AdS-inspired noncommutative gravity on the Moyal plane

TL;DR

This paper develops a noncommutative gravity model inspired by AdS space using the Moyal plane, employing the Seiberg-Witten map to derive second-order corrections to the Einstein-Hilbert action.

Contribution

It introduces a gauge-theoretic noncommutative gravity framework based on the MacDowell-Mansouri action and computes second-order corrections in the noncommutative parameter.

Findings

First order correction vanishes as expected.

Second order correction is explicitly calculated.

The model reduces to classical gravity in the commutative limit.

Abstract

We consider noncommutative gravity on a space with canonical noncommutativity that is based on the commutative MacDowell-Mansouri action. Gravity is treated as gauge theory of the noncommutative $SO(1,3)_\star$ group and the Seiberg-Witten (SW) map is used to express noncommutative fields in terms of the corresponding commutative fields. In the commutative limit the noncommutative action reduces to the Einstein-Hilbert action plus the cosmological term and the topological Gauss-Bonnet term. After the SW expansion in the noncommutative parameter the first order correction to the action, as expected, vanishes. We calculate the second order correction and write it in a manifestly gauge covariant way.