标题： 关于$AdS_3$引力中全息环面应力张量关联函数的注记 显示英文标题

标题： Note on holographic torus stress tensor correlators in $AdS_3$ gravity

摘要： 在AdS$_3$/CFT$_2$框架中，欧几里得BTZ黑洞对应其对偶场理论的主导高温相。 我们最初采用微扰方法将爱因斯坦方程作为边界值问题求解，提供能量动量张量算符在低点的关联函数。 利用我们在之前工作中建立的算符方程，我们进一步计算了高温相中能量动量张量算符的任意高点关联函数以及这些高点函数的递归关系。 同时，我们采用Chern-Simons形式推导出一致的结果。 此外，使用截断的AdS/$T\bar{T}$-变形CFT对偶性，我们计算了能量动量张量关联函数，有助于全面理解系统的动力学。 最后，应力张量关联函数使我们能够确定低温下的相应KdV算符关联函数。 显示英文摘要

摘要： In the AdS$_3$/CFT$_2$ framework, the Euclidean BTZ black hole corresponds to the dominant high-temperature phase of its dual field theory. We initially employ perturbative methods to solve the Einstein equations as boundary value problems, providing correlators for the energy-momentum tensor operator at low points. Utilizing operator equations established in our previous work, we further compute arbitrary high-point correlators for the energy-momentum tensor operator in the high-temperature phase and recursive relations for these high-point functions. Concurrently, we employ the Chern-Simons formalism to derive consistent results. Further, using the cut-off AdS/$T\bar{T}$-deformed CFT duality, we calculate the energy-momentum tensor correlators, contributing to the comprehensive understanding of the system's dynamics. Finally, stress tensor correlators enable us to ascertain the corresponding KdV operator correlators at low-temperature.