MacDowell-Mansouri gravity and Cartan geometry

The geometric content of the MacDowell-Mansouri formulation of general relativity is best understood in terms of Cartan geometry. In particular, Cartan geometry gives clear geometric meaning to the MacDowell-Mansouri trick of combining the Levi-Civita connection and coframe field, or soldering form, into a single physical field. The Cartan perspective allows us to view physical spacetime as tangentially approximated by an arbitrary homogeneous "model spacetime", including not only the flat Minkowski model, as is implicitly used in standard general relativity, but also de Sitter, anti de Sitter, or other models. A "Cartan connection" gives a prescription for parallel transport from one "tangent model spacetime" to another, along any path, giving a natural interpretation of the MacDowell-Mansouri connection as "rolling" the model spacetime along physical spacetime. I explain Cartan geometry, and "Cartan gauge theory", in which the gauge field is replaced by a Cartan connection. In particular, I discuss MacDowell-Mansouri gravity, as well as its more recent reformulation in terms of BF theory, in the context of Cartan geometry.Comment: 34 pages, 5 figures. v2: many clarifications, typos correcte

Mutation Symmetries in BPS Quiver Theories: Building the BPS Spectra

We study the basic features of BPS quiver mutations in 4D $\mathcal{N}=2$ supersymmetric quantum field theory with $G=ADE$ gauge symmetries.\ We show, for these gauge symmetries, that there is an isotropy group $\mathcal{G}_{Mut}^{G}$ associated to a set of quiver mutations capturing information about the BPS spectra. In the strong coupling limit, it is shown that BPS chambers correspond to finite and closed groupoid orbits with an isotropy symmetry group $\mathcal{G}_{strong}^{G}$ isomorphic to the discrete dihedral groups $Dih_{2h_{G}}$ contained in Coxeter$(G)$ with $$ the Coxeter number of G. These isotropy symmetries allow to determine the BPS spectrum of the strong coupling chamber; and give another way to count the total number of BPS and anti-BPS states of $\mathcal{N}=2$ gauge theories. We also build the matrix realization of these mutation groups $\mathcal{G}_{strong}^{G}$ from which we read directly the electric-magnetic charges of the BPS and anti-BPS states of $\mathcal{N}=2$ QFT$_{4}$ as well as their matrix intersections. We study as well the quiver mutation symmetries in the weak coupling limit and give their links with infinite Coxeter groups. We show amongst others that $\mathcal{G}_{weak}^{su_{2}}$ is contained in ${GL}({2,}\mathbb{Z})$; and isomorphic to the infinite Coxeter ${I_{2}^{\infty}}$. Other issues such as building $\mathcal{G}$ and $\mathcal{G}_{weak}^{su_{3}}$ are also studied.Comment: LaTeX, 98 pages, 18 figures, Appendix I on groupoids adde

The Lie algebroid Poisson sigma model

The Poisson--Weil sigma model, worked out by us recently, stems from gauging a Hamiltonian Lie group symmetry of the target space of the Poisson sigma model. Upon gauge fixing of the BV master action, it yields interesting topological field theories such as the 2--dimensional Donaldson-Witten topological gauge theory and the gauged A topological sigma model. In this paper, generalizing the above construction, we construct the Lie algebroid Poisson sigma model. This is yielded by gauging a Hamiltonian Lie groupoid symmetry of the Poisson sigma model target space. We use the BV quantization approach in the AKSZ geometrical version to ensure consistent quantization and target space covariance. The model has an extremely rich geometry and an intricate BV cohomology, which are studied in detail.Comment: 52 pages, Late

