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Searching for realistic 4d string models with a Pati–Salam symmetry. Orbifold grand unified theories from heterotic string compactification on a \(Z_{6}\) orbifold. (English) Zbl 1198.81158
Summary: 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 \(2+1\) 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.

MSC:
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
81V22 Unified quantum theories
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