Gauge Theories on Fuzzy Spaces and Gravity

TL;DR

This paper reviews gauge theories of gravity, discusses their formulation on noncommutative spaces, and presents recent work constructing gravity as a gauge theory on fuzzy de Sitter space.

Contribution

It introduces a novel approach to formulating gravity as a gauge theory on fuzzy noncommutative spaces, specifically on fuzzy de Sitter space.

Findings

Gravity can be formulated as a gauge theory on fuzzy spaces.

The construction of gravity on fuzzy de Sitter space is demonstrated.

Connections between noncommutative geometry and gravitational theories are explored.

Abstract

We start by briefly reviewing the description of gravity theories as gauge theories in four dimensions. More specifically we recall the procedure leading to the results of General Relativity and Weyl Gravity in a gauge-theoretic manner. Then, after a brief reminder of the formulation of gauge theories on noncommutative spaces, we review our recent work, where gravity is constructed as a gauge theory on the fuzzy $dS_4$.