Nontrivial UV behavior of rank-4 tensor field models for quantum gravity

Understand

We investigate the universality classes of rank-4 colored bipartite U(1) tensor field models near the Gaussian fixed point with the functional renormalization group.

• In a truncation that contains all power counting relevant and marginal operators, we find a one-dimensional UV attractor that is connected with the Gaussian fixed point.
• Hence this is first evidence that the model could be asymptotically safe due to a mechanism similar to the one found in the Grosse-Wulkenhaar model, whose UV behavior near the Gaussian fixed point is also described by one-dimensional attractor that contains the Gaussian fixed point.
• However, the cancellation mechanism that is responsible for the simultaneous vanishing of the beta functions is new to tensor models, i.e.