In this thesis we will address the study of quantum field theories of gravity coupled with matter using the exact renormalization group technique.
In the first part we investigate some aspects of the renormalization group flow of gravity in the presence of fermions.
We calculate the graviton contributions to the beta functions by imposing the cutoffs on the irreducible spin components of the tetrad. In this way we can probe the gauge dependence of the off-shell flow. The results resemble closely those of the metric formalism, except for an increased scheme and (off shell) gauge dependence.
In the second part we discuss the compatibility of minimally coupled matter with asymptotically safe quantum gravity. Within certain approximations we find that for a given number of gauge fields there is a maximal number of scalar and fermion degrees of freedom compatible with an interacting fixed point at positive Newton coupling. The bounds impose severe constraints on the viability of specific matter models.
