Supersymmetric Standard Model from the Heterotic String (II)

TL;DR

This work embeds the MSSM within a heterotic string framework by carefully engineering a Z6-II orbifold with local SO(10) GUTs. Quarks and leptons arise as three SO(10) 16-plets, with two localized at fixed points and the third partly twisted, yielding a realistic chiral spectrum and gauge-coupling unification. The model achieves decoupling of exotics through singlet VEVs, supports spontaneous SUSY breaking via hidden-sector gaugino condensation, and accommodates a phenomenologically attractive vacuum family preserving B−L at the GUT scale while producing Froggatt–Nielsen-like Yukawa hierarchies. Top Yukawa coupling originates from gauge interactions, while other Yukawas are suppressed by singlet insertions, offering a concrete ultraviolet completion with testable low-energy textures and proton-stability features.

Abstract

We desribe in detail a Z_6 orbifold compactification of the heterotic E_8 x E_8 string which leads to the (supersymmetric) standard model gauge group and matter content. The quarks and leptons appear as three 16-plets of SO(10), two of which are localized at fixed points with local SO(10) symmetry. The model has supersymmetric vacua without exotics at low energies and is consistent with gauge coupling unification. Supersymmetry can be broken via gaugino condensation in the hidden sector. The model has large vacuum degeneracy. Certain vacua with approximate B-L symmetry have attractive phenomenological features. The top quark Yukawa coupling arises from gauge interactions and is of the order of the gauge couplings. The other Yukawa couplings are suppressed by powers of standard model singlet fields, similarly to the Froggatt-Nielsen mechanism.

Figures (12)

• Figure 1: Twisted and untwisted strings. The dots denote orbifold fixed points.
• Figure 2: $\mathrm{G}_{2} \times \mathrm{SU}(3) \times \mathrm{SO}(4)$ torus lattice of the $\mathbbm{Z}_{6-\mathrm{II}}$ orbifold. Possible Wilson lines are denoted by $W_3$, $W_2$ and $W_2'$.
• Figure 3: $\mathbbm{Z}_{3}$ fixed points.
• Figure 4: $\mathbbm{Z}_{2}$ fixed points.
• Figure 5: The $\mathrm{G}_{2}$ plane. The two simple roots of $\mathrm{G}_{2}$ are given by the arrows in (a) with the shaded area spanned by them being the fundamental region of the torus. The fundamental region of the orbifold is one sixth of this region (darker area) and can be represented by the 'pillow' in (b). The latter corresponds to folding the fundamental region along the dashed edge and gluing the other edges together (cf. Quevedo:1996sv2Hebecker:2003jt).