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

Abstract

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