Quantum gravity and spectral running cutoff

We have recently shown that a natural way to implement the Wilsonian paradigm in gauge theories is through the introduction of a “spectral cutoff,” a cut on the eigenvalues of the covariant Laplacian, pointing out that this provides the route toward the renormalization group (RG) construction. Here, we apply this idea to quantum gravity, resorting to two realizations of the spectral running cutoff: “hard” and “smooth.” We derive the RG equations for the Newton and cosmological constant and find the RG pattern of the asymptotic safety scenario, with a non-Gaussian UV-attractive fixed point.