Generalizations of vector field theories to tensors allow to similarly apply large-N techniques but find a richer though often still tractable structure. Generating discrete geometries via their perturbative series, they are furthermore candidates for Quantum Gravity covering in particular the Group-Field Theory definition of Spin-Foam models. However, the potential of such tensor theories has not been fully exploited since only a symmetry-reduced ``isotropic'' part of their phase space has been studied so far.
In this talk I will show how applying the functional renormalization group to tensor fields of rank r in the full, anisotropic cyclic-melonic potential approximation unveals a plethora of new non-Gaussian fixed points. From the Quantum-Gravity perspective, these fixed points correspond to continuum limits of distinguished ensembles of triangulations raising hope to find new classes of continuum geometry in this way.
