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Quantization of the Superstring in Ramond-Ramond Backgrounds
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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.
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Covariant quantization of the superstring in $\rm AdS_3 \times S^3 \times T^4$ with mixed flux
A manifestly supersymmetric and quantizable worldsheet action for the mixed-flux AdS3 x S3 x T4 superstring is constructed and shown to be one-loop conformal.
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