A novel functorial relationship in perturbative quantum field theory is pointed out that associates Feynman diagrams (FD) having no external line in one theory \(\mathbf{Th}_1\) with singlet operators in another one \(\mathbf{Th}_2\) having an additional \(U(\mathcal{N})\) symmetry and is illustrated by the case where \(\mathbf{Th}_1\) and \(\mathbf{Th}_2\) are respectively the rank \(r-1\) and the rank r complex tensor model. The values of FD in \(\mathbf{Th}_1\) agree with the large \(\mathcal{N}\) limit of the Gaussian average of those operators in \(\mathbf{Th}_2\). The recursive shift in rank by this FD functor converts numbers into vectors, then into matrices, then into rank 3 tensors and so on. This FD functor can straightforwardly act on the d dimensional tensorial quantum field theory (QFT) counterparts as well. In the case of rank 2-rank 3 correspondence, it can be combined with the geometrical pictures of the dual of the original FD, namely, equilateral triangulations (Grothendieck’s dessins d’enfant) to form a triality which may be regarded as a bulk-boundary correspondence.

中文翻译：

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张量模型中量子场论中费曼图与算符的对应关系

指出了微扰量子场理论中的一种新的函数关系，即将一个理论\（\ mathbf {Th} _1 \）中没有外线的费曼图（FD ）与另一个\（\ mathbf {Th} _2 \）具有额外的\（U（\ mathcal {N}）\）对称性，并以\（\ mathbf {Th} _1 \）和\（\ mathbf {Th} _2 \）分别为等级的情况加以说明\（r-1 \）和秩r复张量模型。\（\ mathbf {Th} _1 \）中FD的值与\（\ mathbf {Th} _2 \）中这些算子的高斯平均值的较大\（\ mathcal {N} \）限制一致。该FD函子的秩递归移位将数字转换为矢量，然后转换为矩阵，然后转换为3级张量，依此类推。该FD函子也可以直接作用于d维张量量子场论（QFT）的对应物。在2级至3级对应的情况下，可以将其与原始FD对偶的几何图片（即等边三角剖分）（Grothendieck的dessins d'enfant）结合起来，形成可被视为批量的边界对应。