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

TL;DR

This paper reviews the Coset Space Dimensional Reduction (CSDR) approach and introduces its extension to fuzzy coset spaces, resulting in a trinification GUT model based on higher-dimensional theories.

Contribution

It extends the CSDR framework to fuzzy coset spaces and constructs a new trinification GUT model within this setting.

Findings

Successful reduction over nearly-Kähler manifold $SU(3)/U(1)×U(1)$

Development of CSDR with fuzzy coset spaces

Construction of a trinification GUT model

Abstract

We first briefly review the Coset Space Dimensional Reduction (CSDR) programme and present the results of the best model so far, based on the $\mathcal{N} = 1$, $d = 10$, $E_8$ gauge theory reduced over the nearly-K\"ahler manifold $SU(3)/U(1)\times U(1)$. Then, we present the adjustment of the CSDR programme in the case that the extra dimensions are considered to be fuzzy coset spaces and then, the best model constructed in this framework, too, which is the trinification GUT, $SU(3)^3$.