Anomalous higher order Ward identities in tensorial group field theories without closure constraint

TL;DR

This paper investigates the Ward-Takahashi identities in tensorial group field theories, revealing that for certain complex models with Laplacian kinetic terms, the usual first-order expansion approach is insufficient, indicating more complex underlying structures.

Contribution

The study demonstrates that higher-order Ward identities are necessary for complex tensor models with Laplacian kinetic terms, challenging the adequacy of first-order expansions.

Findings

First-order Ward identities are insufficient for certain tensor models.

Higher-order identities are required to accurately describe these models.

Implications for nonperturbative renormalization in tensorial group field theories.

Abstract

The Ward-Takahashi identities are considered as the generalization of the Noether currents available to quantum field theory and include quantum fluctuation effects. Usually, they take the form of relations between correlation functions, which ultimately correspond to the relation between coupling constants of the theory. For this reason, they play a central role in the construction of renormalized theory, providing strong relations between counter-terms. Since last years, they have been intensively considered in the construction of approximate solutions for nonperturbative renormalization group of tensorial group field theories. The construction of these identities is based on the formal invariance of the partition function under a unitary transformation, and Ward's identities result from a first-order expansion around the identity. Due to the group structure of the transformation under consideration, it is expected that a first-order expansion is indeed sufficient. We show in this article that this does not seem to be the case for a complex tensor theory model, with a kinetic term involving a Laplacian.