Quantization of the particle with a linear massless solution

TL;DR

This paper investigates a massless particle solution using pure spinors, quantizes the model with BRST formalism, and proposes a new superparticle model with partial worldline supersymmetry.

Contribution

It introduces a new model for the superparticle with partial worldline supersymmetry derived from first principles.

Findings

Wave functions generate massless solutions for arbitrary spin.

The gauge algebra is analyzed within the Batalin-Vilkovisky formalism.

The model describes the pure spinor superparticle times a decoupled sector.

Abstract

In this work, a solution linear in the momentum for the massless constraint $P^{m}P_{m}=0$ is investigated. It is presented in terms of a $SO(2n,\mathbb{C})$ to $U(n)$ decomposition and interpreted in terms of projective pure spinors, which are known to parametrize the $\tfrac{SO(2n)}{U(n)}$ coset. The worldline action is quantized using the BRST formalism and, using the results of Berkovits and Cherkis, the ghost number zero wave function is shown to generate massless solutions for field equations of arbitrary spin. The model can be covariantly expressed by the action recently proposed in $D=10$ by Berkovits, in terms of a twistor-like constraint. However, a thorough account of its gauge symmetries does not lead to a spacetime supersymmetric theory. In order to derive from first principles the superparticle in the pure spinor formalism, a new model is proposed with partial worldline supersymmetry. The gauge algebra is then analyzed within the Batalin-Vilkovisky formalism and the gauge fixed action is finally shown to describe the pure spinor superparticle times a $U(1)$ decoupled sector.