On the physical mechanism underlying Asymptotic Safety

TL;DR

This paper uncovers a physical mechanism behind Asymptotic Safety in Quantum Einstein Gravity, highlighting the dominance of paramagnetic interactions over diamagnetic ones in driving antiscreening effects in spacetime dimensions above three.

Contribution

It identifies the paramagnetic interactions as the key factor in gravitational antiscreening and clarifies the beta function behavior of Newton's constant in 2+ε dimensions.

Findings

Paramagnetic interactions dominate in dimensions above 3.

Spacetimes in QEG behave as a polarizable medium with paramagnetic response.

Resolved the longstanding puzzle of Newton's constant beta function in 2+ε dimensions.

Abstract

We identify a simple physical mechanism which is at the heart of Asymptotic Safety in Quantum Einstein Gravity (QEG) according to all available effective average action-based investigations. Upon linearization the gravitational field equations give rise to an inverse propagator for metric fluctuations comprising two pieces: a covariant Laplacian and a curvature dependent potential term. By analogy with elementary magnetic systems they lead to, respectively, dia- and paramagnetic-type interactions of the metric fluctuations with the background gravitational field. We show that above 3 spacetime dimensions the gravitational antiscreening occurring in QEG is entirely due to a strong dominance of the ultralocal paramagnetic interactions over the diamagnetic ones that favor screening. (Below 3 dimensions both the dia- and paramagnetic effects support antiscreening.) The spacetimes of QEG are interpreted as a polarizable medium with a "paramagnetic" response to external perturbations, and similarities with the vacuum state of Yang-Mills theory are pointed out. As a by-product, we resolve a longstanding puzzle concerning the beta function of Newton's constant in 2+{\epsilon} dimensional gravity.