# Ward-constrained melonic renormalization group flow

## TL;DR

This paper introduces a new effective vertex expansion framework for tensorial group field theories, enabling a comprehensive analysis of the renormalization group flow constrained by Ward identities, especially in the ultraviolet regime.

## Contribution

It develops an innovative method to analyze infinite sectors of the theory space, improving upon previous truncation approaches by incorporating Ward identities.

## Key findings

- Provides a complete description of the RG flow in the UV regime.
- Demonstrates the importance of Ward identities in constraining the flow.
- Extends the analysis to infinite sectors of the theory space.

## Abstract

In recent years, some interesting investigations of the non-perturbative renormalization group equations for tensorial group field theories have been done in the truncation method, and completely discarding the Ward identities from their analysis. In this letter, in continuation of our recent series of papers, we present a new framework of investigation, namely the effective vertex expansion, allowing to consider infinite sectors rather than finite dimensional subspaces of the full theory space. We focus on the ultraviolet behavior, and provide a new and complete description of the renormalization group flow constrained with Ward identities.