Functional Renormalization Group for a Rank-4 Renormalizable Tensorial Group Field Theory with Derivative Necklace Couplings

Abstract

We apply the functional renormalization group to an Abelian Group Field Theory extended beyond the branched-polymer (melonic) sector by including interactions that are subdominant from a power-counting perspective but enhanced by derivative couplings. Focusing on a rank-4 model, we consider a class of non-melonic interactions with a necklace structure. Due to their index contraction pattern, their leading-order behavior is analogous to that of large-N random matrix models and is associated with a planar graph structure. Within this setting, we identify the emergence of a nontrivial ultraviolet fixed point, reminiscent of mechanisms previously observed in matrix models, and discuss its reliability within the present truncation. The robustness of this fixed point will be further investigated through modified Ward identities, following strategies previously developed in the melonic sector.