The Gravitational Two-Loop Counterterm is Asymptotically Safe

TL;DR

This paper provides new evidence supporting Weinberg's asymptotic safety scenario for quantum gravity by demonstrating a non-Gaussian fixed point when including the two-loop counterterm, suggesting a consistent quantum gravity theory.

Contribution

The study extends the asymptotic safety framework by incorporating the two-loop counterterm, showing the existence of a non-Gaussian fixed point with favorable properties.

Findings

Identification of a non-Gaussian fixed point with three scale-dependent couplings.

The fixed point has two UV attractive and one repulsive direction.

Results counter previous criticisms about the stability of asymptotic safety with counterterms.

Abstract

Weinberg's asymptotic safety scenario provides an elegant mechanism to construct a quantum theory of gravity within the framework of quantum field theory based on a non-Gau{\ss}ian fixed point of the renormalization group flow. In this work we report novel evidence for the validity of this scenario, using functional renormalization group techniques to determine the renormalization group flow of the Einstein-Hilbert action supplemented by the two-loop counterterm found by Goroff and Sagnotti. The resulting system of beta functions comprises three scale-dependent coupling constants and exhibits a non-Gau{\ss}ian fixed point which constitutes the natural extension of the one found at the level of the Einstein-Hilbert action. The fixed point exhibits two ultraviolet attractive and one repulsive direction supporting a low-dimensional UV-critical hypersurface. Our result vanquishes the longstanding criticism that asymptotic safety will not survive once a "proper perturbative counterterm" is included in the projection space.