Noncommutative deformation of four dimensional Einstein gravity

TL;DR

This paper develops a four-dimensional noncommutative gravity model that reduces to Einstein gravity in the commutative limit, using a gauge formulation with constraints and the Seiberg-Witten map to derive first-order corrections.

Contribution

It introduces a novel gauge-based noncommutative gravity model that correctly deforms Einstein gravity and explicitly computes first-order noncommutative corrections.

Findings

The model reduces to Einstein-Hilbert action in the commutative limit.

Explicit first-order noncommutative corrections to gravity are derived.

The choice of gauge group and constraints is crucial for correct deformation.

Abstract

We construct a model for noncommutative gravity in four dimensions, which reduces to the Einstein-Hilbert action in the commutative limit. Our proposal is based on a gauge formulation of gravity with constraints. While the action is metric independent, the constraints insure that it is not topological. We find that the choice of the gauge group and of the constraints are crucial to recover a correct deformation of standard gravity. Using the Seiberg-Witten map the whole theory is described in terms of the vierbeins and of the Lorentz transformations of its commutative counterpart. We solve explicitly the constraints and exhibit the first order noncommutative corrections to the Einstein-Hilbert action.