# Ward-constrained melonic renormalization group flow for the rank-four $\phi^6$ tensorial group field theory

## TL;DR

This paper investigates the renormalization group flow of a rank-four $$phi$^6$ tensorial group field theory, demonstrating the existence of nontrivial fixed points consistent with Ward identities and confirming its asymptotic freedom.

## Contribution

It introduces a Ward-constrained renormalization group analysis for a rank-four $$phi$^6$ tensorial group field theory, revealing fixed points compatible with Ward identities.

## Key findings

- Identifies nontrivial fixed points within the Ward-constrained subspace.
- Shows the model remains asymptotically free.
- Demonstrates compatibility of fixed points with Ward identities.

## Abstract

The nontrivial fixed point discovered for $\phi^4$-marginal couplings in tensorial group field theories have been showed to be incompatible with Ward-Takahashi identities. In this previous analysis we have stated that the case of models with interactions of order greater than four could probably lead to a fixed point compatible with local Ward's identities. In this paper we focus on a rank-4 Abelian $\phi^6$-just renormalizable tensorial group field theory and describe the renormalization group flow over the sub-theory space where Ward constraint is satisfied along the flow, by using an improved version of the effective vertex expansion. We show that this model exhibit a nontrivial fixed points in this constrained subspace. Finally, the well-known asymptotically freedom of this model is highlighted.