On orbifolds and free fermion constructions

This work develops the correspondence between orbifolds and free fermion models. A complete classification is obtained for orbifolds X/G with X the product of three elliptic curves and G an abelian extension of a group (Z(2))(2) of twists acting on X. Each such quotient X/G is shown to give a geometric interpretation to an appropriate free fermion model, including the geometric NAHE+ model. However, the semi-realistic NAHE free fermion model is proved to be non-geometric: its Hodge numbers are not reproduced by any orbifold X/G. In particular cases it is shown that X/G can agree with some Borcea-Voisin three folds, an orbifold limit of the Schoen threefold, and several further orbifolds thereof This yields free fermion models with geometric interpretations on such special three folds. (C) 2009 Elsevier B.V. All rights reserved.