Description
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. 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.
Here I will show how applying the renormalization group to tensor fields of rank r in the full, anisotropic cyclic-melonic potential approximation unveils 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.
This talk is based on arxiv.org/abs/2406.01368 with Leonardo Juliano.
