Non-commutativity in Unified Theories and Gravity

Understand

First, we briefly review the Coset Space Dimensional Reduction scheme and the results of the best model so far.

• Then, we present the introduction of fuzzy coset spaces used as extra dimensions and perform a dimensional reduction.
• In turn, we describe a construction which mimics the results of a reduction, starting from a 4-dimensional theory and we present a successful example of a dynamical generation of fuzzy spheres.
• Finally, we propose a construction of the 3-d gravity as a gauge theory on specific non-commutative spaces.