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

This manuscript reports the first order β-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 φ64 and φ56 models. We show in this work that both models are asymptotically free in the UV. © 2013 American Physical Society.