The Asymptotic Safety Scenario in Quantum Gravity -- An Introduction

TL;DR

This paper reviews the asymptotic safety scenario in quantum gravity, discussing evidence from various approaches and emphasizing the role of perturbation theory in establishing a renormalizable, unitary quantum gravity theory with two-dimensional selfinteractions at high energies.

Contribution

It provides a comprehensive overview of evidence supporting asymptotic safety in quantum gravity, integrating multiple theoretical approaches and highlighting the significance of perturbation theory.

Findings

Evidence from 2+ε expansion supports asymptotic safety.

Higher derivative gravity theories and large N expansion are consistent with the scenario.

Flow equations suggest two-dimensional behavior of selfinteractions in the ultraviolet.

Abstract

The asymptotic safety scenario in quantum gravity is reviewed, according to which a renormalizable quantum theory of the gravitational field is feasible which reconciles asymptotically safe couplings with unitarity. All presently known evidence is surveyed: (a) from the 2+\eps expansion, (b) from the perturbation theory of higher derivative gravity theories and a `large N' expansion in the number of matter fields, (c) from the 2-Killing vector reduction, and (d) from truncated flow equations for the effective average action. Special emphasis is given to the role of perturbation theory as a guide to `asymptotic safety'. Further it is argued that as a consequence of the scenario the selfinteractions appear two-dimensional in the extreme ultraviolet. Two appendices discuss the distinct roles of the ultraviolet renormalization in perturbation theory and in the flow equation formalism.