Holographic backgrounds from D-brane probes

TL;DR

This thesis develops a method to derive holographic backgrounds from field theory using probe D-branes without supergravity equations, and applies it to various deformations and configurations in string theory.

Contribution

It introduces a novel approach to determine holographic backgrounds directly from field theory via probe D-branes, avoiding supergravity equations, and applies it to multiple deformations and setups.

Findings

Derived duals to Coulomb, β, and non-commutative deformations of N=4 super-Yang-Mills.

Explained the enhançon mechanism in N=2 quiver gauge theories using fractional D-instantons.

Obtained the near-horizon D4-brane geometry from D0-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.