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We discuss motivation and goals of renormalization analyses of group fieldtheory models of simplicial 4d quantum gravity, and review briefly the statusof this research area. We present some new computations of perturbative GFT(spin foam) amplitudes, concerning in particular the scaling behaviour ofradiative corrections to N-point functions. Finally, we single out key openissues and suggest a number of research directions for further progress in thisarea.

Renormalization of group field theories for quantum gravity: new scaling results and some suggestions