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 [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.