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arXiv · 1807.09563

Superstring Field Theory, Superforms and Supergeometry

R. Catenacci·P. A. Grassi·S. Noja
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Abstract

Inspired by superstring field theory, we study differential, integral, and inverse forms and their mutual relations on a supermanifold from a sheaf-theoretical point of view. In particular, the formal distributional properties of integral forms are recovered in this scenario in a geometrical way. Further, we show how inverse forms extend the ordinary de Rham complex on a supermanifold, thus providing a mathematical foundation of the Large Hilbert Space used in superstrings. Last, we briefly discuss how the Hodge diamond of a supermanifold looks like, and we explicitly compute it for super Riemann surfaces.

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R. Catenacci, P. A. Grassi, S. Noja. 2018-07-25. Superstring Field Theory, Superforms and Supergeometry. https://arxiv.org/abs/1807.09563

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