Filling the gaps with PCO’s

• Published in: The journal of high energy physics Vol. 2015; no. 9; pp. 1 - 35
• Main Authors: Sen, Ashoke, Witten, Edward
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2015; Springer Nature B.V
• Subjects: Algorithms; Classical and Quantum Gravitation; Descriptions; Elementary Particles; High energy physics; Insertion; Perturbation theory; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; Riemann surfaces; Scattering amplitude; Singularities; String Theory; Strings; Superstrings and Heterotic Strings; String theory and cosmic strings
• ISSN: 1029-8479; 1126-6708; 1127-2236; 1029-8479
• DOI: 10.1007/JHEP09(2015)004

A bstract 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. Here, we spell out in detail what vertical integration means if carried out systematically. This involves a hierarchical procedure with corrections of high order. One might anticipate such a structure from the viewpoint of super Riemann surfaces.