36 research outputs found

    The No-Triangle Hypothesis for N=8 Supergravity

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    We study the perturbative expansion of N=8 supergravity in four dimensions from the viewpoint of the ``no-triangle'' hypothesis, which states that one-loop graviton amplitudes in N=8 supergravity only contain scalar box integral functions. Our computations constitute a direct proof at six-points and support the no-triangle conjecture for seven-point amplitudes and beyond.Comment: 43page

    Selberg Supertrace Formula for Super Riemann Surfaces III: Bordered Super Riemann Surfaces

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    This paper is the third in a sequel to develop a super-analogue of the classical Selberg trace formula, the Selberg supertrace formula. It deals with bordered super Riemann surfaces. The theory of bordered super Riemann surfaces is outlined, and the corresponding Selberg supertrace formula is developed. The analytic properties of the Selberg super zeta-functions on bordered super Riemann surfaces are discussed, and super-determinants of Dirac-Laplace operators on bordered super Riemann surfaces are calculated in terms of Selberg super zeta-functions.Comment: 43 pages, amste

    Synergies and trade-offs between ecosystem service supply, biodiversity, and habitat conservation status in Europe

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    In the European Union (EU) efforts to conserve biodiversity have been consistently directed towards the protection of habitats and species through the designation of protected areas under the Habitats Directive (92/43/ECC). These biodiversity conservation efforts also have the potential to maintain or improve the supply of ecosystem services; however, this potential has been poorly explored across Europe. This paper reports on a spatial assessment of the relationships between biodiversity, ecosystem services, and conservation status of protected habitats at European scale. We mapped at 10 km resolution ten spatial proxies for ecosystem service supply (four provisioning services, five regulating services and one cultural service) and three proxies for biodiversity (Mean Species Abundance, tree species diversity and the relative area of Natura 2000 sites). Indicators for biodiversity and aggregated ecosystem service supply were positively related but this relationship was influenced by the spatial trade-offs among ecosystem services, in particular between crop production and regulating ecosystem services. Using multinomial logistic regression models we demonstrated that habitats in a favourable conservation status provided more biodiversity and had a higher potential to supply, in particular, regulating and cultural ecosystem services than habitats in an unfavourable conservation status. This information is of utmost importance in identifying regions in which measures are likely to result in cost-effective progress towards both new biodiversity conservation and ecosystem services targets adopted by the Convention on Biological Diversity (CBD) and the EU Biodiversity Strategy to 2020
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