NC $SO(2,3)_\star$ gravity: noncommutativity as a source of curvature and torsion

TL;DR

This paper develops a noncommutative gravity model based on $SO(2,3)_\star$ gauge theory, expanding the action to second order and analyzing its low energy solutions, including corrections to Minkowski space.

Contribution

It introduces a noncommutative gravity framework using $SO(2,3)_\star$ gauge theory and computes the second-order Seiberg-Witten expansion, exploring its low energy implications.

Findings

Derived equations of motion for NC gravity.

Calculated noncommutative corrections to Minkowski space.

Discussed symmetry breaking in the model.

Abstract

Noncommutative (NC) gravity is constructed on the canonical noncommutative (Moyal-Weyl) space-time as a noncommutative $SO(2,3)_\star$ gauge theory. The NC gravity action consists of three different terms: the first term is of Mac-Dowell Mansouri type, while the other two are generalizations of the Einstein-Hilbert action and the cosmological constant term. The expanded NC gravity action is then calculated using the Seiberg-Witten (SW) map and the expansion is done up second order in the deformation parameter. We analyze in details the low energy sector of the full model. We calculate the equations of motion, discuss their general properties and present one solution: the NC correction to Minkowski space-time. Using this solution, we explain breaking of the diffeomorphism symmetry as a consequence of working in a particular coordinate system given by the Fermi normal coordinates.