  We study a just renormalizable tensorial group field theory of rank six with
quartic melonic interactions and Abelian group U(1). We introduce the formalism
of the intermediate field, which allows a precise characterization of the
leading order Feynman graphs. We define the renormalization of the model,
compute its (perturbative) renormalization group flow and write its expansion
in terms of effective couplings. We then establish closed equations for the two
point and four point functions at leading (melonic) order. Using the effective
expansion and its uniform exponential bounds we prove that these equations
admit a unique solution at small renormalized coupling.
