Does M8-H Duality Reduce Classical TGD to Octonionic Algebraic Geometry? (Part I)

Abstract

TGD leads to several proposals for the exact solution of field equations defining space-time surfaces as preferred extremals of twistor lift of Kahler action. So called M⁸-H duality is one of these approaches. The beauty of M⁸-H duality is that it could reduce classical TGD to algebraic geometry and would immediately provide deep insights to cognitive representation identified as sets of rational points of these surfaces.

In part I of this two-part article, I shall consider the following topics: (1) Basic notions of algebraic geometry such as algebraic variety, surface, and curve; (2) Redution of M⁸-H duality to octonionic algebraic geometry; (3) Products of polynomials as correlates for free many-particle states with interactions described by added interaction polynomial; (4) Discussions of the octonionic polynomials with real coefficients giving rise to associative (co-associative) surfaces as the zero loci of their  real part ; (5) Generalization of Cauchy-Riemann conditions for complex analytic functions to quaternions and octonions; and (6) Polynomials with  universal dynamics of criticality.