S. Stefas

Abstract: Based on the observation that the dimension of the tangent space is not necessarily equal to the dimension of the corresponding curved manifold and on the known fact that gravitational theories can be formulated in a gauge theoretic way, we discuss how to describe all known interactions in a unified manner. This is achieved by enlarging the tangent group of the four-dimensional manifold to SO(2, 16), which permits the inclusion of both gauge groups, the one that describes gravity as a gauge theory as well as the SO(10) describing the internal interactions. Moreover it permits the use of both Weyl and Majorana conditions imposed on the fermions, as to avoid the duplication of fermion multiplets of SO(10) appearing in previous attempts. The gravity theory discussed in the present work is the Conformal Gravity which, after a spontaneous symmetry breaking, can lead either to Weyl Gravity or to the usual Einstein Gravity.

TL;DR: In this article , the authors present the construction of fuzzy gravity theories on these non-commutative spaces following the gauge theoretic formulation of gravity, based on the three-and four-dimensional fuzzy spaces.

TL;DR: In this paper , the authors discuss the construction of fuzzy gravity theories based on the gauge-theoretic approach of ordinary gravity, and present a matrix model for the latter in three and four dimensions.