Twistor Origin of the Superstring

TL;DR

This paper presents a twistor-based reformulation of the superstring theory in ten dimensions, deriving the pure spinor formalism through quantization of a twistor-like constraint, connecting twistors with superstring variables.

Contribution

It introduces a novel twistor origin for the superstring, deriving the pure spinor formalism from twistor-like constraints and ghost variables, offering a new geometric perspective.

Findings

Reformulation of superstring using twistor-like constraints

Derivation of pure spinor formalism from twistor quantization

Connection between twistors and superspace variables

Abstract

After introducing a d=10 pure spinor $\lambda^\alpha$, the Virasoro constraint $\partial x^m \partial x_m =0$ can be replaced by the twistor-like constraint $\partial x^m (\gamma_m \lambda)_\alpha=0$. 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.