Twistor Origin of the Superstring

After introducing a d=10 pure spinor ${\lambda }^{\alpha }$, the Virasoro constraint $\mathrm{\partial }{x}^m\mathrm{\partial }{x}_m=0$ can be replaced by the twistor-like constraint $\mathrm{\partial }{x}^m({\gamma }_m\lambda {)}_{\alpha }=0$. Quantizing this twistor-like constraint leads to the pure spinor formalism for the superstring where the fermionic superspace variables ${\theta }^{\alpha }$ and their conjugate momenta come from the ghosts and antighosts of the twistor-like constraint.