Almost-commutative geometries beyond the standard model: III. Vector doublets

We will present a new extension of the standard model of particle physics in its almost-commutative formulation. This extension has as its basis the algebra of the standard model with four summands (Iochum et al 2004 J. Math. Phys. 45 5003 (Preprint hep-th/0312276), Jureit J-H and Stephan C 2005 J. Math. Phys. 46 043512 (Preprint hep-th/0501134), Schuecker T 2005 Krajewski diagrams and spin lifts Preprint hep-th/0501181, Jureit et al 2005 J. Math. Phys. 46 072303 (Preprint hep-th/0503190), Jureit J-H and Stephan C 2006 On a classification of irreducible almost commutative geometries: IV (Preprint hep-th/0610040)), and enlarges only the particle content by an arbitrary number of generations of left-right symmetric doublets which couple vectorially to the U(1)Y x SU(2)w subgroup of the standard model. As in the model presented in Stephan (2007 Almost-commutative geometries beyond the standard model: II. New Colours Preprint hep-th/0706.0595), which introduced particles with a new colour, grand unification is no longer required by the spectral action. The new model may also possess a candidate for dark matter in the hundred TeV mass range with neutrino-like cross section