AI 中文总结
该研究证明任意张量模型中melon族大N矩的冗余性，减少张量自举核心半正定矩阵的独立项，相关结论适用于非melon张量模型，简化了张量自举方法。
AI 中文摘要
我们证明了任意张量模型中一类称为melon族的大N矩的冗余性，这减少了构成张量自举核心的半正定矩阵的独立项数量（对于张量模型，已有多种分别推广格点规范理论和随机矩阵自举的半正定Toeplitz矩阵与Hankel矩阵的形式）。更具体地说，我们证明大N下任意melon算子C的期望值仅通过其度数依赖于C，且此处表明melon矩的施温格-戴森方程也满足类似结论。该结果的优势在于其适用范围不限于melon张量模型。
英文摘要
We prove the redundancy of a family (the so-called melonic family) of large-$N$ moments in arbitrary tensor models. This reduces the number of independent entries in the positive semidefinite matrices that build the core of the tensor bootstrap (for tensor models there are already several generalizations of the positive semidefinite Toeplitz and Hankel matrices of lattice gauge theory and random matrix bootstrap, respectively). More concretely, we prove that any melonic operator $C$ at large-$N$ has an expectation value that depends on $C$ exclusively through its degree. A similar statement is shown here to hold for the Schwinger-Dyson equations of melonic moments. The strength of our result is also its scope, which is not limited to melonic tensor models.
Comments25 pp, (too) many figures
