Supersymmetric exceptional gauge unification

Abstract

We discuss the accommodation of quark-lepton generations, classified by SU(5), in the adjoint representations of simple Lie groups. We find SO(11), E/sub 6/, E/sub 7/, and E/sub 8/ as the only possible embedding groups, with the respective contents of one, one, three, and five conventional generations, together with their (V+A) conjugates and other particles. SU(4) supersymmetric unification models based on these gauge groups and which unify, via one coupling constant, the interactions of one vector boson, four spin-1/2 fermion, and six Higgs scalar multiplets, all being in the adjoint representation, are considered. Attention is focused on E/sub 7/ and E/sub 8/. The latter algebras are represented in the familiar SU(8) and SU(9) basis. We discuss quark-lepton assignments and propose patterns of symmetry breaking which can be triggered by the adjoint Higgs scalars, and which are compatible with the observed values of the strong and the weak couplings, as well as the weak mixing angle. Remarks are given with regard to the breaking of supersymmetry and the possible role of radiative corrections and renormalization effects in generating the gauge hierarchy.