Notes on the pure spinor b ghost

TL;DR

This paper investigates specific BRST-exact deformations of the b ghost in the pure spinor formalism and analyzes their effects on the associated topological string algebra, introducing novel composite fields.

Contribution

It introduces a class of BRST-exact deformations of the b ghost and explores their impact on the topological string algebra, including a new composite c ghost-like field.

Findings

Deformations can be explicitly constructed with the U(1) current in a conventional form.

A new composite c ghost-like field with an unusual construction is proposed.

The impact on the $ abla$-algebra structure is analyzed.

Abstract

In this work, a particular BRST-exact class of deformations of the b ghost in the non-minimal pure spinor formalism is investigated and the impact of this construction in the $\mathcal{N}=2$ $\hat{c}=3$ topological string algebra is analysed. As an example, a subclass of deformations is explicitly shown, where the U(1) current appears in a conventional form, involving only the ghost number currents. Furthermore, a c ghost like composite field is introduced, but with an unusual construction.