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

TL;DR

This paper applies the functional renormalization group to a rank-4 tensorial group field theory with derivative necklace couplings, revealing a nontrivial ultraviolet fixed point influenced by non-melonic interactions.

Contribution

It extends the analysis of tensorial group field theories beyond melonic interactions by including derivative necklace couplings and identifies a new ultraviolet fixed point.

Findings

Identification of a nontrivial ultraviolet fixed point.

Analysis of non-melonic, necklace-structured interactions.

Planar graph behavior analogous to large-N matrix models.

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.