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The asymptotic safety scenario in gravity is accessed within the systematic vertex expansion scheme for functional renormalisation group flows put forward in \cite{Christiansen:2012rx,Christiansen:2014raa}, and implemented in…

Asymptotic safety is a promising mechanism for obtaining a consistent and predictive quantum theory for gravity. The ADM formalism allows to introduce a (Euclidean) time-direction in this framework. It equips spacetime with a foliation…

Asymptotic safety generalizes asymptotic freedom and could contribute to understanding physics beyond the Standard Model. It is a candidate scenario to provide an ultraviolet extension for the effective quantum field theory of gravity…

We study renormalization group equations of quantum gravity in four dimensions. We find an ultraviolet fixed point in accordance with the asymptotic safety conjecture, and infrared fixed points corresponding to general relativity with…

The scaling properties of quantum gravity are discussed by employing a class of proper-time regulators in the functional flow equation for the conformal factor within the formalism of the background field method. Renormalization group…

Weinberg's asymptotic safety scenario provides an elegant mechanism to construct a quantum theory of gravity within the framework of quantum field theory based on a non-Gau{\ss}ian fixed point of the renormalization group flow. In this work…

We highlight how the existence of an ultraviolet completion for interacting Standard-Model type matter puts constraints on the viable microscopic dynamics of asymptotically safe quantum gravity within truncated Renormalization Group flows.…

We analyse the renormalisation group flow of quantum gravity at sixth order in the derivative expansion within the background field approximation. Non-linear field redefinitions are used to ensure that only essential couplings flow. Working…

A new approximation scheme for nonperturbative renormalisation group equations for quantum gravity is introduced. Correlation functions of arbitrarily high order can be studied by resolving the full dependence of the renormalisation group…

The renormalization group flow of unimodular quantum gravity is investigated within two different classes of truncations of the flowing effective action. In particular, we search for non-trivial fixed-point solutions for polynomial…

We present a comprehensive non-perturbative study of the phase structure of the asymptotically safe Standard Model. The physics scales included range from the asymptotically safe trans-Planckian regime in the ultraviolet, the intermediate…

The importance of the proper treatment of the wave function renormalization in the renormalization group analysis of quantum gravity is pointed out. The renormalization factor, sometimes called an inessential coupling, can be used to fix…

A short introduction is given on the functional renormalization group method, putting emphasis on its nonperturbative aspects. The method enables to find nontrivial fixed points in quantum field theoretic models which make them free from…

Form factors constitute the key building block when organising the gravitational dynamics in terms of a curvature expansion. They generalise the concept of momentum-dependent couplings to curved spacetime. Moreover, they may capture…

We report on a recently introduced Functional Renormalization Group (RG) Equation, and we apply it to quantum gravity in Lorentzian spacetimes. While the RG flow is state-dependent, it is possible to evaluate state and background…

Asymptotic Safety constitutes a promising mechanism for a consistent and predictive high-energy completion of the gravitational interactions. To date, most results on the interacting renormalization group fixed point underlying the…

High-energy completeness of quantum electrodynamics (QED) can be induced by an interacting ultraviolet fixed point of the renormalization flow. We provide evidence for the existence of two of such fixed points in the subspace spanned by the…

A new exact renormalization group equation for the effective average action of Euclidean quantum gravity is constructed. It is formulated in terms of the component fields appearing in the transverse-traceless decomposition of the metric. It…

Asymptotic safety is a set of conditions, based on the existence of a nontrivial fixed point for the renormalization group flow, which would make a quantum field theory consistent up to arbitrarily high energies. After introducing the basic…

We study fixed points of quantum gravity with renormalisation group methods, and a procedure to remove convergence-limiting poles from the flow. The setup is tested within the $f(R)$ approximation for gravity by solving exact recursive…