Pure and Applied Mathematics Quarterly

Volume 15 (2019)

Number 1

Special Issue on Super Riemann Surfaces and String Theory

Guest Editor: Edward Witten

Perturbative superstring theory revisited

Pages: 213 – 516

DOI: https://dx.doi.org/10.4310/PAMQ.2019.v15.n1.a3


Edward Witten (School of Natural Sciences, Institute for Advanced Study, Princeton, New Jersey, U.S.A.)


Perturbative superstring theory is revisited, with the goal of giving a simpler and more direct demonstration that multiloop amplitudes are gauge-invariant (apart from known anomalies), satisfy space-time supersymmetry when expected, and have the expected infrared behavior. The main technical tool is to make the whole analysis, including especially those arguments that involve integration by parts, on supermoduli space, rather than after descending to ordinary moduli space.

Research partly supported by NSF grant PHY-0969448. I thank N. Berkovits, L. Brink, P. Goddard, J. Maldacena, V. Pestun, J. Polchinski, M. Rangamani, A. Sen, N. Seiberg, H. Verlinde, and B. Zwiebach and especially K. Becker, P. Deligne, G. Moore, D. Robbins, B. Safdi, and C. Thorn for helpful comments and discussions. M. Turansick assisted with the figures.

Received 6 September 2018

Published 2 April 2019