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We give the complete twisted Yukawa couplings for all the Z n orbifold constructions in the most general case, i.e. when orbifold deformations are considered. This includes a certain number of tasks. Namely, determination of the allowed couplings, calculation of the explicit dependence of the Yukawa couplings values on the moduli expectation values (i.e. the parameters determining the size and shape of the compactified space), etc. The final expressions are completely explicit, which allows a counting of the different Yukawa couplings for each orbifold (with and without deformations). This knowledge is crucial to determine the phenomenological viability of the different schemes, since it is directly related to the fermion mass hierarchy. Other facts concerning the phenomenological profile of Z n orbifolds are also discussed, e.g. the existence of nondiagonal entries in the fermion mass matrices, which is related to a nontrivial structure of the Kobayashi-Maskawa matrix. Some theoretical results are also given, e.g. the non-participation of (1,2) moduli in twisted Yukawa couplings. Likewise, (1,1) moduli associated with fixed tori which are involved in the Yukawa coupling, do not affect the value of the coupling. We discuss the relevance of these facts for the supersymmetry breaking process.
Casas et al. (Sat,) studied this question.