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.

中文翻译：

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无闭包约束的张量群场论中的异常高阶 Ward 恒等式


Ward-Takahashi 恒等式被认为是量子场论可用的 Noether 电流的推广，包括量子涨落效应。通常，它们采用相关函数之间关系的形式，最终对应于理论的耦合常数之间的关系。因此，它们在重构理论的构建中发挥着核心作用，在反项之间提供了牢固的关系。自去年以来，在张量群场论的非扰动重整化群的近似解的构建中，它们被深入考虑。这些恒等式的构造是基于幺正变换下分区函数的形式不变性，而 Ward 的恒等式是围绕恒等式的一阶扩展的结果。由于正在考虑的转换的组结构，预计一阶扩展确实足够了。我们在本文中表明，对于复杂的张量理论模型来说，情况似乎并非如此，其中的动力学项涉及拉普拉斯算子。