Twistors are closely related to spinors, objects that may be understood as “square roots of vectors”. I like to say that twistors may similarly be interpreted as “square roots of spacetime points”.
Witten enters the scene
In 2003, Edward Witten published his papers on the twistor treatment of the maximally supersymmetric Yang-Mills theory in four dimensions. For the first time, geometry in the twistor space was used to calculate scattering amplitudes – quantities knowing about some real dynamics and interactions in physics.
— Lubos Motl
2011.05.11 Wednesday ACHK