Three family Z3 orbifold trinification, MSSM and doublet–triplet splitting problem

A Z3 orbifold compactification of E8×E8′ heterotic string is considered toward a trinification SU(3)3 with three light families. The GUT scale VEVs of the SU(2)W×U(1)Y×SU(3)c singlet chiral fields in two sets of the trinification spectrum allow an acceptable symmetry breaking pattern toward MSSM. We show that a doublet–triplet splitting is related to the absence of a ΔB nonzero operator.