Building Bulk Geometry from the Tensor Radon Transform

Abstract

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.

Animations for dynamical processes are found here: (https://www.youtube.com/playlist?list=PLCjJ3kjqxOfw1aIa5c0X6KSpox1-AjM5b) 23 pages excluding appendices. 21 figures

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• Bulk reconstruction of metrics inside black holes by complexity
• Reconstructing black hole exteriors and interiors using entanglement and complexity
• Inverse problem of correlation functions in holography
• Holographic geometry/real-space entanglement correspondence and metric reconstruction
• Subregion duality, wedge classification and no global symmetries in AdS/CFT
• Building bulk from Wilson loops