Degenerate orbifolds

We present evidence for the existence of new four-dimensional string theories, obtained from a smooth variation of background fields in the twisted sectors of symmetric and asymmetric orbifolds. Flat directions only in the untwisted sector are shown to reproduce previously constructed models in terms of Wilson lines, exhibiting a Three-Higgs-Rule (THR). The new models provide a mechanism to lower the rank of the gauge group, lead to more flexible Yukawa couplings and give a strict separation of hidden and observable sectors, which are usually mixed in (2, 0)-models. Even though Fayet-Iliopoulos terms are induced in some of the models due to the presence of anomalous U(1)'s supersymmetry remains, in general, unbroken. Particular examples of the new models correspond to "blown up" versions of (2, 0)-orbifolds.