论文标题
全息纠缠的时空拓扑
Spacetime topology from holographic entanglement
论文作者
论文摘要
连接两个或多个边界的渐近广告几何形状由一个纠缠状态给出，可以在每个CFT的Hilbert空间的乘积基础上扩展，每个CFT生活在边界上。我们得出了一个处方，以计算这种扩展，以描述在任意维度中具有一般空间拓扑的空间的状态。对于大N，扩展与Schmidt分解相吻合，并且系数由特定欧几里得几何形状上的$ N $ - 点相关函数给出。 我们表明，这适用于所有时空，该时期接受了hartle-hawking类型的波功能，通过在空间拓扑上的标准假设，可以（一对一）映射到在渐近边界上定义的CFT状态。还观察到这些状态具有量子相干性能。 将其用作全息工程，可以通过准备双重量子系统的纠缠状态来构建具有某些预定拓扑的新兴空间几何形状。例如，我们应用方法来计算膨胀并表征一个时空，其初始空间拓扑是（属）手柄。
An asymptotically AdS geometry connecting two or more boundaries is given by a entangled state, that can be expanded in the product basis of the Hilbert spaces of each CFT living on the boundaries. We derive a prescription to compute this expansion for states describing spacetimes with general spatial topology in arbitrary dimension. To large N, the expansion coincides with the Schmidt decomposition and the coefficients are given by $n$-point correlation functions on a particular Euclidean geometry. We show that this applies to all spacetime that admits a Hartle-Hawking type of wave functional, which via a standard hypothesis on the spatial topology, can be (one to one) mapped to CFT states defined on the asymptotic boundary. It is also observed that these states are endowed with quantum coherence properties. Applying this as holographic engineering, one can to construct an emergent space geometry with certain predetermined topology by preparing an entangled state of the dual quantum system. As an example, we apply the method to calculate the expansion and characterize a spacetime whose initial spatial topology is a (genus one) handlebody.
