Scattering amplitudes in superconformal field theories do not enjoy this
symmetry, because the definition of asymptotic states involve a notion of
infinity. Concentrating on planar Yang-Mills, we consider a
generalization of scattering amplitudes which depends on twice as many
Grassmann variables. We conjecture that it restores at least half of the
superconformal symmetries, and all of the dual superconformal symmetries. The
object arises naturally as the dual of a null polygonal Wilson loop in an
superspace. We support the conjecture by using it to
obtain the total differential of all -point two-loop MHV amplitudes, and
showing that the result passes consistency checks. Potential all-loop
constraints are also discussed.Comment: 25 pages, 2 figures and 1 noteboo
Neighborhood radius estimation in Variable-neighborhood Random Fields
We consider random fields defined by finite-region conditional probabilities
depending on a neighborhood of the region which changes with the boundary
conditions. To predict the symbols within any finite region it is necessary to
inspect a random number of neighborhood symbols which might change according to
the value of them. In analogy to the one dimensional setting we call these
neighborhood symbols the context of the region. This framework is a natural
extension, to d-dimensional fields, of the notion of variable-length Markov
chains introduced by Rissanen (1983) in his classical paper. We define an
algorithm to estimate the radius of the smallest ball containing the context
based on a realization of the field. We prove the consistency of this
estimator. Our proofs are constructive and yield explicit upper bounds for the
probability of wrong estimation of the radius of the context
A note on the non-commutative Chern-Simons model on manifolds with boundary
We study field theories defined in regions of the spatial non-commutative
(NC) plane with a boundary present delimiting them, concentrating in particular
on the U(1) NC Chern-Simons theory on the upper half plane. We find that
classical consistency and gauge invariance lead necessary to the introduction
of -space of square integrable functions null together with all their
derivatives at the origin. Furthermore the requirement of closure of
under the *-product leads to the introduction of a novel notion of the
*-product itself in regions where a boundary is present, that in turn yields
the complexification of the gauge group and to consider chiral waves in one
sense or other. The canonical quantization of the theory is sketched
identifying the physical states and the physical operators. These last ones
include ordinary NC Wilson lines starting and ending on the boundary that yield
correlation functions depending on points on the one-dimensional boundary. We
finally extend the definition of the *-product to a strip and comment on
possible relevance of these results to finite Quantum Hall systems.Comment: 15 pages, references added, to appear in International Journal of
Modern Physic
Can the Discourse on ĂSoft PowerĂ Help the EU to Bridge its Capability-Expectations Gap?
Recently, a new buzz word has appeared in official speeches in the field of the European UnionĂs external relations: ĂSoft powerĂ. The notion was first coined for American foreign policy and is now at the heart of EU foreign policy discourses, especially the European Neighbourhood Policy (ENP). The ENP launched in 2003 for the new EU neighbours draws heavily on the experience of the past enlargements by exporting internal norms, values and policies abroad. The article explores the hypothesis that the discourse on Ăsoft powerĂ represents an attempt to go beyond a traditional understanding of foreign policy and of conditionality. By developing its own definition of Ăsoft powerĂ, the EU tries to position itself on the international stage by preferring civilian over coercive means and thus seeks to increase the ENPĂs legitimacy through attraction instead of accession. Nevertheless, it will need to improve its internal consistency if it wants to avoid serious criticism of the ENP and bridge its famous capability-expectations gap.European Neighbourhood Policy, soft power, capability-expectations gap
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