Filling the gaps with PCO’s

Ashoke Sen, Edward Witten

Research output: Contribution to journalArticlepeer-review

48 Scopus citations


Abstract: 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.

Original languageEnglish (US)
Article number4
JournalJournal of High Energy Physics
Issue number9
StatePublished - Sep 10 2015
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Nuclear and High Energy Physics


  • String theory and cosmic strings
  • Superstrings and Heterotic Strings


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