The Asymptotic Safety Scenario in Quantum Gravity

Max Niedermaier

Laboratoire de Mathematiques et Physique Theorique
Université de Tours
Parc de Grandmont
37200 Tours, France

Martin Reuter

Institute of Physics
University of Mainz
Staudingerweg 7
55099 Mainz, Germany


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. The evidence from symmetry truncations and from the truncated flow of the effective average action is presented in detail. A dimensional reduction phenomenon for the residual interactions in the extreme ultraviolet links both results. For practical reasons the background effective action is used as the central object in the quantum theory. In terms of it criteria for a continuum limit are formulated and the notion of a background geometry self-consistently determined by the quantum dynamics is presented. Self-contained appendices provide prerequisites on the background effective action, the effective average action, and their respective renormalization flows.