论文标题
OPE系数和欧几里得虫洞的随机统计数据
Random Statistics of OPE Coefficients and Euclidean Wormholes
论文作者
论文摘要
我们提出了一个在混乱的共形场理论中的OPE系数的ANSATZ，该理论概括了本征状热假说，并描述了任何涉及重型操作员作为具有高斯分布的随机变量的OPE系数。在二维中，这个ANSATZ使我们能够计算OPE系数的较高矩，并分析OPE系数的两个和四点函数，这与Genus-2分区函数及其正方形有关。我们将ANSATZ的结果与ADS $ _3 $中的Einstein Gravity解决方案进行了比较，其中包括连接两个属2表面的欧几里得虫洞。我们的Ansatz再现了对虫洞的非扰动校正，从OPE统计上给出了物理解释。我们提出，在半古典的低能引力理论中执行的计算仅对OPE系数的随机性质敏感，这解释了分区函数产物中显然缺乏分解。
We propose an ansatz for OPE coefficients in chaotic conformal field theories which generalizes the Eigenstate Thermalization Hypothesis and describes any OPE coefficient involving heavy operators as a random variable with a Gaussian distribution. In two dimensions this ansatz enables us to compute higher moments of the OPE coefficients and analyse two and four-point functions of OPE coefficients, which we relate to genus-2 partition functions and their squares. We compare the results of our ansatz to solutions of Einstein gravity in AdS$_3$, including a Euclidean wormhole that connects two genus-2 surfaces. Our ansatz reproduces the non-perturbative correction of the wormhole, giving it a physical interpretation in terms of OPE statistics. We propose that calculations performed within the semi-classical low-energy gravitational theory are only sensitive to the random nature of OPE coefficients, which explains the apparent lack of factorization in products of partition functions.
