AI 中文总结
该研究启动自举程序，通过构造热OPE块的傅里叶变换，推导反演公式，将热OPE数据与推迟关联函数解析结构联系起来，在多种理论中验证，还得到重算子热OPE系数渐近公式，经测试与蒙特卡罗数据吻合。
AI 中文摘要
我们启动了一个自举程序，将热算符乘积展开（OPE）中编码的紫外数据与红外可观测量联系起来，即低频行为和准正则模。从单个热OPE块的KMS对称完备化出发，构造其傅里叶变换，得到在任意空间动量下有效的推迟热关联函数的渐近展开。利用这些结果推导反演公式，将热OPE数据与复频率平面中推迟关联函数的解析结构联系起来。在亚纯性假设下，反演公式用准正则模频率表示OPE系数，得到非平凡的求和规则、对准正则谱的约束及其在大空间动量下的渐近性质。我们在自由理论、二维共形场论、O(N)模型的大N极限和ε展开以及强耦合N = 4 SYM在零空间动量下的R流关联函数中说明了这些结果。作为副产品，我们推导了重算子热OPE系数的通用渐近公式，解决了它们对自旋的依赖并扩展了零空间分离时的先前结果。我们在三维伊辛共形场论中测试了这些公式，发现得到的截断关联函数与蒙特卡罗数据之间有很好的一致性。
英文摘要
We initiate a bootstrap program that relates ultraviolet data, encoded in the thermal OPE, to infrared observables, namely, the low-frequency behavior and quasinormal modes. Starting from KMS-symmetric completions of individual thermal OPE blocks, which play the role of thermal Polyakov blocks, we construct their Fourier transform, yielding an asymptotic expansion of retarded thermal correlators valid at any spatial momentum. We use these results to derive inversion formulae and connect thermal OPE data to the analytic structure of retarded correlators in the complex frequency plane. Under the assumption of meromorphicity, the inversion formulae express OPE coefficients in terms of the quasinormal-mode frequencies, leading to nontrivial sum rules, constraints on the quasinormal spectrum, and its asymptotics at large spatial momentum. We illustrate these results in free theories, two-dimensional CFTs, the large-$N$ limit and $\varepsilon$-expansion of the $\mathrm{O}(N)$ model, and the $R$-current correlator of strongly coupled $\mathcal N = 4$ SYM at zero spatial momentum. As a byproduct, we derive universal asymptotic formulae for thermal OPE coefficients of heavy operators, resolving their dependence on spin and extending previous results at zero spatial separation. We test these formulae in the three-dimensional Ising CFT, finding good agreement between the resulting truncated correlators and Monte Carlo data.
Comments65 pages+ appendices, 8 Figures
