A note on the noncommutative correction to gravity

TL;DR

This paper clarifies that noncommutative gravity corrections begin at second order in the NC parameter, resolving previous contradictions and emphasizing the role of symmetries in the vanishing of first order effects.

Contribution

The paper provides a direct computation demonstrating that first order noncommutative gravity corrections vanish, correcting prior reports of leading order effects and highlighting symmetry roles.

Findings

First order NC corrections are zero due to symmetries.

Leading noncommutative corrections start at second order.

Resolved apparent contradiction in the literature.

Abstract

An apparent contradiction in the leading order correction to noncommutative (NC) gravity reported in the literature has been pointed out. We show by direct computation that actually there is no such controvarsy and all perturbative NC corrections start from the second order in the NC parameter. The role of symmetries in the vanishing of the first order correction is manifest in our calculation.