E{sub 6} grand unified theory with three generations from heterotic string theory

We construct two more supersymmetric E{sub 6} grand unified models with three generations within the framework of Z{sub 12} asymmetric orbifold compactification of the heterotic string theory. Such an asymmetric orbifold is missing in the classification in the literature, which concludes that only one E{sub 6} model is possible. In both of the new models, an adjoint Higgs field is obtained in virtue of the diagonal embedding method. This method mods out the three E{sub 6} factors of an even self-dual momentum-lattice by a permutation symmetry. In order to realize the (E{sub 6}){sup 3} even self-dual lattice, we utilize the lattice engineering technique. Among the eight possible orbifold actions in our setup, two lead to new E{sub 6} models. Though these models still share the unsatisfactory issues with the known one, our discovery raises hopes that excellent models that solve all the problems in the supersymmetric grand unified models will be found in this framework.