Emergent Space and the Example of AdS_5XS^5

TL;DR

This paper demonstrates how to derive emergent space geometries from field theoretic observables, explicitly constructing the AdS_5×S^5 background from N D3-branes in type IIB string theory.

Contribution

It provides a concrete method to build and compute emergent spacetime geometries directly from field theory, exemplified by the derivation of the AdS_5×S^5 metric.

Findings

Explicit derivation of AdS_5×S^5 geometry from field theory

Construction of observables encoding geometric properties

Emergence of full spacetime metric and fluxes at large N

Abstract

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 AdS_5XS^5 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.