Integral representations in supermanifolds: super Hodge duals, PCOs and Liouville forms

Abstract

We present few types of integral transforms and integral representations that are very useful for extending to supergeometry many familiar concepts of differential geometry. Among them we discuss the construction of the super Hodge dual, the integral representation of picture changing operators of string theories and the construction of the super-Liouville form of a symplectic supermanifold.

A section of the present paper was already presented in a previous preprint arXiv:1511.05105. This is the complete, extended version of that work. 21 pages. No figures. Names of authors corrected in the metadata. Minor corrections, version accepted for publication Lett. Math. Phys