Renormalizable Group Field Theory beyond melonic diagrams: an example in rank four

Understand

We prove the renormalizability of a gauge-invariant, four-dimensional GFT model on SU(2), whose defining interactions correspond to necklace bubbles (found also in the context of new large-N expansions of tensor models), rather than melonic ones, which are not renormalizable in this case.

• The respective scaling of different interactions in the vicinity of the Gaussian fixed point is determined by the renormalization group itself.
• This is possible because the appropriate notion of canonical dimension of the GFT coupling constants takes into account the detailed combinatorial structure of the individual interaction terms.
• This is one more instance of the peculiarity (and greater mathematical richness) of GFTs with respect to ordinary local quantum field theories.