# Progress in the solving nonperturbative renormalization group for tensorial group field theory

## TL;DR

This paper advances the functional renormalization group approach to tensorial group field theory, introducing a new effective vertex expansion method to analyze flow equations and fixed points, with implications for phase transitions.

## Contribution

It introduces the effective vertex expansion method for solving Wetterich flow equations in tensorial group field theory and explores the impact of Ward-Takahashi constraints on fixed points.

## Key findings

- Identification of non-Gaussian fixed points in tensorial models.
- Disappearance of global fixed points when Ward-Takahashi constraints are considered.
- Proposal of an alternative phase transition scenario involving reduced phase space.

## Abstract

This manuscript aims at giving our new advance on the functional renormalization group applied to tensorial group field theory. It is based on a series of our three papers [arXiv:1803.09902], [arXiv:1809.00247] and [arXiv:1809.06081]. We consider the polynomial Abelian $U(1)^d$ models without closure constraint, especially we discuss the case of quartic melonic interaction. We present a new approach to solve the exact Wetterich flow equation called the effective vertex expansion method, and investigate the resulting flow equations, especially about the existence of non-Gaussian fixed points for their connection with phase transitions. To complete this method, we consider a non-trivial constraint arising from the Ward-Takahashi identities, and discuss the disappearance of the global non-trivial fixed points taking into account this constraint. Finally, we argue in favor of an alternative scenario involving a phase transition into the reduced phase space given by the Ward constraint.