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 $M_I\le M_R$ 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.

Comments: 15 pages, Latex2e, three figures included, comments added, published version