Just Renormalizable TGFT's on U(1)^d with Gauge Invariance

Abstract

We study the polynomial Abelian or U(1)^d Tensorial Group Field Theories equipped with a gauge invariance condition in any dimension d. From our analysis, we prove the just renormalizability at all orders of perturbation of the phi^4_6 and phi^6_5 random tensor models. We also deduce that the phi^4_5 tensor model is super-renormalizable.Comment: 33 pages, 22 figures. One added paragraph on the different notions of connectedness, preciser formulation of the proof of the power counting theorem, more general statements about traciality of tensor graph