Building Bulk Geometry from the Tensor Radon Transform

TL;DR

This paper develops a numerical framework using the tensor Radon transform to reconstruct bulk geometries from boundary entanglement entropies in AdS/CFT, enabling detection of geometric duals and explicit metric reconstruction.

Contribution

It introduces a novel numerical method for bulk geometry reconstruction from boundary data in AdS/CFT, including a measure for geometric dual detection and explicit metric recovery.

Findings

Detects whether boundary entanglement entropies correspond to a geometric bulk.

Successfully reconstructs bulk metric tensor in AdS3/CFT2 scenarios.

Demonstrates the effectiveness of numerical methods in holographic bulk reconstruction.

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.