AI 中文总结
本文扩展AdS/CFT，通过第三量子化哈密顿量描述时空虫洞拓扑变化，结合AdS₃引力具体构建框架，为因子化问题提供输入并讨论副本虫洞等过程。
AI 中文摘要
我们提出了AdS/CFT的一种扩展形式，其中连通体几何的量子引力波函数被组装成一个宇宙的福克空间。第三量子化哈密顿量中的分裂与合并相互作用则为体连通性和拓扑的变化提供了量子描述。约化相空间量子化给出了物理的单宇宙希尔伯特空间以及径向薛定谔演化，拓扑变化的相互作用可据此排序。我们在具有环面边界的AdS₃引力中具体构建了该框架，其中这些要素可被明确描述。轻谱被视为固定的非归一化背景数据，而黑洞阈值以上的归一化态则被量子化为动力学模式。通过选择一个相干态来确定常规边界理论，该相干态的宇宙场期望值与固定背景贡献共同在渐近边界给出一致的CFT数据。一般的单宇宙波函数不一定具有此类解释，这使得CFT可实现的波函数在引力态空间中可能是非一般的，且不闭合于引力态的任意叠加。已知的双环面时空虫洞振幅是因子化问题的核心，为第三量子化理论的拓扑变化相互作用提供了具体输入。当所得引力扇区允许一致的边界理论解释时，互补的切割-粘合描述会给出有效系综解释，且无需假设边界理论的基本系综。我们还在同一框架内讨论了副本虫洞和婴儿宇宙过程。
英文摘要
We propose an extension of AdS/CFT in which quantum gravitational wavefunctions of connected bulk geometries are assembled into a Fock space of universes. Splitting and joining interactions in a third-quantized Hamiltonian then provide a quantum description of changes in bulk connectivity and topology. Reduced phase-space quantization supplies the physical one-universe Hilbert space and a radial Schrödinger evolution with respect to which the topology-changing interactions are ordered. We develop the construction concretely in AdS$_3$ gravity with a torus boundary, where these ingredients can be described explicitly. The light spectrum is treated as fixed, non-normalizable background data, whereas the normalizable states above the black-hole threshold are quantized as dynamical modes. A conventional boundary theory is selected by choosing a coherent state whose universe-field expectation value, together with the fixed background contribution, yields consistent CFT data at the asymptotic boundary. Generic one-universe wavefunctions need not admit such an interpretation. This raises the possibility that CFT-realizable wavefunctions are nongeneric in the gravitational state space and are not closed under arbitrary superpositions of gravitational states. The known two-torus spacetime-wormhole amplitude, which lies at the heart of the factorization problem, provides concrete input for the topology-changing interactions of the third-quantized theory. A complementary cutting-and-gluing description yields an effective ensemble interpretation when the resulting gravitational sectors admit consistent boundary-theory interpretations, without assuming a fundamental ensemble of boundary theories. We also discuss replica wormholes and baby-universe processes within the same framework.
Comments55 pages, 5 figures; v2: added references to recent related work, minor typographical corrections
