Beta functions of $U(1)^d$ gauge invariant just renormalizable tensor models

Abstract

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.