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We prove that the rank 3 analogue of the tensor model defined in[arXiv:1111.4997 [hep-th]] is renormalizable at all orders of perturbation. Theproof is given in the momentum space. The one-loop $\gamma$- and$\beta$-functions of the model are also determined. We find that the model witha unique coupling constant for all interactions and a unique wave functionrenormalization is asymptotically free in the UV.

3D Tensor Field Theory: Renormalization and One-loop $\beta$-functions