  This article provides a Wilsonian description of the perturbatively
renormalizable Tensorial Group Field Theory introduced in arXiv:1303.6772
[hep-th] (Commun. Math. Phys. 330, 581-637). It is a rank-3 model based on the
gauge group SU(2), and as such is expected to be related to Euclidean quantum
gravity in three dimensions. By means of a power-counting argument, we
introduce a notion of dimensionality of the free parameters defining the
action. General flow equations for the dimensionless bare coupling constants
can then be derived, in terms of a discretely varying cut-off, and in which all
the so-called melonic Feynman diagrams contribute. Linearizing around the
Gaussian fixed point allows to recover the splitting between relevant,
irrelevant, and marginal coupling constants. Pushing the perturbative expansion
to second order for the marginal parameters, we are able to determine their
behaviour in the vicinity of the Gaussian fixed point. Along the way, several
technical tools are reviewed, including a discussion of combinatorial factors
and of the Laplace approximation, which reduces the evaluation of the
amplitudes in the UV limit to that of Gaussian integrals.
