Taming the 11D pure spinor b-ghost

TL;DR

This paper introduces a new compact expression for the 11D pure spinor b-ghost using non-minimal variables, simplifying the derivation of vertex operators and superfields in 11D supergravity.

Contribution

It presents an alternative formulation of the 11D pure spinor b-ghost with new operators, enabling straightforward derivation of vertex operators and superfields.

Findings

Simplified derivation of the ghost number two vertex operator

Construction of the ghost number three vertex operator in covariant form

Easy construction of the 11D supergravity two-particle superfield

Abstract

We provide an alternative compact expression for the 11D pure spinor b-ghost by introducing a new set of negative ghost number operators made out of non-minimal pure spinor variables. Using the algebraic properties satisfied by these operators, it will be straightforwardly shown that $\{Q, b\}={P^2\over 2}$, as well as $\{b,b\} = Q\Omega$. As an application of this novel formulation, the ghost number two vertex operator will easily be obtained in a completely covariant manner from a standard descent relation, the ghost number three vertex operator will be shown to satisfy the generalized Siegel gauge condition, and the 11D supergravity two-particle superfield will be constructed in a quite simple way.