论文标题
重新归一化的纠缠熵和曲率不变性
Renormalized entanglement entropy and curvature invariants
论文作者
论文摘要
可以使用副本技巧来定义重新归一化的纠缠熵，以进行任何重新归一化方案；全息环境中重新归一化的纠缠熵是根据极端表面重新归一化的区域表示的。在本文中，我们展示了如何以表面的Euler不变和重新归一化的曲率不变性表示全息质量化的纠缠熵。对于奇数CFT中的球形纠缠区域，重新归一化的纠缠熵与全息纠缠表面的Euler不变性成正比，其比例系数捕获了（更拟定的）F量。纠缠熵的变化可以用重新归一化的曲率不变性来优雅地表达，从而促进了纠缠第一定律的一般证据。
Renormalized entanglement entropy can be defined using the replica trick for any choice of renormalization scheme; renormalized entanglement entropy in holographic settings is expressed in terms of renormalized areas of extremal surfaces. In this paper we show how holographic renormalized entanglement entropy can be expressed in terms of the Euler invariant of the surface and renormalized curvature invariants. For a spherical entangling region in an odd-dimensional CFT, the renormalized entanglement entropy is proportional to the Euler invariant of the holographic entangling surface, with the coefficient of proportionality capturing the (renormalized) F quantity. Variations of the entanglement entropy can be expressed elegantly in terms of renormalized curvature invariants, facilitating general proofs of the first law of entanglement.
