Heterotic E₆ GUTs and partition functions

The E₆ grand unified theory is an attractive candidate intermediate theory between the standard model and string theory. However, only one E₆ grand unified model with three generations and at least one adjoint Higgs field has been derived from string theory in the literature, and this model is phenomenologically unsatisfactory. Recently, in arXiv:1012.1690, we have constructed two new such E₆ grand unified models in heterotic asymmetric orbifolds. Although our new models themselves cannot resolve the unsatisfactory point in the previous model, our discovery raises hopes that one can construct many other such models in this framework and find better models. Here, by giving partition functions explicitly, we explain the details of our construction. Utilizing the lattice engineering technique and the diagonal embedding method, we can construct models systematically. We hope that these techniques and the details of our construction will lead to more phenomenologically desirable models.