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A Critical Re-examination of M8–H Duality: Part I

Matti Pitkänen


This article is the first part of an article representing a critical re-examination of M8 - H duality, which is one of the cornerstones of Topological Geometrodynamics (TGD). The original version of M8 - H duality assumed that space-time surfaces in M4 can be identified as associative or co-associative surfaces. If the surface has associative tangent or normal space and contains a complex or co-complex surface, it can be mapped to a 4-surface in $H= M4 x CP2. Later emerged the idea that octonionic analyticity realized in terms of real polynomials P algebraically continued to polynomials of complexified octonion could fulfill the dream. The vanishing of the real part ReQ(P)(imaginary part ImQ(P)) in the quaternionic sense would give rise to an associative (co-associative) space-time surface. The realization of the general coordinate invariance motivated the notion of strong form of holography (SH) in H allowing realization of a weaker form of M8 - H duality by assuming that associativity/co-associativity conditions are needed only at 2-D string world sheet and partonic 2-surfaces and possibly also at their light-like 3-orbits.

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