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. We prove the just renormalizability at all orders of perturbation of the ϕ4 6 and ϕ6 5 random tensor models. We also deduce that the ϕ4 5 tensor model is super-renormalizable.