Filling the gaps with PCO’s

摘要: 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 constraint must placed PCO insertions avoid spurious singularities. Accordingly, it has been long known that simplest version of procedure valid only locally moduli space Riemann surfaces, and correct PCO-based algorithm compute scattering amplitudes based piecing together local descriptions. Recently, “vertical integration” was proposed as relatively simple method do this. Here, we spell in detail what vertical integration means if systematically. This involves hierarchical with corrections high order. One might anticipate such structure from viewpoint super surfaces.