Superstring field theory, superforms and supergeometry

Inspired by superstring field theory, we study differential, integral, and inverse formsand their mutual relations on a supermanifold from a sheaf-theoretical point of view.In particular, the formal distributional properties of integral forms are recovered inthis scenario in a geometrical way. Further, we show how inverse forms ‘‘extend’’the ordinary de Rham complex on a supermanifold, thus providing a mathematicalfoundation of the Large Hilbert Space used in superstrings. Last, we briefly discuss howtheHodgediamondofasupermanifoldlookslike,andweexplicitlycomputeitforsuperRiemann surfaces.