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

TL;DR

This paper explores an $SO(10)$ grand unified theory derived from $M$ theory on $G_2$ manifolds, proposing a novel solution to the doublet-triplet splitting problem and predicting light states detectable at the LHC.

Contribution

It introduces a new approach to doublet-triplet splitting in $SO(10)$ GUTs from $M$ theory, utilizing discrete symmetries and Wilson line breaking to preserve unification.

Findings

Proposes a solution to the doublet-triplet splitting problem.

Predicts light vector-like states with specific quantum numbers.

Maintains gauge unification through extra multiplets.

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.