Topological string theory revisited I: The stage

Abstract

In this paper, we reformulate topological string theory using supermanifolds and supermoduli spaces, following the approach worked out by Witten (Superstring perturbation theory revisited, arXiv:1209.5461 ). We intend to make the construction geometrical in nature, by using supergeometry techniques extensively. The goal is to establish the foundation of studying topological string amplitudes in terms of integration over appropriate supermoduli spaces.