Supersymmetric Standard Model from the Heterotic String

We present a ${\mathbb{Z}}_6$ orbifold compactification of the ${\mathrm{E}}_8\times {\mathrm{E}}_8$ heterotic string which leads to the (supersymmetric) standard model gauge group and matter content. The quarks and leptons appear as three $\mathbf{16}$-plets of SO(10), whereas the Higgs fields do not form complete SO(10) multiplets. The model has large vacuum degeneracy. For generic vacua, no exotic states appear at low energies and the model is consistent with gauge coupling unification. The top quark Yukawa coupling arises from gauge interactions and is of the order of the gauge couplings, whereas the other Yukawa couplings are suppressed.

Figure 1

${\mathrm{G}}_2\times \mathrm{SU}(3)\times \mathrm{SO}(4)$ torus lattice of a ${\mathbb{Z}}_6\mathrm{\text{−}}\mathrm{II}$ orbifold.

Figure 2

Local gauge symmetries in the SO(4) plane [at the origin in the ${\mathrm{G}}_2$ and SU(3) planes]. Two $\mathbf{16}$-plets arise from the orbifold fixed points.

Figure 3

A 6D orbifold GUT limit with a large SO(4)-plane compactification radius.