Higher-Dimensional Unified Theories with Fuzzy Extra Dimensions

Understand

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.