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The Ward-Takahashi identities are considered as the generalization of theNoether currents available to quantum field theory and include quantumfluctuation effects. Usually, they take the form of relations betweencorrelation functions, which ultimately correspond to the relation betweencoupling constants of the theory. For this reason, they play a central role inthe construction of renormalized theory, providing strong relations betweencounter-terms. Since last years, they have been intensively considered in theconstruction of approximate solutions for nonperturbative renormalization groupof tensorial group field theories. The construction of these identities isbased on the formal invariance of the partition function under a unitarytransformation, and Ward's identities result from a first-order expansionaround the identity. Due to the group structure of the transformation underconsideration, it is expected that a first-order expansion is indeedsufficient. We show in this article that this does not seem to be the case fora complex tensor theory model, with a kinetic term involving a Laplacian.

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