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

TL;DR

This paper reviews the Coset Space Dimensional Reduction (CSDR) approach and introduces a fuzzy coset space framework, demonstrating that the trinification GUT $SU(3)^3$ emerges as the best model in both cases.

Contribution

It extends the CSDR programme to fuzzy coset spaces, showing the trinification GUT as a consistent model in this new setting.

Findings

The best model in both frameworks is the trinification GUT $SU(3)^3$.

Fuzzy coset spaces can be used as extra dimensions in gauge theories.

The approach unifies continuous and fuzzy extra dimensions in model building.

Abstract

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-K\"ahler 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 $SU(3)^3$.