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

Abstract

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 Re_Q(P)(imaginary part Im_Q(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.