Topological String Theory Revisited I: The Stage

TL;DR

This paper reformulates topological string theory using supergeometry, aiming to establish a geometric foundation for studying string amplitudes via integration over supermoduli spaces.

Contribution

It introduces a supermanifold-based reformulation of topological string theory, extending Witten's superstring approach to a purely geometric framework.

Findings

Framework for topological string amplitudes using supergeometry

Connection between supermoduli spaces and string theory amplitudes

Foundation for future geometric studies in topological strings

Abstract

In this note we reformulate topological string theory using supermanifolds and supermoduli spaces, following the approach worked out by Witten for superstring perturbation theory in 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.