Editing Twistor theory (section)

===Supertwistors===

Supertwistors are a [[supersymmetry|supersymmetric]] extension of twistors introduced by Alan Ferber in 1978.<ref name="Fer">{{Citation|bibcode=1978NuPhB.132...55F|doi = 10.1016/0550-3213(78)90257-2|title=Supertwistors and conformal supersymmetry|year=1978|last1=Ferber|first1=A.|journal=Nuclear Physics B|volume=132|issue = 1|pages=55–64|postscript=. }}</ref> Non-projective twistor space is extended by [[fermion]]ic coordinates where <math>\mathcal{N}</math> is the [[extended supersymmetry|number of supersymmetries]] so that a twistor is now given by <math>\left(\omega^A,\, \pi_{A'},\, \eta^i\right), i = 1, \ldots, \mathcal{N}</math> with <math>\eta^i</math> anticommuting. The super conformal group <math>SU(2,2|\mathcal{N})</math> naturally acts on this space and a supersymmetric version of the Penrose transform takes cohomology classes on supertwistor space to massless supersymmetric multiplets on super Minkowski space. The <math>\mathcal{N} = 4</math> case provides the target for Penrose's original twistor string and the <math>\mathcal{N} = 8</math> case is that for Skinner's supergravity generalisation.