Higher-Dimensional Unified Theories with Fuzzy Extra Dimensions

TL;DR

This paper reviews approaches to constructing unified particle physics models using higher-dimensional gauge theories with fuzzy, non-commutative extra dimensions, highlighting methods of dimensional reduction and dynamical generation.

Contribution

It compares two methods for incorporating fuzzy extra dimensions into unified models, including fermion inclusion and chiral theory construction.

Findings

Dimensional reduction over fuzzy spaces yields realistic four-dimensional models.

Dynamical generation of fuzzy extra dimensions is feasible within four-dimensional gauge theories.

Inclusion of fermions allows for chiral theories in higher-dimensional frameworks.

Abstract

Theories defined in higher than four dimensions have been used in various frameworks and have a long and interesting history. Here we review certain attempts, developed over the last years, towards the construction of unified particle physics models in the context of higher-dimensional gauge theories with non-commutative extra dimensions. These ideas have been developed in two complementary ways, namely (i) starting with a higher-dimensional gauge theory and dimensionally reducing it to four dimensions over fuzzy internal spaces and (ii) starting with a four-dimensional, renormalizable gauge theory and dynamically generating fuzzy extra dimensions. We describe the above approaches and moreover we discuss the inclusion of fermions and the construction of realistic chiral theories in this context.