Notes on the 11D pure spinor wordline vertex operators

TL;DR

This paper revisits the construction of vertex operators in 11D pure spinor superparticle theory, introducing new methods and clarifying the relations between different ghost number operators using non-minimal pure spinor superspace.

Contribution

It provides an alternative definition of ghost number one vertex operators and clarifies their relation to ghost number three operators in 11D pure spinor formalism.

Findings

Explicit construction of ghost number zero and one vertex operators.

Introduction of a ghost number -2 operator in 11D pure spinor superspace.

Presentation of non-Lorentz covariant b-ghost and descent equations.

Abstract

The construction of the ghost number zero and one vertex operators for the 11D pure spinor superparticle will be revisited. In this sense, an alternative way of defining the ghost number one vertex operator will be given after introducing a ghost number -2 operator made out of physical operators defined on the 11D non-minimal pure spinor superspace. This procedure will make explicit and transparent the relation between the ghost number three and one vertex operators. In addition, using a non-Lorentz covariant b-ghost, ghost number zero and two vertex operators satisfying standard descent equations will be presented in full form.