Fixed-Functionals of three-dimensional Quantum Einstein Gravity

TL;DR

This paper investigates the non-perturbative renormalization group flow of three-dimensional f(R)-gravity within Quantum Einstein Gravity, identifying fixed points and analyzing their properties to support the Asymptotic Safety scenario.

Contribution

It derives an exact PDE for the RG flow of f(R) in 3D quantum gravity and finds fixed points with finite UV-critical hypersurfaces, advancing the understanding of Asymptotic Safety.

Findings

Existence of scale-independent solutions generalizing RG fixed points.

Solutions are bounded and have positive kinetic terms.

Finite-dimensional UV-critical hypersurfaces despite infinite couplings.

Abstract

We study the non-perturbative renormalization group flow of f(R)-gravity in three-dimensional Asymptotically Safe Quantum Einstein Gravity. Within the conformally reduced approximation, we derive an exact partial differential equation governing the RG-scale dependence of the function f(R). This equation is shown to possess two isolated and one continuous one-parameter family of scale-independent, regular solutions which constitute the natural generalization of RG fixed points to the realm of infinite-dimensional theory spaces. All solutions are bounded from below and give rise to positive definite kinetic terms. Moreover, they admit either one or two UV-relevant deformations, indicating that the corresponding UV-critical hypersurfaces remain finite dimensional despite the inclusion of an infinite number of coupling constants. The impact of our findings on the gravitational Asymptotic Safety program and its connection to new massive gravity is briefly discussed.