Abstract
For orbifolds with tetrahedral or octahedral point group and embedding of the complete space group in the gauge group, we study simultaneously the conditions for modular invariance to be satisfied, for complete generations of quarks and leptons to survive, and for realistic gauge symmetry breaking to occur either by “Wilson lines” alone or with additional intermediate scale breaking by a 27 + 27 . Models with four complete generations and a realistic gauge group are obtained.
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