Asymptotic safety in three-dimensional SU(2) Group Field Theory: evidence in the local potential approximation

Understand

We study the functional renormalization group of a three-dimensional tensorial Group Field Theory (GFT) with gauge group SU(2).

• This model generates (generalized) lattice gauge theory amplitudes, and is known to be perturbatively renormalizable up to order 6 melonic interactions.
• We consider a series of truncations of the exact Wetterich--Morris equation, which retain increasingly many perturbatively irrelevant melonic interactions.
• This tensorial analogue of the ordinary local potential approximation allows to investigate the existence of non-perturbative fixed points of the renormalization group flow.