Towards Bulk Metric Reconstruction in AdS/CFT
The AdS/CFT correspondence provides an indirect definition of a nonperturbative theory of quantum gravity via an ordinary (non-gravitational) quantum field theory. The goal of bulk reconstruction is to identify the emergence of gravitational phenomena from appropriate limits of this boundary field theory. I will focus on the emergence of a bulk geometry, which significant evidence suggests must be tied to the entanglement structure of the boundary. When the bulk geometry is classical, this observation leads to a geometric question: do the areas of extremal surfaces anchored to the boundary of a spacetime fix the geometry in the interior? By extending recent results of Alexakis, Balehowsky, and Nachman, I will give a uniqueness argument that the answer is in the affirmative. I will then discuss extensions of this result; specifically, I will discuss (i) what ingredients are necessary to obtain an explicit reconstructive result, as well as (ii) how to move towards recovering perturbative quantum corrections to the bulk geometry.