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 AdS3/CFT2. We find that, given the boundary entanglement entropies of a 2d 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.
Highlights
The Anti-de Sitter/Conformal Field Theory (AdS/conformal field theory (CFT)) correspondence [16, 17], some proposals relating geometry and entanglement apply to flat or de Sitter geometries [5, 7, 18,19,20]
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 AdS3/CFT2
Given the boundary entanglement entropies of a 2d CFT, this framework provides a quantitative measure that detects whether the bulk dual is geometric in the perturbative limit
Summary
We begin with the vacuum state |0 CFT of a hologaphic CFT. Because this state has conformal symmetry at all scales, it must be dual to empty AdS [16]. If we have access to a boundary state, in the sense of knowing its von Neumann entropies on all (connected) subregions, the RT formula translates these entropic quantities into a set of boundary anchored minimal surface areas Because these minimal surfaces all lie on the spatial slice Σ, recovering the bulk geometry from entanglement reduces to a pure geometry problem where we try to find the interior metric gij of a Riemannian manifold M while knowing only the areas of minimal surfaces that are anchored to its boundary ∂M. Given a generic non-vacuum state |ψ CFT, can we apply the same principles to reconstruct the metric tensor for the bulk geometry from the set of boundary-anchored geodesic lengths? We will see that the algorithm can be applied to a more general class of states, with interesting results
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