Structure constants of shs[λ][\lambda]: the deformed-oscillator point of view

We derive and spell out the structure constants of the $\mathbb{Z}_2$-graded algebra $\mathfrak{shs}[\lambda]\,$ by using deformed-oscillators techniques in $Aq(2;\nu)\,$, the universal enveloping algebra of the Wigner-deformed Heisenberg algebra in 2 dimensions. The use of Weyl ordering of the deformed oscillators is made throughout the paper, via the symbols of the operators and the corresponding associative, non-commutative star product. The deformed oscillator construction was used by Vasiliev in order to construct the higher spin algebras in three spacetime dimensions. We derive an expression for the structure constants of $\mathfrak{shs}[\lambda]\,$ and show that they must obey a recurrence relation as a consequence of the associativity of the star product. We solve this condition and show that the $\mathfrak{hs}[\lambda]\,$ structure constants are given by those postulated by Pope, Romans and Shen for the Lone Star product.Comment: 22 pages, no figures. Contribution to the proceedings of the workshop "About various kinds of interactions", 4-5 June 2015 at UMONS, in honour of Philippe Spindel; v2: references and comments on Moyal product added; v3: Expanded version of the proceedings, covering the fermionic sector of $Aq(2;\nu)$. 1+27 pages, no figure

A note about a pure spin-connection formulation of General Relativity and spin-2 duality in (A)dS

We investigate the problem of finding a pure spin-connection formulation of General Relativity with non-vanishing cosmological constant. We first revisit the problem at the linearised level and find that the pure spin-connection, quadratic Lagrangian, takes a form reminiscent to Weyl gravity, given by the square of a Weyl-like tensor. Upon Hodge dualisation, we show that the dual gauge field in (A)dS$_D$ transforms under $GL(D)$ in the same representation as a massive graviton in the flat spacetime of the same dimension. We give a detailed proof that the physical degrees of freedom indeed correspond to a massless graviton propagating around the (anti-) de Sitter background and finally speculate about a possible nonlinear pure-connection theory dual to General Relativity with cosmological constant.Comment: 21 page

Mixed-symmetry fields in de Sitter space: a group theoretical glance

We derive the characters of all unitary irreducible representations of the (d+1)-dimensional de Sitter spacetime isometry algebra so(1,d+1), and propose a dictionary between those representations and massive or (partially) massless fields on de Sitter spacetime. We propose a way of taking the flat limit of representations in (anti-) de Sitter spaces in terms of these characters, and conjecture the spectrum resulting from taking the flat limit of mixed-symmetry fields in de Sitter spacetime. We identify the equivalent of the scalar singleton for the de Sitter (dS) spacetime. © 2017, The Author(s)4511Nsciescopu

Elastomer Characterization Method for Trapped Rubber Processing

The increasing high-volume demand for polymer matrix composites (PMCs) brings into focus the need for autoclave alternative processing. Trapped rubber processing (TRP) of PMCs is a method capable of achieving high pressures during polymer matrix composite processing by utilizing thermally induced volume change of a nearly incompressible material inside a closed cavity mold. Recent advances in rubber materials and computational technology have made this processing technique more attractive. Elastomers can be doped with nanoparticles to increase thermal conductivity and this can be further tailored for local variations in thermal conductivity for TRP. In addition, recent advances in computer processing allow for simulation of coupled thermomechanical processes for full part modeling. This study presents a method of experimentally characterizing prospective rubber materials. The experiments are designed to characterize the dynamic in situ change in temperature, the dynamic change in volume, and the resulting real-time change in surface pressure. The material characterization is specifically designed to minimize the number and difficulty of experimental tests while fully capturing the rubber behavior for the TRP scenario. The experimental characterization was developed to provide the necessary data for accurate thermomechanical material models of nearly incompressible elastomeric polymers for use in TRP virtual design and optimization

Flato-Fronsdal theorem for higher-order singletons

We prove a generalised Flato-Fronsdal theorem for higher-order, scalar and spinor, singletons. In the resulting infinite tower of bulk higher-spin fields, we point out the occurrence of partially-massless fields of all depths. This leads us to conjecture a holographic duality between a higher-spin gravity theory around $AdS_{d+1}$ with the aforementioned spectrum of fields, and a free $CFT_d$ of fundamental (higher-order) scalar and spinor singletons. As a first check of this conjecture, we find that the total Casimir energy vanishes at one loop.Comment: 19 pages, no figure

