创造空间的螺母和螺栓
Nuts and Bolts for Creating Space
摘要：
我们讨论的方式，其中场论量组装的三维anti-de Sitter空间（AdS 3）的空间几何。场论成分是边界区间的纠缠熵。AdS 3中的一个点对应于边界区间的一个集合，该集合由我们讨论的变分原理选择。AdS 3中的坐标是所得运动方程的积分常数。我们提出了一个距离函数，这个集合的点，它服从三角形不等式作为一个后果的强次可加性的熵。我们的构造正确地再现了AdS 3的静态切片和测地线和纠缠熵之间的Ryu-Takayanagi关系。我们讨论了这些结果如何扩展到AdS 3的替代物-圆锥形缺陷和BTZ几何形状。在这些情况下，纠缠熵的集合必须由其他的场论量来补充，这些量可以携带关于非最小测地线长度的信息。
英文摘要：
We discuss the way in which field theory quantities assemble the spatial geometry of three-dimensional anti-de Sitter space (AdS3). The field theory ingredients are the entanglement entropies of boundary intervals. A point in AdS3 corresponds to a collection of boundary intervals, which is selected by a variational principle we discuss. Coordinates in AdS3 are integration constants of the resulting equation of motion. We propose a distance function for this collection of points, which obeys the triangle inequality as a consequence of the strong subadditivity of entropy. Our construction correctly reproduces the static slice of AdS3 and the Ryu-Takayanagi relation between geodesics and entanglement entropies. We discuss how these results extend to quotients of AdS3 -- the conical defect and the BTZ geometries. In these cases, the set of entanglement entropies must be supplemented by other field theory quantities, which can carry the information about lengths of non-minimal geodesics.
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