M^{8}H Duality and the Two Manners to Describe ParticlesThe chapter TGD view about McKay Correspondence, ADE Hierarchy, Inclusions of Hyperfinite Factors, and Twistors summarizes a considerable in TGD. In twistor Grassmannian approach to N =4 SYM twistors are replaced with supertwistors and the extreme elegance of the description of various helicity states using twistor space wave functions suggests that supertwistors are realize at the level of M^{8} geometry. These supertwistors are realized at the level of momentum space. In TGD framework M^{8}H duality allows to geometrize the notion of supertwistor in the sense that different components of superfield correspond to components of superoctonion each of which corresponds to a spacetime surfaces satisfying minimal surface equations with string world sheets as singularities  this is geometric counterpart for masslessness. The progress in understanding of M^{8}H duality throws also light to the problem whether SUSY is realized in TGD and what SUSY breaking does mean. It is now clear that sparticles are predicted and SUSY remains exact but that padic thermodynamics causes thermal massivation: unlike Higgs mechanism this massivation mechanism is universal and has nothing to do with dynamics. This is due to the fact that zero energy states are superpositions of states with different masses. The selection of padic prime characterizing the sparticle causes the mass splitting between members of supermultiplets although the mass formula is same for all of them. Superoctonion components of polynomials have different orders so that also the extension of rational assignable to them is different and therefore also the ramified primes so that padic prime as one them can be different for the members of SUSY multiplet and mass splitting is obtained. See the chapter Does the QFT Limit of TGD Have SpaceTime SuperSymmetry? or the article Do Supertwistors Make Sense in TGD?.
