On the Pure Spinor Heterotic Superstring $b$ Ghost

TL;DR

This paper explores the structure of the pure spinor heterotic superstring $b$ ghost, providing insights into its non-holomorphic nature and identifying a potential operator $\,Omega$ that relates to BRST symmetry.

Contribution

It introduces a candidate for the operator $\,Omega$ that satisfies the relation $ar\,partial b = [ Q , \,Omega ]$ in the context of the pure spinor heterotic superstring.

Findings

Identified a possible $\,Omega$ operator related to the $b$ ghost.

Clarified the non-holomorphic property of the $b$ ghost.

Enhanced understanding of BRST symmetry in curved heterotic backgrounds.

Abstract

A simplified pure spinor superstring $b$ ghost in a curved heterotic background was constructed recently. The $b$ ghost is a composite operator and it is not holomorphic. However, it satisfies $\bar\partial b = [ Q , \Omega ]$, where $Q$ is the BRST charge. In this paper, we find a possible $\Omega$.