A Topological Formulation of the Standard Model

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 × S which has 23 intrinsic degrees of freedom, discrete Z3 and Z2 × Z3 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 ×S1 ×S1 is then required for a dynamical universe, i.e. a universe which supports forces. Some links with M-theory are pointed out.