  In the work [Int. J. Theor. Phys. 50, 2819 (2011)], it has been proved that
the radiative corrections of the 2-point function in the SU(2) Boulatov tensor
model generates a relevant (in the Renormalization Group sense) contribution of
the form of a Laplacian. Such a term which was missing in the initial Boulatov
model action should be added in that action before discussing the
renormalization analysis of this model. In this work, by linearizing the group
manifold, we prove that the amplitudes associated with Feynman graphs with
external legs of the colored Boulatov model over U(1)^3 endowed with a
Laplacian dynamics are all convergent. We conjecture that the same feature
happens for the corresponding Boulatov model over SU(2). Higher rank models are
also discussed.
