Paper detail

Pure spinors, twistors, and emergent supersymmetry

Starting with a classical action whose matter variables are a d=10 spacetime vector $x^m$ and a pure spinor $λ^α$, the pure spinor formalism for the superstring is obtained by gauge-fixing the twistor-like constraint $\partial x^m (γ_m λ)_α=0$. The fermionic variables $θ^α$ 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 $θ^α$ has ghost-number zero and $λ^α$ has ghost-number one, the BRST cohomology describes the usual spacetime supersymmetric states of the superstring.