Taming the 11D pure spinor b-ghost

Abstract

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 $$ \left\{Q,b\right\}=\frac{P^2}{2} $$ Q b = P 2 2 , as well as {b, b} = QΩ. 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.