|Résumé :||The gauge/string correspondence provides a non-perturbative definition of string theory and hence quantum gravity in some backgrounds, making it possible to translate statements about strongly coupled quantum field theories into results about gravity.
In this thesis, we focus on the derivation of holographic backgrounds from the field theory, without using any supergravity input. Instead, we rely crucially on the addition of probe D-branes to the stack of D-branes generating the background.
From the field theory description of the probe branes in the presence of the background branes, one can compute an effective action for the probes (in a suitable low-energy/near-horizon limit) by integrating out the background branes. Comparing this action with the D-brane probe action in a generic supergravity background then allows to determine the holographic background dual to the considered field theory vacuum.
In the first part, the required pre-requisites of field and string theory are recalled and this strategy to derive holographic backgrounds is explained in more detail on the basic case of D3-branes in flat space probed by a small number of D-instantons.
The second part contains the original results of this thesis, obtained by applying this strategy to several specific examples. We first derive the duals to three continuous deformations (Coulomb branch, β and non-commutative deformations) of the basic case, in the limit in which the D-instantons can probe the full geometry. We then derive the enhançon mechanism in a dual to a simple N=2 quiver gauge theory by using a fractional D-instanton as a probe and exploiting recent exact results on the Coulomb branch of N=2 quivers.
Finally, we obtain the near-horizon D4-brane geometry by probing the D4-branes with a small number of D0-branes.