标题： 共形场论中模流的互信息 显示英文标题

标题： Mutual information from modular flow in CFTs

摘要： 复制技巧框架下扭曲算符的算符积展开（OPE）能够在共形场论（CFT）中实现互信息（MI）的长距离展开。 在此展开中，各项由主算符标记，因为来自次级算符的贡献可以重新求和到共形块中。 然而，对于互信息，展开涉及到多副本理论中的主算符，这些主算符远多于原始理论中的算符。 在这项工作中，我们开发了一种方法来重新求和这个级数，从而以原始理论的主算符形式进行展开，特别是限制在两份拷贝的扇区中。 这是通过用非局域方式表达不同副本间的扭曲算符，并使用模流表示法获得Rényi指数的n -> 1极限实现的。 我们明确计算了由此产生的“增强型共形块”，令人惊讶的是，它们在整个交叉比范围内对广义自由场的互信息提供了极好的近似。 值得注意的是，在大时空维度的极限情况下，这种近似似乎精确成立。 显示英文摘要

摘要： The operator product expansion (OPE) of twist operators in the replica trick framework enables a long-distance expansion of the mutual information (MI) in conformal field theories (CFTs). In this expansion, the terms are labeled by primary operators, as contributions from descendant operators can be resummed into conformal blocks. However, for the MI, the expansion involves primaries from the multi-replica theory, which includes far more operators than those in the original theory. In this work, we develop a method to resum this series, yielding an expansion in terms of the primaries of the original theory, specifically restricted to the two-copy sector. This is achieved by expressing the twist operators in a non-local manner across different replicas and using a modular flow representation to obtain the n -> 1 limit of the R\'enyi index. We explicitly compute the resulting "enhanced conformal blocks", which, surprisingly, provide excellent approximations to the MI of generalized free fields across the full range of cross ratios. Remarkably, this approximation appears to be exact in the limit of large spacetime dimensions.