Topological Dynamics and Grand Unified Theory

TL;DR

This paper proposes a non-perturbative Grand Unified Theory incorporating gravitational phenomena, linking string theory, topology, and cosmology, and predicts a potential dark matter candidate from topological defects.

Contribution

It introduces a novel formalism based on a three-torus for unifying gravity and particle physics, naturally deriving known string properties and cosmological features.

Findings

Derives the Higgs field from the unified theory's equations of motion.

Predicts a scalar topological defect as a dark matter candidate.

Shows the universe's spatial dimension is three under quantum mechanics.

Abstract

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 T^3 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 T^3 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 m_Planck/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.