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

Matti Pitkänen


This article is the second part of an article representing a critical re-examination of M8 - H duality. This re-examination has yielded several surprises. The first surprise was that space-time surfaces in M8 must and can be co-associative so that they can be constructed also as images of a map defined by local G2,c(octonionic automorphisms) transformation applied to co-associative sub-space M4 of complexified octonions Oc in which the complexified octonion norm squared reduces to the real M4 norm squared. An alternative manner to construct them would be as roots for the real part ReQ(P) of an octonionic algebraic continuation of a real polynomial P. The outcome was an explicit solution expressing space-time surfaces in terms of ordinary roots of the real polynomial defining the octonionic polynomials. The equations for ReQ(P)=0 reduce to simultaneous roots of the real polynomials defined by the odd and even parts of P having interpretation as complex values of mass squared mapped to light-cone proper time constant surfaces in H. The second surprise was that space-time surface in M8 can be mapped to H as a whole so that the strong form of holography (SH) is not needed at the level of H being replaced with much stronger number theoretic holography at the level of M8.

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