Y-formalism in pure spinor quantization of superstrings

We present the Y-formalism in the pure spinor quantization of superstring theory in detail. Even if the ω-λ OPE is not completely free owing to the presence of the projector reflecting the pure spinor constraint, it is shown that one can construct at the quantum level a conformal field theory in full agreement with the Berkovits' pure spinor formalism. The OPEs of the two formalisms are the same if we define the relevant operators involving ω in a suitable manner. Moreover, the Y-formalism at hand is utilized to find the full expression of the covariant, picture-raised b antighost bB, with a reasonable amount of effort.