String scale unification in an SU(6) × SU(2) GUT

Abstract We construct and analyze an SU(6) × SU(2) GUT. The model is k = 1 string embedable in the sense that we employ only chiral representations allowed at the k = 1 level of the associated Kac-Moody Algebra. Both cases SU(6) × SU(2)L and SU(6) × SU(2)R are realized. The model is characterized by the SU(6) × SU(2) → SU(4) × SU(2) × SU(2) breaking scale MX, and the SU(4) × SU(2) × SU(2) → SU(3)C × SU(2)L × U(1)Y breaking scale MR. The spectrum bellow MR includes an extra pair of charge- 1 3 colour-triplets of mass MI ≤ MR that does not couple to matter fields and, possibly, an extra pair of isodoublets. Above MX the SU(6) and SU(2) gauge couplings always unify at a scale which can be taken to be the string unification scale Ms ∼ 5 × 1017 GeV. The model has Yukawa coupling unification since quarks and leptons obtain their masses from a single Yukawa coupling. Neutrinos obtain acceptably small masses through a see-saw mechanism. Coloured triplets that couple to matter fields are naturally split from the coexisting isodoublets without the need of any numerical fine tuning.