Perturbative Noncommutative Quantum Gravity

TL;DR

This paper investigates perturbative noncommutative quantum gravity, revealing damping effects in non-planar loops, and finds the theory is non-renormalizable beyond one loop without matter, with discussions on nonlocal interactions.

Contribution

It provides a detailed analysis of one-loop corrections in noncommutative quantum gravity and highlights the limitations of renormalizability in this framework.

Findings

Non-planar graviton loops are damped by oscillating factors.

The theory is not renormalizable beyond one loop for matter-free gravity.

Nonlocal gravitational interactions arise from noncommutative spacetime geometry.

Abstract

We study perturbative noncommutative quantum gravity by expanding the gravitational field about a fixed classical background. A calculation of the one loop gravitational self-energy graph reveals that only the non-planar graviton loops are damped by oscillating internal momentum dependent factors. The noncommutative quantum gravity perturbation theory is not renormalizable beyond one loop for matter-free gravity and all loops for matter interactions. Comments are made about the nonlocal gravitational interactions produced by the noncommutative spacetime geometry.