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2015

The Geometry of Supermanifolds and New Supersymmetric Actions

Castellani, L., Catenacci, R., Grassi, P. A.

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We construct the Hodge dual for supermanifolds by means of the Grassmannian Fourier transform of superforms.

In the case of supermanifolds it is known that the superforms are not sufficient to construct a consistent integration theory and that the integral forms are needed.
They are distribution-like forms which can be integrated on supermanifolds as a top form can be integrated on a conventional manifold.
In our construction of the Hodge dual of superforms they arise naturally.

The Geometry of Supermanifolds and New Supersymmetric Actions · Around

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T. Voronov and A. Zorich: Integral transformations of pseudodifferential forms, Usp. Mat. Nauk, 41 (1986) 167-168; T. Voronov and A. Zorich: Complex of forms on a supermanifold, Funktsional. Anal. i Prilozhen., 20 (1986) 58-65; T. Voronov and A. Zorich: Theory of bordisms and homotopy properties of supermanifolds, Funktsional. Anal. i Prilozhen., 21 (1987) 77-78; T. Voronov and A. Zorich: Cohomology of supermanifolds, and integral geometry, Soviet Math. Dokl., 37 (1988) 96-101
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A. Belopolsky, New geometrical approach to superstrings, [arXiv:hep-th/9703183]. A. Belopolsky, Picture changing operators in supergeometry and superstring theory, [arXiv:hep-th/9706033]

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L. Castellani, R. Catenacci and P. A. Grassi, “Hodge Dualities on Supermanifolds,” arXiv:1507.01421 [hep-th]

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