Holographic backgrounds from D-brane probes

Abstract: This thesis focuses on the derivation of holographic backgrounds from the field theory side, without using any supergravity equations of motion. Instead, we rely 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, 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 generic probe D-brane action 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 our original results, which have already appeared in arXiv:1301.3738, arXiv:1301.7062 and arXiv:1312.0621. We first derive the duals to three continuous deformations (Coulomb branch, $\beta$ and non-commutative deformations) of N=4 super-Yang-Mills. We then derive the enhan\c{c}on mechanism in a simple N=2 quiver gauge theory setup 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.