Continuum limit in matrix models for quantum gravity from the functional renormalization group

We consider the double-scaling limit in matrix models for two-dimensional quantum gravity, and establish the nonperturbative functional renormalization group as a novel technique to compute the corresponding interacting fixed point of the renormalization group flow. We explicitly evaluate critical exponents and compare them to the exact results. The functional renormalization group method allows a generalization to tensor models for higher-dimensional quantum gravity and to group field theories. As a simple example of how this method works for such models, we compute the leading-order beta function for a colored matrix model that is inspired by recent developments in tensor models.