论文标题
全息婴儿宇宙：可观察的故事
Holographic baby universes: an observable story
论文作者
论文摘要
我们通过为观察到的量子重力而不是希尔伯特空间的代数发挥原始作用来严格地制定婴儿宇宙的结构。利用差异不变性，我们通过拓扑变化研究婴儿宇宙的创造和an灭。然后，我们为全息理论构建边界可观察物的代数，并表明它增强了包含“额外”的ABELIAN张量因子来描述量子状态中的大量；通过重力路径积分，我们在GNS表示的背景下，在希尔伯特空间的层面上实现了这种额外的张量因子。我们使用GNS代表制定了“婴儿宇宙假设”的必要假设。当满足婴儿宇宙假设时，我们证明了相应的引力路径积分中的“奇迹般的取消”在Abelian $ c^\ ast $ -Algebras的性格理论方面具有自然的解释。我们发现婴儿宇宙假设的必要数学条件可以持有，并将其转录为足够的身体状况。我们发现它们与ADS/CFT对应关系的任何散装过程影响的婴儿宇宙形成不兼容。我们通过将其应用于两个设置来说明我们的构建，从而导致某些重力拓扑模型的重新解释，并与仪表理论的拓扑真空进行类比。
We formulate the baby universe construction rigorously by giving a primordial role to the algebra of observables of quantum gravity rather than the Hilbert space. Utilizing diffeomorphism invariance, we study baby universe creation and annihilation via change in topology. We then construct the algebra of boundary observables for holographic theories and show that it enhances to contain an 'extra' Abelian tensor factor to describe the bulk in the quantum regime; via the gravitational path integral we realize this extra tensor factor, at the level of the Hilbert space, in the context of the GNS representation. We reformulate the necessary assumptions for the "baby universe hypothesis" using the GNS representation. When the baby universe hypothesis is satisfied, we demonstrate that the "miraculous cancellations" in the corresponding gravitational path integral have a natural explanation in terms of the character theory of Abelian $C^\ast$-algebras. We find the necessary and sufficient mathematical condition for the baby universe hypothesis to hold, and transcribe it into sufficient physical conditions. We find that they are incompatible with a baby universe formation that is influenced by any bulk process from the AdS/CFT correspondence. We illustrate our construction by applying it to two settings, which leads to a re-interpretion of some topological models of gravity, and to draw an analogy with the topological vacua of gauge theory.
