**Sie sind hier:**- > Arbeitsgruppe
- > Prof. Dr. Katrin Wendland

In a project with Prof. Ron Donagi we investigate the geometry underlying semi-realistic string models. We are studying the "realistic free fermion models" constructed by Antoniadis, Ellis, Hagelin, Nanopoulos, Faraggi, Yuan, Cleaver and others, and we search for a mathematical understanding of the orbifolds involved.

The paper

On orbifolds and free fermion models

- Journal of Geometry and Physics
**59**(2009), 942-968 - arXiv:0809.0330
- Augsburg Preprint Number 032/2008

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. These orbifolds exhaust all
candidates for geometric interpretations of the realistic free fermion models
mentioned above. Each such orbifold 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
threefolds, an orbifold limit of the Schoen threefold, and several further
orbifolds thereof. Thus we obtain free fermion models with geometric
interpretations on such special threefolds. This may be of considerable
interest in model building, since free fermion models are mathematically rather
simple and hence could dramatically simplify constructions of models on these
threefolds. Indeed, along with our classification scheme this result is
repeatedly used by Vaudrevange and his coworkers in the construction of an MSSM
with three generations. Our classification also fits neatly into the
classification of so-called Calabi-Yau 3-folds of type K proposed by Hashimoto
and Kanazawa.