Filling The Gaps With PCO's

Understand

Superstring perturbation theory is traditionally carried out by using picture-changing operators (PCO's) to integrate over odd moduli.

• Naively the PCO's can be inserted anywhere on a string worldsheet, but actually a constraint must be placed on PCO insertions to avoid spurious singularities.
• Accordingly, it has been long known that the simplest version of the PCO procedure is valid only locally on the moduli space of Riemann surfaces, and that a correct PCO-based algorithm to compute scattering amplitudes must be based on piecing together local descriptions.
• Recently, "vertical integration" was proposed as a relatively simple method to do this.