AI 中文总结
该研究提出从AdS₃纯广义相对论半经典希尔伯特空间到CFT₂的全息映射，区分内外测地线，将其参数对应CFT原初态共形权重，还应用于体规范对偶、视界测地线测量及闭合宇宙半经典性问题。
AI 中文摘要
我们提出了从AdS₃中纯广义相对论的半经典希尔伯特空间到CFT₂的全息映射。我们通过在柯西切片Σ上固定面积网络的基矢中对半经典相空间进行量子化来定义体希尔伯特空间。固定面积网络是Σ上测地线的最大非相交集合，其长度和角动量已被固定。我们的全息映射区分了与∂Σ的连通分量同伦的“外部”测地线和不与该分量同伦的“内部”测地线。外部测地线的长度和角动量成为对应∂Σ分量上CFT希尔伯特空间中原初态的共形权重。固定面积网络决定了波函数，该波函数由原初态的OPE系数网络给出，其权重由对应长度决定。对于足够半经典的态，体内积与边界内积一致。我们将该提议应用于各类物理问题：体规范的边界对偶是足够半经典态的涌现基矢；我们还定义了测量视界后方测地线长度的边界算符，同样针对半经典态；最后，我们将映射应用于闭合宇宙，发现简单情形下半经典性失效，添加大质量探针可部分缓解该问题。
英文摘要
We propose a holographic map from the semiclassical Hilbert space of pure general relativity in $\text{AdS}_{3}$ to that of $\text{CFT}_{2}$. We define the bulk Hilbert space by semiclassically quantising the phase space in the basis of a fixed-area network on a Cauchy slice $Σ$. A fixed-area network is a maximal non-intersecting set of geodesics on $Σ$ whose lengths and angular momenta have been fixed. Our holographic map differentiates between `external' geodesics that are homotopic to a connected component of $\partial Σ$, and `internal' geodesics which are not. The lengths and angular momenta of external geodesics become conformal weights of primaries in the Hilbert space of the CFT living on the corresponding component of $\partial Σ$. The fixed-area network determines the wave function, which is given by a network of OPE coefficients of primaries whose weights are determined by the corresponding lengths. For sufficiently semiclassical states, there is an agreement between bulk and boundary inner products. We apply this proposal to various physics questions. The boundary dual of a bulk gauge turns out to be an emergent basis for sufficiently semiclassical states. We also define boundary operators that measure the lengths of geodesics behind the horizon, again in semiclassical states. Finally, we apply our map to closed universes and find a failure of semiclassicality in simple cases, which can be partially alleviated by the addition of a massive probe.
Comments67 pages
