基于张量Radon变换的体几何构造
Building Bulk Geometry from the Tensor Radon Transform
摘要：
使用张量Radon变换和相关的数值方法，我们研究了如何在特定的情况下，$\mathrm{AdS}_3/\mathrm{CFT}_2$体几何可以明确地重建从边界纠缠熵。我们发现，给定的边界纠缠熵的$2$ d CFT，这个框架提供了一个定量的措施，检测是否散装双几何微扰（近AdS）限制。在一个定义良好的散装几何存在的情况下，我们明确重建唯一的散装度量张量一旦规范的选择。然后，我们研究了全息和多体系统中静态和动态场景的涌现体几何。除了物理结果，我们的工作表明，数值方法是可行的，有效的研究在AdS/CFT体重构。
英文摘要：
Using the tensor Radon transform and related numerical methods, we study how bulk geometries can be explicitly reconstructed from boundary entanglement entropies in the specific case of $\mathrm{AdS}_3/\mathrm{CFT}_2$. We find that, given the boundary entanglement entropies of a $2$d CFT, this framework provides a quantitative measure that detects whether the bulk dual is geometric in the perturbative (near AdS) limit. In the case where a well-defined bulk geometry exists, we explicitly reconstruct the unique bulk metric tensor once a gauge choice is made. We then examine the emergent bulk geometries for static and dynamical scenarios in holography and in many-body systems. Apart from the physics results, our work demonstrates that numerical methods are feasible and effective in the study of bulk reconstruction in AdS/CFT.
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