Beta functions ofU(1)dgauge invariant just renormalizable tensor models

Abstract

This manuscript reports the first order $\ensuremath{\beta}$-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 ${\ensuremath{\varphi}}_{6}^{4}$ and ${\ensuremath{\varphi}}_{5}^{6}$ models. We show in this work that both models are asymptotically free in the UV.