1997/04/14 by Marco Spaans, Spaans, Marco
Computer Science · Physics and Astronomy · #Computability, Logic, AI Algorithms #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Phenomenology (hep-ph) #gr-qc #hep-ph
paper · pdf · doi:10.48550/arxiv.gr-qc/9704036
10 pages, uses elsart
arxiv created 1997/04/14 · openalex publication_date 1997/04/14 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A formalism is presented to construct a non-perturbative Grand Unified Theory when gravitational Planck-scale phenomena are included. The fundamental object on the Planck scale is the three-torus T3 from which the known properties of superstrings, such as the geometric action and duality, follow directly. The low energy theory is 11-dimensional and compactification to a Lorentzian four-manifold is an automatic feature of the unified model. In particular, the simply-connected K3 Calabi-Yau manifold follows naturally from the model and provides a direct link with M-theory. The high energy theory is formulated on a T3 lattice with handles which exhibits the necessary symmetry groups for the standard model, and yields a consistent amplitude for the cosmic microwave background fluctuations. The equation of motion for the supersymmetric, unified theory is derived and leads to the Higgs field. This formulation predicts a remnant, scalar topological defect of mass < 9 mPlanck/46 from the Planck epoch, which is a candidate for dark matter. Finally, it is shown that if the universe is quantum-mechanical, its spatial dimension is equal to three and the laws of nature are Lorentz invariant when gravity can be neglected.