AI 中文总结
该研究将O(n)模型的味数n视为变量，利用O(n)与Sp(-n)的对偶性，揭示算子标度维数的简并，推导φ^k型算子的两圈反常维数，得到重整化群混合矩阵的新非重整化结果。
AI 中文摘要
将味数n视为O(n)模型中的变量，可得到算子谱的非微扰约束。利用O(n)与Sp(-n)的对偶性，我们将这些关系扩展到n为负偶数的情况，并通过将具有一般味结构的算子分解为不可约表示来明确这些关系。在微扰论中，我们利用该结构揭示不同算子标度维数的新简并，且该简并对任意n均成立。这使我们无需额外圈计算即可从现有结果推导出任意φ^k型算子的两圈反常维数。相同机制决定了重整化群混合矩阵中的模式，在特定算子基中得到新的非重整化结果。我们还讨论了将该框架扩展到算子乘积展开系数间的关系，以及时空维数延拓下渐逝性（evanescence）产生的类似约束。
英文摘要
Treating the number of flavors $n$ as a variable in the $O(n)$ model leads to non-perturbative constraints on the spectrum of operators. Using the duality between $O(n)$ and $Sp(-n)$, we extend these relations to negative even values of $n$ and we make them explicit by decomposing operators with general flavor structure into irreducible representations. In perturbation theory, we exploit this structure to reveal novel degeneracies in the scaling dimensions of different operators, which persist for arbitrary $n$. This allows us to derive the two-loop anomalous dimension of any $ϕ^k$-type operator from existing results without additional loop calculations. The same mechanism dictates patterns in renormalization group mixing matrices, yielding new non-renormalization results in a specific operator basis. We comment on extending this framework to relations between operator product expansion coefficients and to analogous constraints arising from evanescence under continuation in the number of spacetime dimensions.
Comments28 pages, 2 figures, comments are welcome
