Renormalizing TGFTs: a 3d example on SU(2)

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I will recall the
main motivations for considering spin foam models in their Group Field Theory
(GFT) versions, which are quantum field theories defined on group manifolds. As
for any other quantum field theory, a fully consistent definition of the latter
must involve renormalization. I will briefly review a specific class of GFTs,
called tensorial, for which progress in this direction has recently been possible.
A new just-renormalizable model, in three dimensions and on the SU(2) group,
will be presented. Interestingly, it includes the geometric constraint of the
Boulatov model, and might as such be related to Euclidean quantum gravity in
three dimensions. Furthermore, this opens the way to a similar analysis of
current 4d gravity spin foam models.