arXiv 2606.045752026-06-03hep-thgr-qc

对称轨道面CFT中的涌现封闭宇宙

Emergent Closed Universes in Symmetric Orbifold CFTs

Kyoto University（京都大学）；Rikkyo University（立教大学）；Nagoya University（名古屋大学）

Akihiro Miyata, Keigo Horikoshi, Hiromasa Tajima, Tomonori Ugajin

备注：: 42 pages

AI总结：

通过研究具有全息对偶的大N对称轨道面CFT，发现希尔伯特空间分解为按占据数分布标记的超选择扇区，其中最大熵扇区展现出封闭宇宙的特征，包括纯态与混合态在简单关联函数上的不可区分性以及超有限II$_1$型冯·诺依曼代数，而S_N规范约束后物理希尔伯特空间维度呈多项式增长，重现了虫洞引力路径积分的结果。

摘要：

我们在具有全息对偶的大$N$对称轨道面CFT中识别出封闭宇宙扇区。从由种子理论的有限维低能子空间构建的张量积态出发，我们展示了在未施加轨道面规范约束时，大$N$希尔伯特空间分解为由占据数分布标记的超选择扇区，这些扇区具有指数大的维度，且最大熵扇区在未规范希尔伯特空间中占主导。我们认为该扇区展现出封闭宇宙希尔伯特空间预期的几个特征：在简单关联函数层面上纯态与混合态不可区分，且相关的算子代数自然是一个超有限II$_1$型冯·诺依曼代数。然后我们施加$S_N$规范约束。大的规范冗余极大地减少了独立态的数量。特别地，在大$N$极限下，物理希尔伯特空间的维度仅随$N$多项式增长。因此，在该极限下，施加约束后的每个超选择扇区都是一维的。这重现了虫洞引力路径积分计算所暗示的定性行为。然后我们展示了为何在此设置中，主导封闭宇宙的Hartle-Hawking型半经典近似无法重现CFT结果。然而，一旦CFT自由度与外部观测者自由度耦合，引力路径积分计算的主导鞍点近似就被重建。

英文摘要：

We identify closed universe sectors in large $N$ symmetric orbifold CFTs with holographic duals. Starting from tensor product states built out of a finite dimensional low energy subspace of the seed theory, we show that the large $N$ Hilbert space decomposes into superselection sectors labeled by occupation number distributions. Before imposing the orbifold gauge constraint, these sectors have exponentially large dimensions, and the maximally entropic sector dominates the ungauged Hilbert space. We argue that this sector exhibits several characteristic features expected of a closed universe Hilbert space: pure states become indistinguishable from a mixed state at the level of simple correlation functions, and the associated operator algebra is naturally a hyperfinite type II$_1$ von Neumann algebra. We then impose the $S_N$ gauge constraint. The large gauge redundancy drastically reduces the number of independent states. In particular, in the large $N$ limit, the dimension of the physical Hilbert space grows only polynomially with $N$. Consequently, each superselection sector after imposing the constraint is one dimensional in this limit. This reproduces the qualitative behavior suggested by gravitational path integral calculations with wormholes. We then show why, in this setup, the Hartle-Hawking type semiclassical approximation for the dominant closed universe fails to reproduce the CFT results. Nevertheless, the dominant saddle point approximation for gravitational path integral calculation is reconstructed once the CFT degrees of freedom are coupled to external observer degrees of freedom.

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