  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. it
does not occur in vector or matrix models.
