Relating Noncommutative SO(2,3) Gravity to the Lorentz-Violating Standard-Model Extension

TL;DR

This paper explores a noncommutative gravity model with broken SO(2,3) symmetry, demonstrating its connection to the Lorentz-violating Standard-Model Extension and analyzing geometric relations at quadratic order.

Contribution

It establishes a detailed link between a noncommutative gravity model and the Standard-Model Extension, focusing on torsion-free and quadratic limits.

Findings

The torsion-free noncommutative gravity model fits within the Standard-Model Extension framework.

Explicit geometric quantities are constructed to quadratic order in metric perturbations.

The relation between broken SO(2,3) symmetry and Lorentz violation is clarified.

Abstract

We consider a model of noncommutative gravity that is based on a spacetime with broken local SO(2,3) symmetry. We show that the torsion-free version of this model is contained within the framework of the Lorentz-violating Standard-Model Extension. We analyze in detail the relation between the torsion-free, quadratic limits of the broken SO(2,3) model and the Standard-Model Extension. As part of the analysis,we construct the relevant geometric quantities to quadratic order in the metric perturbation around a flat background.