Pure spinors, twistors, and emergent supersymmetry

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 derivative 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 contains the usual spacetime supersymmetric states of the superstring.