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

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 φ46 and φ65 random tensor models. We also deduce that the φ45 tensor model is super-renormalizable. © 2014 Springer-Verlag Berlin Heidelberg.