Abstract
The asymptotic safety scenario in gravity is accessed within the systematic vertex expansion scheme for functional renormalisation group flows put forward in Christiansen et al. (Phys Lett B 728:114, 2014), Christiansen et al. (Phy Rev D 93:044036, 2016), and implemented in Christiansen et al. (Phys Rev D 92:121501, 2015) for propagators and three-point functions. In the present work this expansion scheme is extended to the dynamical graviton four-point function. For the first time, this provides us with a closed flow equation for the graviton propagator: all vertices and propagators involved are computed from their own flows. In terms of a covariant operator expansion the current approximation gives access to Lambda , R, R^2 as well as R_{mu nu }^2 and higher derivative operators. We find a UV fixed point with three attractive and two repulsive directions, thus confirming previous studies on the relevance of the first three operators. In the infrared we find trajectories that correspond to classical general relativity and further show non-classical behaviour in some fluctuation couplings. We also find signatures for the apparent convergence of the systematic vertex expansion. This opens a promising path towards establishing asymptotically safe gravity in terms of apparent convergence.
Highlights
A consistent formulation of quantum gravity (QG) is an open problem, with many contenders being investigated in great detail
This provides us with a closed flow equation for the graviton propagator: all vertices and propagators involved are computed from their own flows
We have investigated quantum gravity with a vertex expansion and included propagator and vertex flows up to the graviton four-point function
Summary
A consistent formulation of quantum gravity (QG) is an open problem, with many contenders being investigated in great detail. The present approximation allows for the identification of diffeomorphism-invariant structures in the vertex expansion, i.e. R2 and Rμ2 ν tensor structures as well as those of higher derivative invariants This is important for getting access to the number of relevant directions at the asymptotically safe UV fixed point in quantum gravity, 336 Page 2 of 24. As a main result of this paper, we find further significant evidence for a non-trivial UV fixed point in quantum gravity. This fixed point has three relevant directions and two repulsive ones.
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