Quantization of the Type II Superstring in a Curved Six-Dimensional Background

A sigma model action with N=2 D=6 superspace variables is constructed for the Type II superstring compactified to six curved dimensions with Ramond-Ramond flux. The action can be quantized since the sigma model is linear when the six-dimensional spacetime is flat. When the six-dimensional spacetime is $AdS_3\times S^3$, the action reduces to one found earlier with Vafa and Witten.