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

## TL;DR

This paper develops the Y-formalism for non-minimal pure spinor superstring quantization, explicitly constructs the quantum $b$ ghost, and demonstrates its cohomological equivalence to the non-covariant version.

## Contribution

It introduces the Y-formalism into the non-minimal pure spinor framework and explicitly constructs the quantum $b$ ghost, advancing the understanding of superstring quantization.

## Key findings

- Explicit quantum $b$ ghost construction in non-minimal formalism
- Demonstration of cohomological equivalence to non-covariant $b$ ghost
- Clarification of operator relations at the quantum level

## Abstract

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.