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arXiv · 2007.00004

Building Bulk Geometry from the Tensor Radon Transform

ChunJun Cao·Xiao-Liang Qi·Brian Swingle·Eugene Tang
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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.

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ChunJun Cao, Xiao-Liang Qi, Brian Swingle, Eugene Tang. 2020-06-30. Building Bulk Geometry from the Tensor Radon Transform. https://doi.org/10.1007/jhep12(2020)033

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