The Superembedding Origin of the Berkovits Pure Spinor Covariant   Quantization of Superstrings
  We show that the pure spinor formalism proposed by Berkovits to covariantly quantize superstrings is a gauge fixed, twisted version of the complexified n=2 superembedding formulation of the superstring. This provides the Berkovits approach with a geometrical superdiffeomorphism invariant ground. As a consequence, the absence of the worldsheet (super)diffeomorphism ghosts in the pure spinor quantization prescription and the nature of the Berkovits BRST charge and antighost are clarified. Since superembedding is classically equivalent to the Green-Schwarz formulation, we thus also relate the latter to the pure spinor construction. 
Marco Matone, Luca Mazzucato, Ichiro Oda, Dmitri Sorokin and Mario   Tonin