Quantization of the superstring in Ramond-Ramond backgrounds

Abstract

Sigma model actions are constructed for the type II superstring compactified to four- and six-dimensional curved backgrounds which can contain non-vanishing Ramond-Ramond fields. These actions are N = 2 worldsheet superconformally invariant and can be covariantly quantized preserving manifest spacetime supersymmetry. They are constructed using a hybrid version of superstring variables which combines features of the Ramond-Neveu-Schwarz and Green-Schwarz formalisms. For the AdS2 × S2 and AdS3 × S3 backgrounds, these actions differ from the classical Green-Schwarz actions by a crucial kinetic term for the fermions. Parts of this work have been done in collaborations with M Bershadsky, T Hauer, W Siegel, C Vafa, E Witten, S Zhukov and B Zwiebach.