VUV spectroscopic study of the D1Piu state of molecular deuterium

The D^1\Pi_u - X^1\Sigma_g^+ absorption system of molecular deuterium has been re-investigated using the VUV Fourier -Transform (FT) spectrometer at the DESIRS beamline of the synchrotron SOLEIL and photon-induced fluorescence spectrometry (PIFS) using the 10 m normal incidence monochromator at the synchrotron BESSY II. Using the FT spectrometer absorption spectra in the range 72 - 82 nm were recorded in quasi static gas at 100 K and in a free flowing jet at a spectroscopic resolution of 0.50 and 0.20 cm^{-1} respectively . The narrow Q-branch transitions, probing states of \Pi^- symmetry, were observed up to vibrational level v = 22. The states of \Pi^+ symmetry, known to be broadened due to predissociation and giving rise to asymmetric Beutler-Fano resonances, were studied up to v = 18. The 10 m normal incidence beamline setup at BESSY II was used to simultaneously record absorption, dissociation, ionization and fluorescence decay channels from which information on the line intensities, predissociated widths, and Fano q-parameters were extracted. R-branch transitions were observed up to v = 23 for J = 1-3 as well as several transitions for J = 4 and 5 up to v = 22 and 18 respectively. The Q-branch transitions are found to weakly predissociate and were observed from v = 8 to the final vibrational level of the state v = 23. The spectroscopic study is supported by two theoretical frameworks. Results on the \Pi^- symmetry states are compared to ab initio multi-channel-quantum defect theory (MQDT) calculations, demonstrating that these calculations are accurate to within 0.5 cm^-1.Comment: 16 pages, 10 figures, 2 tables, supplemental material with an additional tabl

Cytotoxic and HIV-1 enzyme inhibitory activities of Red Sea marine organisms

BACKGROUND: Cancer and HIV/AIDS are two of the greatest public health and humanitarian challenges facing the world today. Infection with HIV not only weakens the immune system leading to AIDS and increasing the risk of opportunistic infections, but also increases the risk of several types of cancer. The enormous biodiversity of marine habitats is mirrored by the molecular diversity of secondary metabolites found in marine animals, plants and microbes which is why this work was designed to assess the anti-HIV and cytotoxic activities of some marine organisms of the Red Sea. METHODS: The lipophilic fractions of methanolic extracts of thirteen marine organisms collected from the Red Sea (Egypt) were screened for cytotoxicity against two human cancer cell lines; leukaemia (U937) and cervical cancer (HeLa) cells. African green monkey kidney cells (Vero) were used as normal non-malignant control cells. The extracts were also tested for their inhibitory activity against HIV-1 enzymes, reverse transcriptase (RT) and protease (PR). RESULTS: Cytotoxicity results showed strong activity of the Cnidarian Litophyton arboreum against U-937 (IC50; 6.5 μg/ml ±2.3) with a selectivity index (SI) of 6.45, while the Cnidarian Sarcophyton trochliophorum showed strong activity against HeLa cells (IC50; 5.2 μg/ml ±1.2) with an SI of 2.09. Other species showed moderate to weak cytotoxicity against both cell lines. Two extracts showed potent inhibitory activity against HIV-1 protease; these were the Cnidarian jelly fish Cassiopia andromeda (IC50; 0.84 μg/ml ±0.05) and the red algae Galaxura filamentosa (2.6 μg/ml ±1.29). It is interesting to note that the most active extracts against HIV-1 PR, C. andromeda and G. filamentosa showed no cytotoxicity in the three cell lines at the highest concentration tested (100 μg/ml). CONCLUSION: The strong cytotoxicity of the soft corals L. arboreum and S. trochliophorum as well as the anti-PR activity of the jelly fish C. andromeda and the red algae G. filamentosa suggests the medicinal potential of crude extracts of these marine organisms.The Medical Research Council, the Technology Innovation Agency and the University of Pretoria, South Africa.http://www.biomedcentral.com/bmccomplementalternmedam201

A glimpse into Thurston's work

We present an overview of some significant results of Thurston and their impact on mathematics. The final version of this paper will appear as Chapter 1 of the book "In the tradition of Thurston: Geometry and topology", edited by K. Ohshika and A. Papadopoulos (Springer, 2020)

Volatile and Organic Compositions of Sedimentary Rocks in Yellowknife Bay, Gale crater, Mars

H₂O, CO₂, SO₂, O₂, H₂, H₂S, HCl, chlorinated hydrocarbons, NO and other trace gases were evolved during pyrolysis of two mudstone samples acquired by the Curiosity rover at Yellowknife Bay within Gale crater, Mars. H₂O/OH-bearing phases included 2:1 phyllosilicate(s), bassanite, akaganeite, and amorphous materials. Thermal decomposition of carbonates and combustion of organic materials are candidate sources for the CO₂. Concurrent evolution of O₂ and chlorinated hydrocarbons suggest the presence of oxychlorine phase(s). Sulfides are likely sources for S-bearing species. Higher abundances of chlorinated hydrocarbons in the mudstone compared with Rocknest windblown materials previously analyzed by Curiosity suggest that indigenous martian or meteoritic organic C sources may be preserved in the mudstone; however, the C source for the chlorinated hydrocarbons is not definitively of martian origin