算符乘积展开 = 准正则模
OPE = QNM
AI总结：
研究大N CFTs热态线性响应，揭示OPE与QNM在复时间平面有收敛重叠区，建立二者数据映射，获QNM渐近新解析结果及低泛音QNM数值，表明OPE谱与QNM数据通过求和规则紧密相关，还论证了应力张量关联热化情况。
AI中文摘要：
在微观尺度下，大N共形场论（CFT）热态的线性响应由热算符乘积展开（OPE）支配，而在大尺度下，响应由称为准正则模（QNM）的集体激发支配。我们表明，在混合时间和空间动量坐标中，延迟关联函数的OPE和QNM表示在复时间平面上有一个收敛的重叠区域，给出了OPE和QNM数据之间的映射。我们表明，高泛音QNM渐近与OPE奇点有关，而低泛音QNM数据出现在从短时间到长时间的解析延拓中。使用这种方法，我们获得了QNM渐近的新解析结果，并从史瓦西 - AdS₅黑膜的OPE数据中数值获得低泛音QNM。我们进一步表明，通过在梅林空间中推导的一组求和规则，OPE谱与QNM数据密切相关。最后，使用光锥OPE，我们认为随着共形对撞机边界接近饱和，大空间动量下的应力张量关联热化得更慢。这项工作指向一个新的热自举程序，其中OPE和QNM数据相互约束。
英文摘要：
At microscopic scales the linear response of thermal states of large-$N$ CFTs is governed by a thermal operator product expansion (OPE), while at large scales response is governed by collective excitations known as quasinormal modes (QNM). We show that the OPE and QNM representations of the retarded correlator in mixed time and spatial momentum coordinates have an overlapping region of convergence in the complex time plane, giving a map between OPE and QNM data. We show that large-overtone QNM asymptotics are related to OPE singularities, while low-overtone QNM data appear in analytic continuation from short to large times. Using this approach we obtain new analytic results for QNM asymptotics, and numerically obtain low-overtone QNMs from OPE data for the Schwarzschild-AdS$_5$ black brane. We further show that the OPE spectrum is intimately related to QNM data through a set of sum rules which we derive in Mellin space. Finally, using the lightcone OPE, we argue that stress tensor correlators at large spatial momentum thermalise slower as the conformal collider bounds approach saturation. This work points to a new thermal bootstrap programme where OPE and QNM data constrain each other.
