Dependence of Yukawa couplings on the axionic background moduli ofZNorbifolds

The metrical and axionic background moduli which determine a general symmetric ${\mathit{Z}}_{\mathit{N}}$ orbifold model are chosen in such a way that the rotational twist leaves the underlying σ model action invariant. A thorough analysis of this condition is given. We notice that it plays a key role in the evaluation of the four-point correlation functions of ground states which belong to the lowest twisted sectors. Having fixed the normalization of these functions we factorize them with respect to the twisted intermediate channel. This method yields the moduli-dependent part of the twisted sector Yukawa couplings of an orbifoldized heterotic string model. We then perform various discrete mappings (axionic shifts, duality) on the space of background moduli and recognize that the induced linear transformations of the Yukawa couplings are essentially independent of the choice of a specific background. If compensating unitary redefinitions of the twist fields are applied then orbifold models whose backgrounds are related by one of the above mappings cannot be distinguished. For many twist orders we arrive at an explicit form of the phase factors needed to redefine twist fields in order that a general discrete axionic shift can be undone. The requirement of duality invariance is sufficient to determine the moduli dependence of the Yukawa couplings. Hence one may even bypass the evaluation of instanton actions.