AI 中文总结
该研究证明共形场论热有效作用量的定域性给出高温展开的系数关系，可提取a-反常，推广至偶数维CFT并验证，奇数维无类似关系。
AI 中文摘要
任意共形场论（CFT）的自由能$\n\na\n$（$\n\nbeta\n$；$\n\nomega_i\n$）存在两种展开形式：高温（$\n\nbeta\n$→0）与快旋转（$\n\nomega_i\n$→1）展开。我们证明，热有效作用量的定域性迫使$\n\nln Z\n$在高温展开的所有阶次均呈现简单解析形式，且进一步对该展开的系数施加无穷多精确关系；除$\n\nbeta^1\n$阶因外尔（Weyl）反常外，所有关系均为齐次。由此可从配分函数中提取$\n\na\n$-反常。这些关系在快旋转展开中求和后，成为半普适极限及其修正项满足的$\n\nbeta\n$微分方程。我们在多种CFT中验证了这些关系，将其推广至任意偶数维$\n\nd\n$，但未在奇数维$\n\nd\n$中发现类似关系。
英文摘要
The free energy of any CFT, $ \ln Z(β; ω_i)$, admits two expansions: high temperature ($β\rightarrow 0$) and fast rotation ($ω_i \rightarrow 1$). We demonstrate that in $4d$, locality of the thermal effective action forces $\ln Z$ to take a simple analytic form at all orders in the high temperature expansion, and further imposes an infinite number of sharp relations on the coefficients in this expansion. All are homogeneous, except at order $β^1$ due to the Weyl anomaly. From this, the $a$-anomaly can be extracted from the partition function. The relations resum in the fast-spinning expansion into differential equations in $β$ obeyed by the semi-universal limit and its corrections. We verify the relations in a variety of CFTs. We generalize to any even $d$, but find no similar relations at odd $d$.
Comments19 pages, 2 tables; supplemental material included
