  We identify new families of renormalizable of tensor models from anterior
renormalizable tensor models via a mapping capable of reducing or increasing
the rank of the theory without having an effect on the renormalizability
property. Mainly, a version of the rank 3 tensor model as defined in
[arXiv:1201.0176 [hep-th]], the Grosse-Wulkenhaar model in 4D and 2D generate
three different classes of renormalizable models. The proof of the
renormalizability is fully performed for the first reduced model. The same
procedure can be applied for the remaining cases. Interestingly, we find that,
due to the peculiar behavior of anisotropic wave function renormalizations, the
rank 3 tensor model reduced to a matrix model generates a simple
super-renormalizable vector model.
