No Ward-Takahashi identity violation for an Abelian tensorial group field theories with closure constraint

TL;DR

This paper demonstrates that tensorial group field theories with a closure constraint do not violate Ward-Takahashi identities and introduces a new effective vertex expansion to analyze their renormalization group flow.

Contribution

It shows the Ward-Takahashi identity remains trivial under the closure constraint and develops a new expansion method for flow equations in tensorial group field theories.

Findings

Ward-Takahashi identity is trivial due to the closure constraint

New effective vertex expansion closes the flow equations hierarchy

Focus on Wilson-Fisher fixed points in the symmetric phase

Abstract

This paper aims at investigating the nonperturbative functional renormalization group for tensorial group field theories with nontrivial kinetic action and closure constraint. We consider the quartic melonic just-renormalizable $[U(1)]^6$ model and show that due to this closure constraint the first order Ward-Takahashi identity takes the trivial form as for the models with propagators proportional to identity. We then construct the new version of the effective vertex expansion applicable to this class of models, which in particular allows to close the hierarchical structure of the flow equations in the melonic sector. As a consequence, there are no additional constraints on the flow equations, and then we can focus on the existence of the physical Wilson-Fisher fixed-points in the symmetric phase.