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#### Renormalizable Group Field Theory beyond melons: an example in rank four

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##### Citation

Carrozza, S., Lahoche, V., & Oriti, D. (2017). Renormalizable Group Field Theory
beyond melons: an example in rank four.* Physical Review D,* *96*:
066007. doi:10.1103/PhysRevD.96.066007.

Cite as: https://hdl.handle.net/11858/00-001M-0000-002D-0A33-5

##### Abstract

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 of
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. We also explore the renormalization group flow of the model at the
non-perturbative level, using functional renormalization group methods, and
identify a non-trivial fixed point in various truncations. This model is
expected to have a similar structure of divergences as the GFT models of 4d
quantum gravity, thus paving the way to more detailed investigations on them.