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We investigate the ultraviolet behavior of quantum gravity within a functional renormalization group approach. The present setup includes the full ghost and graviton propagators and, for the first time, the dynamical graviton three-point function. The latter gives access to the coupling of dynamical gravitons and makes the system minimally self-consistent. The resulting phase diagram confirms the asymptotic safety scenario in quantum gravity with a nontrivial UV fixed point. A well-defined Wilsonian block spinning requires locality of the flow in momentum space. This property is discussed in the context of functional renormalization group flows. We show that momentum locality of graviton correlation functions is nontrivially linked to diffeomorphism invariance, and is realized in the present setup.
Christiansen et al. (Mon,) studied this question.