Unification Scale, Proton Decay, And Manifolds Of G_2 Holonomy

Models of particle physics based on manifolds of $G_2$ holonomy are in most respects much more complicated than other string-derived models, but as we show here they do have one simplification: threshold corrections to grand unification are particularly simple. We compute these corrections, getting completely explicit results in some simple cases. We estimate the relation between Newton's constant, the GUT scale, and the value of $\alpha_{GUT}$, and explore the implications for proton decay. In the case of proton decay, there is an interesting mechanism which (relative to four-dimensional SUSY GUT's) enhances the gauge boson contribution to $p\to\pi^0e^+_L$ compared to other modes such as $p\to \pi^0e^+_R$ or $p\to \pi^+\bar\nu_R$. Because of numerical uncertainties, we do not know whether to intepret this as an enhancement of the $p\to \pi^0e^+_L$ mode or a suppression of the others.