E6 grand unified theory with three generations from heterotic string

TL;DR

This paper constructs two novel supersymmetric E6 grand unified models with three generations using a unique Z12 asymmetric orbifold of heterotic string theory, expanding the landscape of possible GUT models.

Contribution

It introduces a new class of E6 models via asymmetric orbifold compactification, utilizing lattice engineering and diagonal embedding methods, previously unclassified in the literature.

Findings

Two new E6 models with three generations are constructed.

The models utilize a novel asymmetric orbifold and lattice engineering techniques.

The models share some issues with existing models but open avenues for improved GUT theories.

Abstract

We construct two more supersymmetric E6 grand unified models with three generations within the framework of Z12 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 E6 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 E6 factors of an even self-dual momentum-lattice by a permutation symmetry. In order to realize the E6^3 even self-dual lattice, we utilize the lattice engineering technique. Among the eight possible orbifold actions in our setup, two lead to new E6 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.