$SO(10)$ Grand Unification from $M$ theory on a $G_2$ manifold

Abstract

We consider Grand Unified Theories based on $SO(10)$ which originate from $M$ theory on $G_2$ manifolds. In this framework we are naturally led to a novel solution of the doublet-triplet splitting problem involving an extra $\overline{{\bf 16}}_X+{\bf 16}_X$ vector-like pair by considering discrete symmetries of the extra dimensions and preserving unification. Since Wilson line breaking preserves the rank of the gauge group, the necessary $U(1)$ gauge breaking is generated from extra multiplets. The main prediction of the approach is the existence of light states with the quantum numbers of a $\overline{{\bf 16}}_X+{\bf 16}_X$ vector-like pair which could show up in future LHC searches.