On the b-antighost in the Pure Spinor Quantization of Superstrings

TL;DR

This paper explores the relationship between two different b-ghost fields in the pure spinor superstring formalism, showing they are cohomologically equivalent, which clarifies their roles in amplitude calculations.

Contribution

It demonstrates that the b-ghost from the superembedding approach and Berkovits' b_B are in the same BRST cohomology class, resolving issues related to singularities.

Findings

b and b_B are in the same BRST cohomology class

The singularity in b is harmless when combined with the picture raising operator Z

The relation clarifies the role of b in amplitude computations

Abstract

Recently Berkovits has constructed a picture raised, compound field $b_B$ which is used to compute higher loop amplitudes in the pure spinor approach of superstrings. On the other hand, in the twisted and gauge fixed, superembedding approach with $n=2$ world-sheet (w.s.) supersymmetry that reproduces the pure spinor formulation, a field $b$ appears quite naturally as the current of one of the two twisted charges of the w.s. supersymmetry, the other being the BRST charge. In this paper we study the relation between $b$ and $b_B$. We shall show that $bZ$, where $Z$ is a picture raising operator, and $b_B$ belong to the same BRST cohomological class. This result is of importance since it implies that the cumbersome singularity which is present in $b$, is in fact harmless if $b$ is combined with $Z$.