Towards realistic models from Higher-Dimensional theories with Fuzzy extra dimensions

TL;DR

This paper explores models with fuzzy extra dimensions derived from higher-dimensional theories, demonstrating a pathway to realistic four-dimensional gauge theories with grand unification and supersymmetry breaking.

Contribution

It introduces a fuzzy extra-dimensional framework for dimensional reduction, leading to a realistic trinification GUT and MSSM from higher-dimensional super Yang-Mills theories.

Findings

Fuzzy extra dimensions can mimic higher-dimensional behavior at intermediate scales.

A specific model achieves trinification GUT from fuzzy sphere reductions.

The model can spontaneously break to the MSSM at low energies.

Abstract

We briefly review the Coset Space Dimensional Reduction (CSDR) programme and the best model constructed so far and then we present some details of the corresponding programme in the case that the extra dimensions are considered to be fuzzy. In particular, we present a four-dimensional $\mathcal{N} = 4$ Super Yang Mills Theory, orbifolded by $\mathbb{Z}_3$, which mimics the behaviour of a dimensionally reduced $\mathcal{N} = 1$, 10-dimensional gauge theory over a set of fuzzy spheres at intermediate high scales and leads to the trinification GUT $SU(3)^3$ at slightly lower, which in turn can be spontaneously broken to the MSSM in low scales.