A Pure Spinor Twistor Description of the $D=10$ Superparticle

TL;DR

This paper introduces a new twistor-based formulation of the ten-dimensional superparticle using pure spinor variables, leading to a natural emergence of the super-Pauli-Lubanski form and consistent quantization of super-Yang-Mills states.

Contribution

It presents a novel pure spinor twistor formulation of the D=10 superparticle, connecting pure spinors with twistor geometry and super-Pauli-Lubanski forms.

Findings

The super-Pauli-Lubanski three-form appears as a natural constraint.

Quantization reproduces the correct D=10 super-Yang-Mills spectrum.

The formulation provides a new geometric perspective on superparticle models.

Abstract

We present a novel twistor formulation of the ten-dimensional massless superparticle. This formulation is based on the introduction of pure spinor variables through a field redefinition of another model for the superparticle, and in the new description we find that the super-Pauli-Lubanski three-form naturally arises as a constraint. Quantization is studied in detail for both models and they are shown to correctly describe the $D = 10$ super-Yang-Mills states.