Emergent space and the example of AdS5×S5

We explain how to build field theoretic observables from which the geometrical properties of a dual holographic formulation can be read off straightforwardly. In some cases this construction yields explicit and calculable models of emergent space. We illustrate the idea on the type IIB background generated by N D3-branes in the near horizon limit, for which a full derivation from first principles can be presented. The six transverse dimensions emerge at large N and we find the full AdS5×S5 metric and self-dual Ramond-Ramond field strength on the resulting ten-dimensional space-time, with the correct radii and quantization law. We briefly discuss possible applications and generalizations.