Emergent Space-times and how to find them

The AdS/CFT correspondence is a concrete instance of holographic duality, where a bulk theory of quantum gravity in d+1 dimensions can emerge from a conformal field theory (CFT) in d dimensions. In particular, we expect the semi-classical spacetime of d+1 dimensions to emerge from the entanglement patterns of certain quantum states in the CFT. Therefore, it is crucial to understand what kind of states encode such spacetime geometries and how to explicitly reconstruct these geometries from quantum entanglement. In this talk, I will address these questions using the techniques of tensor Radon transform. We find that, given the boundary entanglement entropies of a 2d CFT, this framework provides a quantitative measure that detects whether the bulk dual has a semi-classical geometry in the perturbative limit. In the case where a well-defined bulk geometry exists, we also reconstruct the bulk metric tensor numerically. We then examine the emergent bulk geometries for static and dynamical cases in holography and in manybody systems. (pizza and drinks served at 12pm; talk starts at 12:10pm)