We initiate a systematic study of high energy matrix elements of local operators in 2d CFT. Knowledge of these is required in order to determine whether the eigenstate thermalization hypothesis (ETH) can hold in such theories. Most high energy states are high level Virasoro descendants, and by employing an oscillator representation of the Virasoro algebra we develop an efficient method for computing matrix elements of primary operators in such states. In parameter regimes where we expect (e.g. from AdS/CFT intuition) thermalization to occur, we observe striking patterns in the matrix elements: diagonal matrix elements are smoothly varying and off-diagonal elements, while nonzero, are power-law suppressed compared to the diagonal elements. We discuss the implications of these universal properties of 2d CFTs in regard to their compatibility with ETH.

中文翻译：

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量子热化和 Virasoro 对称性

我们开始对 2d CFT 中局部算子的高能矩阵元素进行系统研究。需要了解这些知识才能确定本征态热化假设 (ETH) 在这些理论中是否成立。大多数高能量状态是高级 Virasoro 后代，通过使用 Virasoro 代数的振荡器表示，我们开发了一种有效的方法来计算这种状态下主要算子的矩阵元素。在我们期望（例如从 AdS/CFT 直觉）热化发生的参数范围内，我们观察到矩阵元素中的惊人模式：对角矩阵元素平滑变化，非对角元素非零，与对角线元素。我们讨论了 2d CFT 的这些通用属性在它们与 ETH 的兼容性方面的影响。