AI 中文总结
该研究在全息对偶框架下，通过计算BTZ黑洞对偶热CFT的四类全息纠缠度量，利用其导数重构出完整BTZ度规，证明仅纠缠熵数据可确定对偶引力背景，实现引力的全息涌现。
AI 中文摘要
我们在全息对偶的框架下研究从边界纠缠熵涌现的体几何。考虑与BTZ黑洞对偶的热1+1维共形场论，我们计算四种不同的全息纠缠度量：标准类空全息纠缠熵（HEE）、其互补类空对应量HEE^s、类时全息纠缠熵（HTEE）及其互补类时对应量HEE^t。这些度量探测黑洞视界的外区和内区。值得注意的是，通过对这些纠缠熵关于边界区间和极值面的转折点取适当导数，我们在不施加爱因斯坦方程的情况下重构出完整的BTZ度规，包括径向分量g_{zz}，且重构得到的几何所有区域的度规分量均正确。我们进一步表明，在零温极限下，我们的结果一致地约化为纯AdS$_3$度规和熟知的真空CFT$_2$纠缠熵。我们的发现证明，仅纠缠熵数据就包含足够信息以唯一确定对偶引力背景，为引力从边界理论的量子信息结构中涌现的全息涌现提供了具体实现。
英文摘要
We investigate the emergence of bulk geometry from boundary entanglement entropy in the context of holographic duality. Considering a thermal $1+1$-dimensional conformal field theory dual to the BTZ black hole, we compute four distinct holographic entanglement measures: the standard spacelike HEE, its complementary spacelike counterpart HEE$^s$, the timelike HTEE and its complementary timelike counterpart HEE$^t$. These measures probe both the exterior and interior regions of the black hole horizon. Remarkably, by taking appropriate derivatives of these entanglement entropies with respect to the boundary intervals and the turning point of the extremal surface, we reconstruct the full BTZ metric, including the radial component $g_{zz}$, without imposing the Einstein equations. The reconstruction yields the correct metric components in all regions of the geometry. We further show that in the zero-temperature limit, our results consistently reduce to the pure AdS$_3$ metric and the familiar vacuum CFT$_2$ entanglement entropies. Our findings demonstrate that entanglement entropy data alone contains sufficient information to uniquely determine the dual gravitational background, offering a concrete realization of holographic emergence where gravity arises from the quantum information structure of the boundary theory.
Comments10 pages
