Notes on super Riemann surfaces and their moduli

These are notes on the theory of super Riemann surfaces and their moduli spaces, aiming to collect results that are useful for a better understanding of superstring perturbation theory in the RNS formalism.

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Research supported in part by NSF grant PHY-0969448. I thank P. Deligne for much valuable advice over the years on supergeometry and super Riemann surfaces, and especially for explaining to me many of the matters that are summarized in section 6, as well as some details in section 5. Helpful comments on the manuscript have also been provided by K. Becker, J. Distler, G. Moore, and especially D. Robbins and B. Safdi.

Received 6 September 2018

Published 2 April 2019