Exact non-perturbative derivation of gravity’s fine structure constant, the mass of the Higgs and elementary black holes

The paper starts by connecting the η mass problem with partial unification based on the exceptional Lie symmetry groups hierarchy and an extended standard model with octonionic Higgs field as well as ‘t Hooft’s conception of elementary particles as mini black holes. We show that mk and mη as well as the Higgs mass are proportional to the corresponding exceptional Lie symmetry groups hierarchy with the MeV and GeV physical units system as the constant of proportionality. Subsequently, we determine both the super symmetric quantum gravity couplings unification as well as the fine structure constant of gravity non-perturbatively. The consistency of the entire analysis depends crucially on the conception of elementary particles as mini Planckian black holes where the point of total unification is intrinsically fuzzy and the running of the coupling constant stop at the Fuzzy singularity. This mini black hole scenario is behind the E-infinity interpretation of the phenomenon of quarks confinement.