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

Abstract

We construct and analyze an $SU(6)\times SU(2)$ 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 Kač-Moody Algebra. Both cases $SU(6)\times SU(2)_{L}$ and $SU(6)\times SU(2)_{R}$ are realized. The model is characterized by the $SU(6)\times SU(2) \to SU(4)\times SU(2)\times SU(2)$ breaking scale $M_X$, and the $SU(4)\times SU(2)\times SU(2) \to SU(3)_{C}\times SU(2)_{L}\times U(1)_{Y}$ breaking scale $M_{R}$ . The spectrum bellow $M_R$ includes an extra pair of charge-1/3 colour-triplets of mass $M_{I}\leq M_{R}$ that does not couple to matter fields and, possibly, an extra pair of isodoublets. Above $M_{X}$ the SU(6) and SU(2) gauge couplings always unify at a scale which can be taken to be the string unification scale $M_{s}\sim 5\times 10^{17} GeV$. 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.