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

Abstract

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 G_2,c(octonionic automorphisms) transformation applied to co-associative sub-space M⁴ of complexified octonions O_c 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 Re_Q(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 Re_Q(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.