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We show that with suitable choices of parametrization, gauge fixing and cutoff, the anomalous variation of the effective action under global rescalings of the background metric is identical to the derivative with respect to the cutoff, i.e. to the beta functional, as defined by the exact RG equation. The Ward identity and the RG equation can be combined, resulting in a modified...

The “exact” or “functional” renormalization group equation describes the renormalization group flow of the effective average action \(\Gamma _k\). The ordinary effective action \(\Gamma _0\) can be obtained by integrating the flow equation from an ultraviolet scale \(k=\Lambda \) down to \(k=0\). We give several examples of such calculations at one-loop, both in renormalizable...

We employ the exponential parametrization of the metric and a “physical” gauge fixing procedure to write a functional flow equation for the gravitational effective average action in an f(R) truncation. The background metric is a four-sphere and the coarse-graining procedure contains three free parameters. We look for scaling solutions, i.e. non-Gaussian fixed points for the...

We write new functional renormalization group equations for a scalar nonminimally coupled to gravity. Thanks to the choice of the parametrization and of the gauge fixing they are simpler than older equations and avoid some of the difficulties that were previously present. In three dimensions these equations admit, at least for sufficiently small fields, a solution that may be...