Pure spinors, twistors, and emergent supersymmetry

TL;DR

This paper derives the pure spinor formalism for superstrings from a twistor-like gauge-fixing procedure, revealing a new perspective on spacetime supersymmetry and ghost structures.

Contribution

It introduces a novel derivation of the pure spinor superstring formalism via gauge-fixing a twistor-like constraint, connecting pure spinors, twistors, and supersymmetry.

Findings

BRST cohomology reproduces superstring supersymmetric states

Fermionic variables act as Faddeev-Popov ghosts

Twisting ghost-number clarifies supersymmetric state structure

Abstract

Starting with a classical action whose matter variables are a d=10 spacetime vector $x^m$ and a pure spinor $\lambda^\alpha$, the pure spinor formalism for the superstring is obtained by gauge-fixing the twistor-like constraint $\partial x^m (\gamma_m \lambda)_\alpha =0$. The fermionic variables $\theta^\alpha$ are Faddeev-Popov ghosts coming from this gauge-fixing and replace the usual (b,c) ghosts coming from gauge-fixing the Virasoro constraint. After twisting the ghost-number such that $\theta^\alpha$ has ghost-number zero and $\lambda^\alpha$ has ghost-number one, the BRST cohomology describes the usual spacetime supersymmetric states of the superstring.