Ultraviolet Fixed Point and Generalized Flow Equation of Quantum Gravity

TL;DR

This paper develops a new exact renormalization group equation for Euclidean quantum gravity, investigates its fixed points, and provides evidence that 4D Einstein gravity is asymptotically safe with potential dimensional reduction at small scales.

Contribution

It introduces a novel flow equation for quantum gravity, analyzes fixed points in the Einstein-Hilbert truncation, and supports the asymptotic safety scenario for 4D gravity.

Findings

Discovery of Gaussian and non-Gaussian fixed points.

Evidence for nonperturbative renormalizability of 4D Einstein gravity.

Indications of dimensional reduction at sub-Planckian scales.

Abstract

A new exact renormalization group equation for the effective average action of Euclidean quantum gravity is constructed. It is formulated in terms of the component fields appearing in the transverse-traceless decomposition of the metric. It facilitates both the construction of an appropriate infrared cutoff and the projection of the renormalization group flow onto a large class of truncated parameter spaces. The Einstein-Hilbert truncation is investigated in detail and the fixed point structure of the resulting flow is analyzed. Both a Gaussian and a non-Gaussian fixed point are found. If the non-Gaussian fixed point is present in the exact theory, quantum Einstein gravity is likely to be renormalizable at the nonperturbative level. In order to assess the reliability of the truncation a comprehensive analysis of the scheme dependence of universal quantities is performed. We find strong evidence supporting the hypothesis that 4-dimensional Einstein gravity is asymptotically safe, i.e. nonperturbatively renormalizable. The renormalization group improvement of the graviton propagator suggests a kind of dimensional reduction from 4 to 2 dimensions when spacetime is probed at sub-Planckian length scales.