595 research outputs found
Optimal Sobolev type inequalities in Lorentz spaces
It is well known that the classical Sobolev embeddings may be improved within the framework of Lorentz spaces L p,q : the space D 1,p (R n ) , 1\u2009<\u2009p\u2009<\u2009n, embeds into L p 17 ,q (R n ) , p\u2009 64\u2009q\u2009 64\u2009 1e. However, the value of the best possible embedding constants in the corresponding inequalities is known just in the case L p 17 ,p (R n ) . Here, we determine optimal constants for the embedding of the space D 1,p (R n ) , 1\u2009<\u2009p\u2009<\u2009n, into the whole Lorentz space scale L p 17 ,q (R n ) , p\u2009 64\u2009q\u2009 64\u2009 1e, including the limiting case q\u2009=\u2009p of which we give a new proof. We also exhibit extremal functions for these embedding inequalities by solving related elliptic problems
Holographic renormalization and supersymmetry
Holographic renormalization is a systematic procedure for regulating divergences
in observables in asymptotically locally AdS spacetimes. For dual boundary
field theories which are supersymmetric it is natural to ask whether this defines a
supersymmetric renormalization scheme. Recent results in localization have brought
this question into sharp focus: rigid supersymmetry on a curved boundary requires
specific geometric structures, and general arguments imply that BPS observables,
such as the partition function, are invariant under certain deformations of these
structures. One can then ask if the dual holographic observables are similarly invariant.
We study this question in minimal N = 2 gauged supergravity in four and
five dimensions. In four dimensions we show that holographic renormalization precisely
reproduces the expected field theory results. In five dimensions we find that
no choice of standard holographic counterterms is compatible with supersymmetry,
which leads us to introduce novel finite boundary terms. For a class of solutions satisfying
certain topological assumptions we provide some independent tests of these
new boundary terms, in particular showing that they reproduce the expected VEVs
of conserved charges
Holographic renormalization and supersymmetry
Holographic renormalization is a systematic procedure for regulating
divergences in observables in asymptotically locally AdS spacetimes. For dual
boundary field theories which are supersymmetric it is natural to ask whether
this defines a supersymmetric renormalization scheme. Recent results in
localization have brought this question into sharp focus: rigid supersymmetry
on a curved boundary requires specific geometric structures, and general
arguments imply that BPS observables, such as the partition function, are
invariant under certain deformations of these structures. One can then ask if
the dual holographic observables are similarly invariant. We study this
question in minimal N = 2 gauged supergravity in four and five dimensions. In
four dimensions we show that holographic renormalization precisely reproduces
the expected field theory results. In five dimensions we find that no choice of
standard holographic counterterms is compatible with supersymmetry, which leads
us to introduce novel finite boundary terms. For a class of solutions
satisfying certain topological assumptions we provide some independent tests of
these new boundary terms, in particular showing that they reproduce the
expected VEVs of conserved charges.Comment: 70 pages; corrected typo
de Sitter Supersymmetry Revisited
We present the basic superconformal field theories in
four-dimensional de Sitter space-time, namely the non-abelian super Yang-Mills
theory and the chiral multiplet theory with gauge interactions or cubic
superpotential. These theories have eight supercharges and are invariant under
the full group of conformal symmetries, which includes the de Sitter
isometry group as a subgroup. The theories are ghost-free and the
anti-commutator is positive. SUSY
Ward identities uniquely select the Bunch-Davies vacuum state. This vacuum
state is invariant under superconformal transformations, despite the fact that
de Sitter space has non-zero Hawking temperature. The theories
are classically invariant under the superconformal group, but this
symmetry is broken by radiative corrections. However, no such difficulty is
expected in the theory, which is presented in appendix B.Comment: 21 pages, 2 figure
Gold nanoparticles supported on functionalized silica as catalysts for alkyne hydroamination: A chemico-physical insight
Highly stable gold nanoparticles anchored on propynylcarbamate-functionalized silica (Au/SiO2@Yne) have been efficiently utilized for the heterogeneous hydroamination of phenylacetylene with aniline under different reaction conditions. In order to ascertain the eventual influence of surface silanol groups on the system activity and selectivity tailored modifications of Au/SiO2@Yne catalysts were pursued according to two different strategies, involving respectively functionalization with trimethylethoxysilane (Au/SiO2@Yne-TMS) or post-treatment with triethylamine (Au/SiO2@Yne-NEt3). The prepared materials were analysed by several complementary techniques such as Solid State NMR (SS NMR), Transmission Electron Microscopy (TEM), X-ray Photoelectron Spectroscopy (XPS), X-ray Diffraction (XRD). A comparison of the resulting catalytic activities with that of the pristine Au/SiO2@Yne revealed a significant improvement for Au/SiO2@Yne-NEt3 in terms of both conversion and selectivity. Recycling and stability studies showed a catalytic activity decrease after the first run, due to the formation of polyphenylacetylene (PPhA) oligomers shielding the active sites. PPhA removal by sonication in acetone fully restored the catalytic activity and empowered the system with a good operational stability, a very crucial issue in view of eventual practical applications
On BPS bounds in D=4 N=2 gauged supergravity II: general matter couplings and black hole masses
We continue the analysis of BPS bounds started in arXiv:1110.2688, extending
it to the full class of N=2 gauged supergravity theories with arbitrary vector
and hypermultiplets. We derive the general form of the asymptotic charges for
asymptotically flat (M_4), anti-de Sitter (AdS_4), and magnetic anti-de Sitter
(mAdS_4) spacetimes. Some particular examples from black hole physics are given
to explicitly demonstrate how AdS and mAdS masses differ when solutions with
non-trivial scalar profiles are considered.Comment: 21 pages; v2 added reference, published version; v3 minor correction
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