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

• Received 1 April 2013

DOI:https://doi.org/10.1103/PhysRevD.88.105003