  We develop the functional renormalization group formalism for a tensorial
group field theory with closure constraint, in the case of an Abelian just
renormalizable model with quartic interactions. The method allows us to obtain
a closed but non-autonomous system of differential equations which describe the
renormalization group flow of the couplings beyond perturbation theory. The
explicit dependence of the beta functions on the running scale is due to the
existence of an external scale in the model, the radius of the unit circle. We
study the occurrence of fixed points and their critical properties in two
different approximate regimes, corresponding to the deep UV and deep IR.
Besides confirming the asymptotic freedom of the model, we find also a
non-trivial fixed point, with one relevant direction. Our results are
qualitatively similar to those found previously for a rank-3 model without
closure constraint, and it is thus tempting to speculate that the presence of a
Wilson-Fisher-like fixed point is a general feature of asymptotically free
tensorial group field theories.
