A minimal b ghost

TL;DR

This paper demonstrates a minimal variable construction of the $b$ ghost operator in pure spinor superfield formalism, showing it can be built without non-minimal variables in super-Yang-Mills theory, suggesting a general feature.

Contribution

It provides the first explicit minimal variable construction of the $b$ ghost in $D=10$ super-Yang-Mills, indicating such minimal representations are possible generally.

Findings

Constructed a minimal $b$ ghost in super-Yang-Mills theory.

Argued the minimal construction is a general feature.

Shows all cohomology has minimal representatives.

Abstract

The $b$ ghost, or $b$ operator, used for fixing Siegel gauge in the pure spinor superfield formalism, is a composite operator of negative ghost number, satisfying $\{q,b\}=\square$, where $q$ is the pure spinor differential (BRST operator). It is traditionally constructed using non-minimal variables. However, since all cohomology has minimal representatives, it seems likely that there should be versions of physically meaningful operators, also with negative ghost number, using only minimal variables. The purpose of this letter is to demonstrate that this statement holds by providing a concrete construction in $D=10$ super-Yang-Mills theory, and to argue that it is a general feature in the pure spinor superfield formalism.