A Topological Formulation of the Standard Model

TL;DR

This paper introduces a topological framework for the Standard Model, deriving particle properties, interactions, and cosmological features from a specific topological manifold with intrinsic degrees of freedom.

Contribution

It presents a novel topological formulation that reproduces Standard Model features, predicts particle masses, and links universe topology to fundamental forces and M-theory.

Findings

Reproduces Standard Model with stable proton and CP violation.

Predicts electron and neutrino masses from topological energy scales.

Connects universe topology to spatial dimension and fundamental forces.

Abstract

A topological theory for the interactions in Nature is presented. The theory derives from the cyclic properties of the topological manifold Q=2T^3 + 3S^1 x S^2 which has 23 intrinsic degrees of freedom, discrete Z_3 and Z_2 x Z_3 internal groups, an SU(5) gauge group, and an anomalous U(1) symmetry. These properties reproduce the standard model with a stable proton, a natural place for CP violation and doublet-triplet splitting. The equation of motion for the unified theory is derived and leads to a Higgs field. The thermodynamic properties of Q are discussed and yield a consistent amplitude for the cosmic microwave background fluctuations. The manifold Q possesses internal energy scales which are independent of the field theory defined on it, but which constrain the predicted mass hierarchy of such theories. In particular the electron and its neutrino are identified as ground states and their masses are predicted. The correct masses of quarks and the CKM mixing angles can be derived as well from these energy scales if one uses the anomalous U(1) symmetry. Furthermore, it is shown that if the Planck scale topology of the universe involves loops as fundamental objects, its spatial dimension is equal to three. The existence of the prime manifold T^3=S^1 x S^1 S^1 is then required for a dynamical universe, i.e. a universe which supports forces. Some links with M-theory are pointed out.