317 research outputs found
Holographic Chern-Simons Theories
Chern-Simons theories in three dimensions are topological field theories that
may have a holographic interpretation for suitable chosen gauge groups and
boundary conditions on the fields. Conformal Chern-Simons gravity is a
topological model of 3-dimensional gravity that exhibits Weyl invariance and
allows various holographic descriptions, including Anti-de Sitter, Lobachevsky
and flat space holography. The same model also allows to address some aspects
that arise in higher spin gravity in a considerably simplified setup, since
both types of models have gauge symmetries other than diffeomorphisms. In these
lectures we summarize briefly recent results.Comment: 20 pp, invited lectures prepared for the 7th Aegean Summer School
"Beyond Einstein's Theory of Gravity", 201
About maximally localized states in quantum mechanics
We analyze the emergence of a minimal length for a large class of generalized
commutation relations, preserving commutation of the position operators and
translation invariance as well as rotation invariance (in dimension higher than
one). We show that the construction of the maximally localized states based on
squeezed states generally fails. Rather, one must resort to a constrained
variational principle.Comment: accepted for publication in PR
The Fuzzy Sphere: From The Uncertainty Relation To The Stereographic Projection
On the fuzzy sphere, no state saturates simultaneously all the Heisenberg
uncertainties. We propose a weaker uncertainty for which this holds. The family
of states so obtained is physically motivated because it encodes information
about positions in this fuzzy context. In particular, these states realize in a
natural way a deformation of the stereographic projection. Surprisingly, in the
large limit, they reproduce some properties of the ordinary coherent states
on the non commutative plane.Comment: 18 pages, Latex. Minor changes in notations. Version to appear in
JHE
A study on PDC drill bits quality
The quality of innovating PDC (Polycrystalline Diamond Compact) bits materials needs to be determined with accuracy by measuring cutting efficiency and wear rate, both related to the overall mechanical properties. An original approach is developed to encompass cutting efficiency and wear contribution to the overall sample quality. Therefore, a lathe-type test device was used to abrade specific samples from various manufacturers. Post-experiment analyzes are based on models establishing coupled relationships between cutting and friction stresses related to the drag bits excavation mechanism. These models are implemented in order to evaluate cutting efficiency and to estimate wear of the diamond insert. Phase analysis by XRD and finite element simulations were performed to explain the role of physicochemical parameters on the calculated quality factor values. Four main properties of PDC material were studied to explain quality results obtained in this study: cobalt content in samples that characterizes hardness/fracture toughness compromise, undesired phase as tungsten carbide weakening diamond structure, diamond grains sizes and residual stresses distribution affecting abrasion resistance
Three-dimensional black holes from deformed anti-de Sitter
We present new exact three-dimensional black-string backgrounds, which
contain both NS--NS and electromagnetic fields, and generalize the BTZ black
holes and the black string studied by Horne and Horowitz. They are obtained as
deformations of the Sl(2,R) WZW model. Black holes resulting from purely
continuous deformations possess true curvature singularities. When discrete
identifications are introduced, extra chronological singularities appear, which
under certain circumstances turn out to be naked. The backgrounds at hand
appear in the moduli space of the Sl(2,R) WZW model. Hence, they provide exact
string backgrounds and allow for a more algebraical CFT description. This makes
possible the determination of the spectrum of primaries.Comment: JHEP style, 33 pages, 1 figur
The Spectrum of Strings on Warped AdS_3 x S^3
String theory on NS-NS AdS_3 x S^3 admits an exactly marginal deformation
which breaks the SL(2,R)_R x SL(2,R)_L isometry of AdS_3 down to SL(2,R)_R x
U(1)_L. The holographic dual is an exotic and only partially understood type of
two-dimensional CFT with a reduced unbroken global conformal symmetry group. In
this paper we study the deformed theory on the string worldsheet. It is found
to be related by a spectral flow which is nonlocal in spacetime to the
undeformed worldsheet theory. An exact formula for the spectrum of massive
strings is presented.Comment: 26 pages, no figure
Existence of solutions for a higher order non-local equation appearing in crack dynamics
In this paper, we prove the existence of non-negative solutions for a
non-local higher order degenerate parabolic equation arising in the modeling of
hydraulic fractures. The equation is similar to the well-known thin film
equation, but the Laplace operator is replaced by a Dirichlet-to-Neumann
operator, corresponding to the square root of the Laplace operator on a bounded
domain with Neumann boundary conditions (which can also be defined using the
periodic Hilbert transform). In our study, we have to deal with the usual
difficulty associated to higher order equations (e.g. lack of maximum
principle). However, there are important differences with, for instance, the
thin film equation: First, our equation is nonlocal; Also the natural energy
estimate is not as good as in the case of the thin film equation, and does not
yields, for instance, boundedness and continuity of the solutions (our case is
critical in dimension in that respect)
Generalized instantons in N = 4 super Yang-Mills theory and spinorial geometry
Using spinorial geometry techniques, we classify the supersymmetric solutions
of euclidean super Yang-Mills theory. These backgrounds represent
generalizations of instantons with nontrivial scalar fields turned on, and
satisfy some constraints that bear a similarity with the Hitchin equations, and
contain the Donaldson equations as a special subcase. It turns out that these
constraints can be obtained by dimensional reduction of the octonionic
instanton equations, and may be rephrased in terms of a selfduality-like
condition for a complex connection. We also show that the supersymmetry
conditions imply the equations of motion only partially.Comment: 29 pages, 3 tables. v2: references added. v3: conclusion extended,
version published in JHE
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