Functional Renormalization Group analysis of a Tensorial Group Field Theory on R³

We study a model of Tensorial Group Field Theory (TGFT) on R 3 from the point of view of the Functional Renormalization Group (FRG). This is the first attempt to apply a renormalization procedure to a TGFT model defined over a non-compact group manifold. IR divergences (with respect to the metric on R ) coming from the non-compactness of the group are regularised via compactification, and a thermodynamic limit is then taken. We identify then IR and UV fixed points of the RG flow and find strong hints of a phase transition of the TGFT system from a symmetric to a broken or condensate phase in the IR.