缺乏体纠缠表面：具有de Sitter内部的AdS虫洞
A paucity of bulk entangling surfaces: AdS wormholes with de Sitter interiors
摘要：
我们研究和构建时空，被称为平面AdS-dS-虫洞，满足零能量条件，并有两个渐近AdS边界连接通过一个（不可穿越）膨胀虫洞。对于其他的虫洞，很自然地期望在适当的纠缠态中用两个不连通的CFTs来描述。但对于我们的情况下，某些预期的大块纠缠表面所使用的Hubeny-Rangamani-Takayanagi（HRT）处方计算CFT熵不存在。特别是，没有真正的余维-2极值表面可以从虫洞的一端运行到另一端。根据HRT，任何两个有限大小的子区域（每个CFT中一个）之间的互信息必须在大$N$中的前导阶处消失-尽管作为整体的两个CFT之间的每单位面积的前导阶互信息可能不为零。一些平面AdS-dS-虫洞也没有平面对称的表面来计算CFT的总熵。我们建议这仍然是真实的不太对称的表面，使HRT熵是不明确的，需要一些修改的处方。它可能是简单地延长HRT或密切相关的极大极小结构的限制程序，虽然复杂的极值曲面也可以发挥重要作用。
英文摘要：
We study and construct spacetimes, dubbed planar AdS-dS-wormholes, satisfying the null energy condition and having two asymptotically AdS boundaries connected through a (non-traversable) inflating wormhole. As for other wormholes, it is natural to expect dual descriptions in terms of two disconnected CFTs in appropriate entangled states. But for our cases certain expected bulk entangling surfaces used by the Hubeny-Rangamani-Takayanagi (HRT) prescription to compute CFT entropy do not exist. In particular, no real codimension-2 extremal surface can run from one end of the wormhole to the other. According to HRT, the mutual information between any two finite-sized subregions (one in each CFT) must then vanish at leading order in large $N$ -- though the leading-order mutual information per unit area between the two CFTs taken as wholes may be nonzero. Some planar AdS-dS-wormholes also fail to have plane-symmetric surfaces that would compute the total entropy of either CFT. We suggest this to remain true of less-symmetric surfaces so that the HRT entropy is ill-defined and some modified prescription is required. It may be possible to simply extend HRT or the closely-related maximin construction by a limiting procedure, though complex extremal surfaces could also play an important role.
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