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 (SME). 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.
Highlights
While noncommutative geometry has been studied for more than 70 years [1], it has been especially popular as a possible framework for physics beyond the Standard Model in recent decades [2,3]
Any physical model that includes noncommutative effects and that reduces to conventional physics in the proper limit is expected to break Lorentz symmetry [13]
We argue that the noncommutative SO(2,3)? gravity model fits into the gravitational sector of the Standard-Model Extension (SME)
Summary
While noncommutative geometry has been studied for more than 70 years [1], it has been especially popular as a possible framework for physics beyond the Standard Model in recent decades [2,3]. Numerous experimental and observational limits exist already on many different a priori independent types of Lorentz violation [19] This effective-field-theory framework should contain any realistic noncommutative model. Gravity model fits into the gravitational sector of the Standard-Model Extension (SME) This serves as an example of the general notion that the SME contains all specific action-based Lorentz-violating models. [12] and we present the relevant results here This theory may be expressed as a model with noncommutative local SO(1,3)? If the vierbein satisfies the usual compatibility condition ∇γ eα a = 0, the adjusted covariant derivative may be expressed as e γ eα a = Γρ γα eρ a This implies the explicit appearance of the Christoffel symbols in the Lagrangian, the consequences of which are discussed . We will assume that terms involving derivatives of θ μν that may appear in a more-realistic model are negligible in comparison to all other terms
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