# Notes on the $D=11$ pure spinor superparticle

## TL;DR

This paper discusses the $D=11$ pure spinor superparticle, its role in describing linearized supergravity, and the challenges in constructing certain vertex operators for amplitude calculations.

## Contribution

It explicitly constructs a ghost number one vertex operator and demonstrates the incompatibility of a ghost number zero vertex operator within the $D=11$ supergravity framework.

## Key findings

- Constructed a ghost number one vertex operator.
- Showed the incompatibility of a ghost number zero vertex operator.
- Highlighted issues in amplitude computation using pure spinor formalism.

## Abstract

The $D=11$ pure spinor superparticle has been shown to describe linearized $D=11$ supergravity in a manifestly covariant way. A number of authors have proposed that its correlation functions be used to compute amplitudes. The use of the scalar structure of the eleven-dimensional pure spinor top cohomology introduces a natural measure for computing such correlation functions. This prescription requires the construction of ghost number one and zero vertex operators. In these notes, we construct explicitly a ghost number one vertex operator but show the incompatibiliy of a ghost number zero vertex operator satisfying a standard descent equation for $D=11$ supergravity.