The Asymptotic Safety Scenario in Quantum Gravity

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 $2+\backslash eps$ expansion, (b) from renormalizable higher derivative gravity theories and a `large $N$' expansion in the number of matter fields, (c) from symmetry reductions modeling the residual selfinteractions in the ultraviolet, 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.