Quantization of the Superstring in Ramond-Ramond Backgrounds

TL;DR

This paper develops covariantly quantized superstring actions in curved backgrounds with Ramond-Ramond fields, using a hybrid formalism that preserves spacetime supersymmetry and differs from classical Green-Schwarz actions.

Contribution

It introduces a new covariant quantization method for superstrings in Ramond-Ramond backgrounds using a hybrid formalism that combines features of RNS and Green-Schwarz formalisms.

Findings

Constructed N=2 superconformally invariant sigma models for specific backgrounds.

Achieved covariant quantization preserving spacetime supersymmetry.

Identified key differences from classical Green-Schwarz actions in certain 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 $AdS_2\times S^2$ and $AdS_3\times S^3$ backgrounds, these actions differ from the classical Greeen-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.