3D Tensor Field Theory: Renormalization and One-Loop β-Functions

We prove that the rank 3 analogue of the tensor model defined in Ben Geloun and Rivasseau (Commun Math Phys, arXiv:1111.4997 [hep-th], 2012) is renormalizable at all orders of perturbation. The proof is given in the momentum space. The one-loop gamma- and beta-functions of the model are also determined. We find that the model with a unique coupling constant for all interactions and a unique wave-function renormalization is asymptotically free in the UV.