The asymptotic safety scenario in quantum gravity: an introduction

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+ǫ 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. * Membre du CNRS.

Gauges and functional measures in quantum gravity I: Einstein theory

“…As an example we may cite the calculation of one-loop divergences in quantum gravity, where it can be shown that there exists a gauge choice for which the coefficient of the logarithmic divergences is zero [21]. Off-shell calculations of beta functions are common in the asymptotic safety approach to quantum gravity [22][23][24], and in such cases one may be interested in minimizing their dependence on the gauge choice.…”

The Renormalization Group flow of unimodular f(R) gravity

“…In the case of gravity, M. Reuter has pioneered the application of the Wetterich equation in [36]. Gravity-specific reviews of the asymptotic safety scenario and the application of the functional Renormalization Group can be found in, e.g., [71][72][73][74][75][76][77][78][79][80].…”

The transfer matrix in four-dimensional CDT

“…A subclass of these geometries is the piecewise linear geometries and a further subclass is the piecewise linear geometries defined by triangulations obtained by gluing together equilateral D-simplices such that they 1 The idea of a time foliation and the fact that there exists a related unitary time evolution are features which CDT shares with Hořava-Lifshitz gravity [6][7][8][9]. However, no spatial higher derivative terms are explicitly added to the action, like in Hořava-Lifshitz gravity, and it is possible that fixed points of the lattice theory can be identified with the non-trivial UV fixed points conjectured in the asymptotic safety scenario suggested by Weinberg [10] and investigated in [11][12][13][14][15][16][17][18][19][20][21][22].…”