Emergent geometry from D-Branes

In this thesis, we explain and illustrate on several examples how to derive supergravity solutions by computing observables in the corresponding dual, lower-dimensional field theory.In particular, no a priori knowledge on the gravitational dual is assumed, including its dimensionality. The basic idea to construct the pre-geometric models is to consider the world-volume theory of probe D-branes in the presence of a large number N of higher-dimensional background branes. In the standard decoupling limit, the probes are moving only in the flat directions parallel to the background D-branes. We show however that the quantum effective action of the probe world-volume theory, obtained at large $N$ using standard vector model techniques, has the required field content to be interpreted as the action describing the probes in a higher-dimensional, curved and classical spacetime. The properties of the emerging supergravity solution are easily found by comparing the quantum effective action of the pre-geometric model with the non-abelian D-brane action. In all the examples we consider, this allows us to derive the metric, the dilaton and various form fields, overall performing exclusively field theoretic computations.The first part of the thesis consists of introductory chapters, where we review vector models at large N, aspects of brane physics in supergravity and string theory and the gauge/gravity correspondence. The second part contains the original contributions of this thesis, consisting of various explicit emergent geometry examples.Doctorat en Sciences