Existence of realistic heterotic E8×E8 orbifold models with hypercharge from both E8 factors

Determine whether realistic heterotic E8×E8 orbifold compactifications exist in which SU(3)C and SU(2)L are embedded entirely within a single E8 factor (i.e., k3^(2)=k2^(2)=0) while the Standard Model hypercharge U(1)Y is realized as a linear combination of U(1) generators from both E8 factors, obtained via twisted-state Higgsing to a diagonal subgroup, such that the resulting four-dimensional theory reproduces the Standard Model spectrum and couplings.

Background

In order to obtain axion-like particles (ALPs) that couple to photons without a corresponding gluon coupling in heterotic string theory, the Standard Model gauge embedding must typically involve hypercharge receiving contributions from both E8 factors. Orbifold constructions often yield multiple U(1) gauge factors originating from both E8 groups, and twisted states with charges under these U(1)s can Higgs combinations to a diagonal subgroup.

Such a diagonal U(1) in the infrared could be identified with hypercharge, potentially enabling light ALPs that evade the QCD line. However, the literature has predominantly focused on models where the Standard Model is embedded in an SU(5) subgroup, and it is explicitly stated that it is unknown whether a realistic model implementing this specific hypercharge construction has been achieved.