General solutions of the Wess-Zumino consistency condition for the Weyl anomalies

The general solutions of the Wess-Zumino consistency condition for the conformal (or Weyl, or trace) anomalies are derived. The solutions are obtained, in arbitrary dimensions, by explicitly computing the cohomology of the corresponding Becchi-Rouet-Stora-Tyutin differential in the space of integrated local functions at ghost number unity. This provides a purely algebraic, regularization-independent classification of the Weyl anomalies in arbitrary dimensions. The so-called type-A anomaly is shown to satisfy a non-trivial descent of equations, similarly to the non-Abelian chiral anomaly in Yang-Mills theory.Comment: 9 pages. RevTeX fil

Note about a pure spin-connection formulation of general relativity and spin-2 duality in (A)dS

peer reviewedWe investigate the problem of finding a pure spin-connection formulation of General Relativity with non-vanishing cosmological constant. We first revisit the problem at the linearised level and find that the pure spin-connection, quadratic Lagrangian, takes a form reminiscent to Weyl gravity, given by the square of a Weyl-like tensor. Upon Hodge dualisation, we show that the dual gauge field in (A)dS_D transforms under GL(D) in the same representation as a massive graviton in the flat spacetime of the same dimension. We give a detailed proof that the physical degrees of freedom indeed correspond to a massless graviton propagating around the (anti-) de Sitter background and finally speculate about a possible nonlinear pure-connection theory dual to General Relativity with cosmological constant

Millimeter dust continuum emission unveiling the true mass of giant molecular clouds in the Small Magellanic Cloud

CO observations have been so far the best way to trace molecular gas in external galaxies, but at low metallicity the gas mass deduced could be largely underestimated. At present, the kinematic information of CO data cubes are used to estimate virial masses and trace the total mass of the molecular clouds. Millimeter dust emission can also be used as a dense gas tracer and could unveil H2 envelopes lacking CO. These different tracers must be compared in different environments. This study compares virial masses to masses deduced from millimeter emission, in two GMC samples: the local molecular clouds in our Galaxy and their equivalents in the Small Magellanic Cloud (SMC), one of the nearest low metallicity dwarf galaxy. In our Galaxy, mass estimates deduced from millimeter emission are consistent with masses deduced from gamma ray analysis and trace the total mass of the clouds. Virial masses are systematically larger (twice on average) than mass estimates from millimeter dust emission. This difference decreases toward high masses and has already been reported in previous studies. In the SMC however, molecular cloud masses deduced from SIMBA millimeter observations are systematically higher (twice on average for conservative values of the dust to gas ratio and dust emissivity) than the virial masses from SEST CO observations. The observed excess can not be accounted for by any plausible change of dust properties. Taking a general form for the virial theorem, we show that a magnetic field strength of ~15 micro Gauss in SMC clouds could provide additional support to the clouds and explain the difference observed. Masses of SMC molecular clouds have therefore been underestimated so far. Magnetic pressure may contribute significantly to their support.Comment: 10 pages, 2 figures, Astronomy & Astrophysics accepte

The Exploitation of Toxic Fish from the Terminal Pleistocene in Maritime Southeast Asia: A Case Study from the Mindoro Archaeological Sites, Philippines

Representatives of the Diodontidae family (porcupinefish) are known to have been fished by prehistoric Indo-Pacific populations; however, the antiquity of the use of this family is thus far unknown. We report here on the presence of Diodontidae in the archaeological sites of Bubog I, II, and Bilat in Mindoro, Philippines, dating back to c. 13,000 BP (Before Present). This evidence demonstrates the early exploitation by islanders of poisonous fish. Every part of porcupinefish can be toxic, but the toxicity is mostly concentrated in some organs, while other parts are edible. The continuous presence of Diodontidae remains throughout the stratigraphic record of these Philippines shell middens suggests that porcupinefish were prepared by human inhabitants of the sites to render them safe for consumption, indicating an advanced cultural knowledge of the preparation needed to separate the toxic principle from the edible parts. This constitutes one of the rare examples of poison processing by humans, aside from the contentious wooden stick poison applicator from Border Cave (South Africa)