Two- and four-loop β-functions of rank-4 renormalizable tensor field theories

A recent rank-4 tensor field model generating 4D simplicial manifolds has been proved to be renormalizable at all orders of perturbation theory (Ben Geloun and Rivasseau 2011 arXiv:1111.4997 [hep-th]). The model is built out of ϕ6 (ϕ6(1/2)), ϕ4 (ϕ4(1)) interactions and an anomalous term (ϕ4(2)). The β-functions of this model are evaluated at two and four loops. We find that the model is asymptotically free in the UV for both the main ϕ6(1/2) interactions, whereas it is safe in the ϕ4(1) sector. The remaining anomalous term turns out to possess a Landau ghost. (paper)