论文标题
EFT渐近学：操作员退化的增长
EFT Asymptotics: the Growth of Operator Degeneracy
论文作者
论文摘要
我们建立了有效现场理论中运算符数量的渐近生长（相对于缩放维度）的公式，或在任意时空维度和通用字段内容中等效地等效地等于$ s $ -matrix元素的数量。我们通过概括了由于Meinardus而概括定理并将其应用于Hilbert Series -（运算符子集的分区）的函数。尽管我们的公式是渐近的，但数值实验揭示了EFT扩展中非常低阶的确切结果的显着一致性，包括用于复杂的现象学理论，例如标准模型EFT。我们的方法还揭示了希尔伯特系列中类似相变的行为。我们讨论了收紧界限并为操作员退化的增长以及将希尔伯特系列的分析研究和实用程序扩展到EFT的前景。
We establish formulae for the asymptotic growth (with respect to the scaling dimension) of the number of operators in effective field theory, or equivalently the number of $S$-matrix elements, in arbitrary spacetime dimensions and with generic field content. This we achieve by generalising a theorem due to Meinardus and applying it to Hilbert series -- partition functions for the degeneracy of (subsets of) operators. Although our formulae are asymptotic, numerical experiments reveal remarkable agreement with exact results at very low orders in the EFT expansion, including for complicated phenomenological theories such as the standard model EFT. Our methods also reveal phase transition-like behaviour in Hilbert series. We discuss prospects for tightening the bounds and providing rigorous errors to the growth of operator degeneracy, and of extending the analytic study and utility of Hilbert series to EFT.
