Searching for realistic 4d string models with a Pati-Salam symmetry. Orbifold grand unified theories from heterotic string compactification on a Z(6) orbifold

Motivated by orbifold grand unified theories, we construct a class of three-family Pati-Salam models in a Z(6) Abelian symmetric orbifold with two discrete Wilson lines. These models have marked differences from previously-constructed three-family models in prime-order orbifolds. In the limit where one of the six compactified dimensions (which lies in a Z(2) sub-orbifold) is large compared to the string length scale, our models reproduce the supersymmetry and gauge symmetry breaking pattern of 5d orbifold grand unified theories on an S-1/Z(2) orbicircle. We find a horizontal 2 divided by 1 splitting in the chiral matter spectra-2 families of matter are localized on the Z(2) orbifold fixed points. and 1 family propagates in the 5d bulk-and identify them as the first-two and third families. Remarkably. the first two families enjoy a non-Abelian dihedral D-4 family symmetry. due to the geometric setup of the compactified space. In all our models there are always some color triplets. i.e.. (6.1.1) representations of the Pati-Salam group, survive orbifold projections. They could be utilized to spontaneously break the Pati-Salam symmetry to that of the Standard Model. One model. with a 5d E-6 symmetry. may give rise to interesting low energy phenomenology. We study gauge coupling unification. allowed Yukawa couplings and some of their phenomenological consequences. The E-6 model has a renormalizable Yukawa coupling only for the third family. It predicts a gauge-Yukawa unification relation at the 5d compactification scale, and is capable of generating reasonable quark/lepton masses and mixings. Potential problems are also addressed, they may point to the direction for refining our models. (C) 2004 Elsevier B.V. All rights reserved.