In this talk, I will combine asymptotically safe quantum gravity and a tensor field theory to exhibit the first example of a theory with gravity and scalar fields in four dimensions which may realize asymptotic safety at a non-vanishing value of the scalar quartic coupling. I will first present (further) evidence that in the asymptotic-safety paradigm, quantum fluctuations of gravity generically screen the quartic couplings in (multi-)scalar models. For a tensor field theory in which the scalar field transforms under an internal O(N)^3 symmetry, this has the effect of replacing asymptotic freedom, recently discovered at large N on a fixed flat background, by an interacting fixed point in the presence of quantum gravity.
