  This manuscript reports the first order $\beta$-functions of recently proved
just renormalizable random tensor models endowed with a $U(1)^d$ gauge
invariance [arXiv:1211. 2618]. The models that we consider are polynomial
Abelian $\vp^4_6$ and $\vp^6_5$ models. We show in this work that both models
are asymptotically free in the UV.
