论文标题
在OPE极限中相互信息的形状依赖性：线性响应
Shape dependence of mutual information in the OPE limit: linear responses
论文作者
论文摘要
相互信息是子系统组件之间相关性的重要度量。在量子场理论（QFTS）的框架中，它们比纠缠熵更好的紫外线行为，因此可以更直接地访问纠缠结构的普遍方面。在本文中，我们研究了形状响应在形状变形下的形状变形，在两个半径$ r $的两个球体之间，由大距离$ l \ gg r $或合并等效的配置之间的两个半径$ r $之间的真空响应。我们的计算利用了先前的OPE结果来获取共同信息\ cite {faulkner2016aug}和相关的模块化汉密尔顿\ cite {faulkner2021aug}。特别是，我们应用纠缠第一定律来计算其中一个球体形状变形下相互信息的线性响应。我们发现，线性响应对选定的OPE贡献表现出高度的通用性。我们证明了与设置相关的“小组”对称性。我们的结果意味着，球形互信息超过了对称组下非零模式的形状变形。
Mutual information serves as an important measure of correlation between subsystem components. In the framework of quantum field theories (QFTs) they have better regulated UV behavior than entanglement entropy, and thus provide more direct access to universal aspects of entanglement structures. In this paper, we study the linear responses under shape deformation of the mutual information in the conformal field theory (CFT) vacuum between two spheres of radius $R$ separated by large distance $L\gg R$ or conformally equivalent configurations. Our calculations make use of the previous OPE results for mutual information \cite{Faulkner2016Aug} and the associated modular Hamiltonian \cite{Faulkner2021Aug}. In particular, we apply the entanglement first law to compute the linear responses of mutual information under shape deformation on one of the spheres. We find that the linear responses exhibit a high degree of universality for a selected class of OPE contributions. We demonstrate that there is a "little group" of symmetries associated with the set-up. Our result implies that the spherical mutual information is extremal over shape deformations of non-zero modes under the symmetry group.
