Y-formalism in Pure Spinor Quantization of Superstrings

TL;DR

This paper introduces the Y-formalism in pure spinor superstring quantization, demonstrating its consistency with existing formalisms and deriving the covariant b ghost expression.

Contribution

The paper develops the Y-formalism for pure spinor superstring quantization, showing its equivalence with Berkovits' formalism and deriving the covariant b ghost.

Findings

The Y-formalism reproduces the OPEs of the standard formalism.

The covariant b ghost expression is explicitly derived.

The formalism maintains conformal invariance at the quantum level.

Abstract

We present the Y-formalism in the pure spinor quantization of superstring theory in detail. Even if the $\omega-\lambda$ 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 OPE's of the two formalisms are the same if we define the relevant operators involving $\omega$ in a suitable manner. Moreover the Y-formalism at hand is utilized to find the full expression of the covariant, picture raised $b$ antighost $b_B$, with a reasonable amount of effort.