The tensor theory space

The tensor track is a background‐independent discretization of quantum gravity which includes a sum over all topologies. We discuss how to define a functional renormalization group flow and the Wetterich equation in the corresponding theory space. This space is different from the Einsteinian theory space of asymptotic safety. It includes all fixed‐rank tensor‐invariant interactions, hence generalizes matrix models and the (Moyal) non‐commutative field theory space.