Physical renormalization schemes and asymptotic safety in quantum gravity

Abstract

The methods of the renormalization group and the ε-expansion are applied to quantum gravity revealing the existence of an asymptotically safe fixed point in spacetime dimensions higher than two. To facilitate this, physical renormalization schemes are exploited where the renormalization group flow equations take a form which is independent of the parameterisation of the physical degrees of freedom (i.e. the gauge fixing condition and the choice of field variables). Instead the flow equation depends on the anomalous dimensions of reference observables. In the presence of spacetime boundaries we find that the required balance between the Einstein-Hilbert action and Gibbons-Hawking-York boundary term is preserved by the beta functions. Exploiting the ε-expansion near two dimensions we consider Einstein gravity coupled to matter. Scheme independence is generically obscured by the loop-expansion due to breaking of two-dimensional Weyl invariance. In schemes which preserve two-dimensional Weyl invariance we avoid the loop expansion and find a unique ultra-violet (UV) fixed point. At this fixed point the anomalous dimensions are large and one must resum all loop orders to obtain the critical exponents. Performing the resummation a set of universal scaling dimensions are found. These scaling dimensions show that only a finite number of matter interactions are relevant. This is a strong indication that quantum gravity is renormalisable.

Asymptotic safety of quantum gravity beyond Ricci scalars

“…In the same spirit, the role of matter fields on the gravitational fixed point can be explored [81,98,127]. Further directions for improvement include alternative routes for the projection [69], ideas from the resummed -expansion [74], and the role of the background field [88,128]. It would be particularly interesting to clarify how findings persist in settings that distinguish between background and fluctuation fields (see [78,82] for recent progress), or which are manifestly background independent (see [129] for related advances in gauge theories).…”

Asymptotically safe f(R)-gravity coupled to matter I: The polynomial case

“…The bound on α G S reported in (32) may be less stringent though, since the quoted value does not take into account possible contributions from the function f k (R) which can only be computed at the level of solutions. Notably, both sets of conditions (30), (31) and (32), (33) can be met simultaneously. This requires non-zero endomorphism parameters α G S and α G V though.…”

Frame (in)equivalence in quantum field theory and cosmology

“…The explicit construction of the metric is a subtle issue and different approaches can be found in the literature [38][39][40][41][42]. A fundamental restriction on the choice of C ab and η αβ which we can impose is that they must lead to a BRST invariant measure for gauge theories [38].…”