Y-formalism and $b$ ghost in the Non-minimal Pure Spinor Formalism of Superstrings

Understand

We present the Y-formalism for the non-minimal pure spinor quantization of superstrings.

• In the framework of this formalism we compute, at the quantum level, the explicit form of the compound operators involved in the construction of the $b$ ghost, their normal-ordering contributions and the relevant relations among them.
• We use these results to construct the quantum-mechanical $b$ ghost in the non-minimal pure spinor formalism.
• Moreover we show that this non-minimal $b$ ghost is cohomologically equivalent to the non-covariant $b$ ghost.