Twistors Grassmannian formalism has made a breakthrough in N = 4 supersymmetric
gauge theories and the Yangian symmetry suggests that much more
than mere technical breakthrough is in question. Twistors seem to be tailor
made for TGD but it seems that the generalization of twistor structure to that
for 8-D imbedding space H = M4 CP2 is necessary. M4 (and S4 as its
Euclidian counterpart) and CP2 are indeed unique in the sense that they are
the only 4-D spaces allowing twistor space with Kahler structure.
The Cartesian product of twistor spaces P3 = SU(2; 2)=SU(2; 1)U(1) and
F3 de nes twistor space for the imbedding space H and one can ask whether
this generalized twistor structure could allow to understand both quantum
TGD and classical TGD de ned by the extremals of Kahler action. In the
following I summarize the background and develop a proposal for how to construct
extremals of Kahler action in terms of the generalized twistor structure.
One ends up with a scenario in which space-time surfaces are lifted to twistor
spaces by adding CP1 ber so that the twistor spaces give an alternative representation
for generalized Feynman diagrams.
There is also a very closely analogy with superstring models. Twistor spaces
replace Calabi-Yau manifolds and the modi cation recipe for Calabi-Yau manifolds
by removal of singularities can be applied to remove self-intersections
of twistor spaces and mirror symmetry emerges naturally. The overall important
implication is that the methods of algebraic geometry used in super-string
theories should apply in TGD framework.
The physical interpretation is totally different in TGD. The landscape is
replaced with twistor spaces of space-time surfaces having interpretation as
generalized Feynman diagrams and twistor spaces as sub-manifolds of P3 F3
replace Witten's twistor strings.
The classical view about twistorialization of TGD makes possible a more
detailed formulation of the previous ideas about the relationship between TGD
and Witten's theory and twistor Grassmann approach.
Keywords: Twistor, twistor space, twistor Grassmannian, twistor
string, Yangian symmetry, non-planarity, positivity, 8-D generalization
of twistor space, octonionic spinor structure.
