Embedding vs. 6D twistors
  We review the relation between the "embedding" formalism and spinorial projective space. The latter is more convenient when treating spin (and indispensable for supersymmetry), as it maintains manifest conformal symmetry while using 4-dimensional indices on fields/operators. It does this by solving all algebraic constraints using 6-dimensional (off-shell) twistors. In an added note we review the supersymmetric generalization, and give some new results for N=3. 
W. Siegel
hep-th