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.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
D. Friedan, S.H. Shenker and E.J. Martinec, Covariant quantization of superstrings, Phys. Lett. B 160 (1985) 55 [INSPIRE].
D. Friedan, E.J. Martinec and S.H. Shenker, Conformal invariance, supersymmetry and string theory, Nucl. Phys. B 271 (1986) 93 [INSPIRE].
E.P. Verlinde and H.L. Verlinde, Multiloop calculations in covariant superstring theory, Phys. Lett. B 192 (1987) 95 [INSPIRE].
A. Sen, Off-shell amplitudes in superstring theory, Fortsch. Phys. 63 (2015) 149 [arXiv:1408.0571] [INSPIRE].
E. Witten, Notes on supermanifolds and integration, arXiv:1209.2199 [INSPIRE].
E. Witten, Superstring perturbation theory revisited, arXiv:1209.5461 [INSPIRE].
T. Erler, S. Konopka and I. Sachs, Resolving Witten’s superstring field theory, JHEP 04 (2014)150 [arXiv:1312.2948] [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1504.00609
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Sen, A., Witten, E. Filling the gaps with PCO’s. J. High Energ. Phys. 2015, 4 (2015). https://doi.org/10.1007/JHEP09(2015)004
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP09(2015)004