Non-commutativity in Unified Theories and Gravity

TL;DR

This paper explores the use of fuzzy coset spaces and non-commutative geometry in dimensional reduction and gravity theories, presenting new models and methods for dynamical generation of fuzzy spheres and 3D gravity as a gauge theory.

Contribution

It introduces a novel approach to dimensional reduction using fuzzy coset spaces and constructs a model of 3D gravity as a gauge theory on non-commutative spaces.

Findings

Successful dynamical generation of fuzzy spheres

Construction of 3D gravity as a gauge theory on non-commutative spaces

Extension of coset space dimensional reduction with fuzzy geometries

Abstract

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.