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Asymptotic Safety

R. Percacci

TL;DR

The paper addresses the problem of UV completion for quantum gravity and argues that a nonperturbative RG framework, specifically the exact renormalization group equation applied to a scale-dependent effective action $Γ_k$, can reveal a non-Gaussian fixed point that renders gravity asymptotically safe. It surveys derivative-expansion truncations (including Einstein–Hilbert and higher-derivative terms) and reports consistent evidence for a finite-dimensional UV critical surface with UV-attractive directions, suggesting a predictive UV completion. The work highlights that gravitational couplings like the cosmological constant and Newton’s constant run to fixed values at the FP, while higher-derivative couplings become fixed or asymptotically free, and discusses robustness across gauges, cutoffs, and matter content. It also connects these results to other nonperturbative approaches (e.g., lattice methods, CDT) and outlines potential implications for cosmology, black holes, and the nature of spacetime at short distances.

Abstract

Asymptotic safety is a set of conditions, based on the existence of a nontrivial fixed point for the renormalization group flow, which would make a quantum field theory consistent up to arbitrarily high energies. After introducing the basic ideas of this approach, I review the present evidence in favor of an asymptotically safe quantum field theory of gravity.

Asymptotic Safety

TL;DR

The paper addresses the problem of UV completion for quantum gravity and argues that a nonperturbative RG framework, specifically the exact renormalization group equation applied to a scale-dependent effective action , can reveal a non-Gaussian fixed point that renders gravity asymptotically safe. It surveys derivative-expansion truncations (including Einstein–Hilbert and higher-derivative terms) and reports consistent evidence for a finite-dimensional UV critical surface with UV-attractive directions, suggesting a predictive UV completion. The work highlights that gravitational couplings like the cosmological constant and Newton’s constant run to fixed values at the FP, while higher-derivative couplings become fixed or asymptotically free, and discusses robustness across gauges, cutoffs, and matter content. It also connects these results to other nonperturbative approaches (e.g., lattice methods, CDT) and outlines potential implications for cosmology, black holes, and the nature of spacetime at short distances.

Abstract

Asymptotic safety is a set of conditions, based on the existence of a nontrivial fixed point for the renormalization group flow, which would make a quantum field theory consistent up to arbitrarily high energies. After introducing the basic ideas of this approach, I review the present evidence in favor of an asymptotically safe quantum field theory of gravity.

Paper Structure

This paper contains 7 sections, 7 equations, 2 figures.

Table of Contents

  1. Asymptotic Safety
  2. Introduction
  3. The general notion of asymptotic safety
  4. The case of gravity
  5. The Gravitational Fixed Point
  6. Other approaches and applications
  7. Acknowledgements

Figures (2)

  • Figure 1.1: The flow in the upper $\tilde{\Lambda}$--$\tilde{G}$ plane for pure gravity with higher derivative terms at one loop, eq.(1.4.8). All other couplings are set to zero. The nontrivial FP at (0.221,1.389) is UV--attractive with eigenvalues $(-4,-2)$, the one in the origin is UV--attractive along the $\tilde{\Lambda}$ axis with eigenvalue $-2$ and repulsive in the direction of the vector $(1/2\pi,1)$ with eigenvalue $2$.
  • Figure 1.2: The flow in the Einstein--Hilbert truncation, see Eq.(1.4.9-10). The nontrivial FP at $\tilde{\Lambda}=0.171$, $\tilde{G}=0.701$ is UV--attractive with eigenvalues $-1.69\pm 2.49i$. The Gauß ian FP is attractive along the $\tilde{\Lambda}$--axis with eigenvalue $-2$ and repulsive in the direction $(0.04,1.00)$ with eigenvalue $2$.