renormalization - How do people go about looking for asymptotic safety in quantum gravity?

Do we have (proposed?) methods to look for fixed points in the renormlaization group flow of the Einstein-Hilbert action? My understanding of the RG is still somewhat sketchy at this point and I am having trouble understanding how one would go about searching for a fixed point in a theory that's non-renormlaizable.

Answer

Here are two papers on the subject:

http://arxiv.org/abs/0805.2909 Investigating the Ultraviolet Properties of Gravity with a Wilsonian Renormalization Group Equation

From the abstract: We review and extend in several directions recent results on the asymptotic safety approach to quantum gravity. The central issue in this approach is the search of a Fixed Point having suitable properties, and the tool that is used is a type of Wilsonian renormalization group equation. We begin by discussing various cutoff schemes, i.e. ways of implementing the Wilsonian cutoff procedure. We compare the beta functions of the gravitational couplings obtained with different schemes, studying first the contribution of matter fields and then the so-called Einstein-Hilbert truncation, where only the cosmological constant and Newton's constant are retained. In this context we make connection with old results, in particular we reproduce the results of the epsilon expansion and the perturbative one loop divergences.

http://arxiv.org/abs/1601.01800 The Gravitational Two-Loop Counterterm is Asymptotically Safe

Abstract: 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 report novel evidence for the validity of this scenario, using functional renormalization group techniques to determine the renormalization group flow of the Einstein-Hilbert action supplemented by the two-loop counterterm found by Goroff and Sagnotti. The resulting system of beta functions comprises three scale-dependent coupling constants and exhibits a non-Gau{\ss}ian fixed point which constitutes the natural extension of the one found at the level of the Einstein-Hilbert action. The fixed point exhibits two ultraviolet attractive and one repulsive direction supporting a low-dimensional UV-critical hypersurface. Our result vanquishes the longstanding criticism that asymptotic safety will not survive once a "proper perturbative counterterm" is included in the projection space.