M⁸-H Duality and the Two Manners to Describe Particles

The 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 super-twistors are realize at the level of M⁸ geometry. These supertwistors are realized at the level of momentum space.

In TGD framework M⁸-H duality allows to geometrize the notion of super-twistor in the sense that different components of super-field correspond to components of super-octonion each of which corresponds to a space-time surfaces satisfying minimal surface equations with string world sheets as singularities - this is geometric counterpart for masslessness.

The progress in understanding of M⁸-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 p-adic 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 p-adic prime characterizing the sparticle causes the mass splitting between members of super-multiplets although the mass formula is same for all of them. Super-octonion 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 p-adic 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 Space-Time Super-Symmetry? or the article Do Supertwistors Make Sense in TGD?.