On the Equivalence between SRS and PCO Formulations of Superstring Perturbation Theory

TL;DR

This paper demonstrates the equivalence between superstring perturbation theory formulations based on supermoduli space integration and those using bosonic moduli space with picture changing operators, clarifying their relationship.

Contribution

It provides a rigorous connection between the SRS and PCO formulations, showing how the PCO approach emerges from a specific supermoduli integration contour construction.

Findings

Established the equivalence between SRS and PCO formulations

Clarified the construction of supermoduli integration contour

Bridged the conceptual gap between two superstring perturbation methods

Abstract

We establish the equivalence between two formulations of superstring perturbation theory, one based on integration over the supermoduli space of super Riemann surfaces (SRS), the other based on integration over the bosonic moduli space with insertions of picture changing operators (PCO) on the worldsheet and the vertical integration prescription, by showing how the latter arises from a specific construction of the supermoduli integration contour.