Higher-Dimensional Unification with continuous and fuzzy coset spaces as extra dimensions

We first review the Coset Space Dimensional Reduction (CSDR) programme and present the best model constructed so far based on the $\mathcal{N} = 1$, $10$-dimensional $E_8$ gauge theory reduced over the nearly-Kähler manifold $SU(3)/U(1)\times U(1)$ with the additional use of the Wilson flux mechanism. Then we present the corresponding programme in the case that the extra dimensions are considered to be fuzzy coset spaces and the best model that has been constructed in this framework too. In both cases the best model appears to be the trinification GUT $SU(3)^3$.

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