hodge dualities on supermanifolds

Clicks: 132
ID: 213911
2015
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Abstract
We discuss the cohomology of superforms and integral forms from a new perspective based on a recently proposed Hodge dual operator. We show how the superspace constraints (a.k.a. rheonomic parametrization) are translated from the space of superforms Ω(p|0) to the space of integral forms Ω(p|m) where 0≤p≤n, n is the bosonic dimension of the supermanifold and m its fermionic dimension. We dwell on the relation between supermanifolds with non-trivial curvature and Ramond–Ramond fields, for which the Laplace–Beltrami differential, constructed with our Hodge dual, is an essential ingredient. We discuss the definition of Picture Lowering and Picture Raising Operators (acting on the space of superforms and on the space of integral forms) and their relation with the cohomology. We construct non-abelian curvatures for gauge connections in the space Ω(1|m) and finally discuss Hodge dual fields within the present framework.
Reference Key
castellani2015nuclearhodge Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors ;L. Castellani;R. Catenacci;P.A. Grassi
Journal biology and fertility of soils
Year 2015
DOI
10.1016/j.nuclphysb.2015.08.002
URL
http://www.sciencedirect.com/science/article/pii/S0550321315002874
Keywords
radioactivity atomic energy nuclear and particle physics

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