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We review a formalism of superstring quantization with manifestsix-dimensional spacetime supersymmetry, and apply it to AdS_3 x S^3backgrounds with Ramond-Ramond flux. The resulting description is a conformalfield theory based on a sigma model whose target space is a certain supergroupSU'(2|2).Comment: 89 pages harvmac. Added four reference

Conformal field theory of AdS background with Ramond-Ramond flux