Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2006-10-05
Class.Quant.Grav.24:R171-230,2007
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
77p, 1 figure; v2: revised and updated; discussion of perturbation theory in higher derivative theories extended. To appear as
Scientific paper
10.1088/0264-9381/24/18/R01
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.
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