Solvay S.A. is a Belgian chemical company founded in 1863, with its head office in Neder-Over-Heembeek, Brussels, Belgium.In 2012, it realized 9.94 billion € in revenues, 1.66 billion € of REBITDA, 40% of its sales in emerging high-growth countries, 90% of its sales in markets where it is ranked among the top three manufacturers. With 117 sites, Solvay employs 29,400 people in 55 countries. Wikipedia.
Ferrari F.,Solvay Group
Nuclear Physics B | Year: 2014
Recently, a new approach to large N gauge theories, based on a generalization of the concept of D-brane probes to any gauge field theory, was proposed. In the present note, we compute the probe action in the one matrix model with a quartic potential. This allows to illustrate several non-trivial aspects of the construction in an exactly solvable set-up. One of our main goal is to test the bare bubble approximation. The approximate free energy found in this approximation, which can be derived from a back-of-an-envelope calculation, matches the exact result for all values of the 't Hooft coupling with a surprising accuracy. Another goal is to illustrate the remarkable properties of the equivariant partial gauge-fixing procedure, which is at the heart of the formalism. For this we use a general ξ-gauge to compute the brane action. The action depends on ξ in a very non-trivial way, yet we show explicitly that its critical value does not and coincides with twice the free energy, as required by general consistency. This is made possible by a phenomenon of ghost condensation and the spontaneous breaking of the equivariant BRST symmetry. © 2014 The Author.
Ferrari F.,Solvay Group
Nuclear Physics B | Year: 2014
Based on a generalization of the string theoretic concept of D-brane probe, we propose a new approach to large N gauge theories which makes the holographic properties manifest. For any gauge theory, we define from first principles an effective action for a fixed number of "probe" D-branes in the presence of N "background" D-branes on which the gauge theory lives. This effective action is shown to encode all the information about the large N gauge theory. The analysis of the planar diagram expansion which computes the effective action yields a simple and generic mechanism explaining the emergence of holographic space dimensions: the probe D-branes move in a higher dimensional dual holographic space-time. The construction yields a new perspective on the notion of bulk space-time locality and draws unexpected links with some aspects of the 't Hooft Abelian projection ideas. It also provides a new non-perturbative approximation scheme, able to capture both the weak and strong coupling regimes. We sketchily illustrate the basic ideas on a few examples, including the pure four dimensional Yang-Mills theory. © 2014 The Authors.
Redigolo D.,Solvay Group
Physical Review D - Particles, Fields, Gravitation and Cosmology | Year: 2012
We study the possibility of constructing Lorentz-violating supersymmetric quantum field theories under the assumption that these theories have to be described by Lagrangians which are renormalizable by weighted power counting. Our investigation starts from the observation that at high energies Lorentz-violation and the usual supersymmetry algebra are algebraically compatible. Demanding linearity of the supercharges, we see that the requirement of renormalizability drastically restricts the set of possible Lorentz-violating supersymmetric theories. In particular, in the case of supersymmetric gauge theories the weighted power counting has to coincide with the usual one and the only Lorentz-violating operators are introduced by some weighted constant c that explicitly appears in the supersymmetry algebra. This parameter does not renormalize and has to be very close to the speed of light at low energies in order to satisfy the strict experimental bounds on Lorentz violation. The only possible models with nontrivial Lorentz-violating operators involve neutral chiral superfields and do not have a gauge invariant extension. We conclude that, under the assumption that high-energy physics can be described by a Lorentz-violating extension of the standard model which is renormalizable by weighted power counting, the Lorentz fine tuning problem does not seem solvable by the requirement of supersymmetry. © 2012 American Physical Society.
Pera-Titus M.,CNRS Research on Catalysis and Environment in Lyon |
Pera-Titus M.,Solvay Group
Chemical Reviews | Year: 2014
CO2 capture, transport, and long-term storage or sequestration (CCS) is visualized as a promising strategy for mitigating CO2 emissions at short- and midterms, especially in stationary sources. In the case of precombustion CO2 capture, carbon-templated microporous silica and MFI membranes constitute the most mature materials for membrane design on the basis not only of the reproducibility of their synthesis protocols, but also of their narrow thickness down to the micrometer level. In the case of postcombustion CO2 capture, MFI membranes can find suitable applications for CO2/N2 separations driven by preferential CO2 adsorption. The presence of moderate Si/Al ratios in these materials provides a trade-off for preferential CO2 adsorption and moderate poisoning by moisture below a threshold value. Finally, in the case of CO2/CH4 separations, the SAPO-34 membranes prepared by Noble and Falconer can show potentials with a proven reproducibility of synthesis protocols.
Oblak B.,Solvay Group
Communications in Mathematical Physics | Year: 2015
Using the Frobenius formula, we evaluate characters associated with certain induced representations of the centrally extended BMS3 group. This computation involves a functional integral over a coadjoint orbit of the Virasoro group; a delta function localizes the integral to a single point, allowing us to obtain an exact result. The latter is independent of the specific form of the functional measure, and holds for all values of the BMS3 central charges and all values of the chosen mass and spin. It can also be recovered as a flat limit of Virasoro characters. © 2015, Springer-Verlag Berlin Heidelberg.