D-branes, gauge/string duality and noncommutative theories

TL;DR

This thesis explores D-branes, gauge/string duality, and noncommutative theories, extending the AdS/CFT correspondence to more realistic models and analyzing properties like unitarity, confinement, and symmetry breaking.

Contribution

It constructs supergravity duals for noncommutative and N=2 pure SYM theories, and studies supersymmetry, unitarity, and holographic properties in these frameworks.

Findings

Supertubes exist in curved backgrounds with preserved supersymmetry

Rotating strings with three angular momenta analyzed within AdS/CFT

Holographic models exhibit UV/IR mixing, confinement, and chiral symmetry breaking

Abstract

In this thesis we elaborate on the three subjects of the title. We first show that supertubes exist and still preserve some supersymmetry in a large variety of curved backgrounds. Within the AdS/CFT correspondence we study the supersymmetry of rotating strings with 3 angular momenta, and we consider the possibility of adding matter in a stable but non-supersymmetric way. We contribute to the extension of the duality to more realistic YM theories by constructing the sugra dual of an N=2 pure SYM in 3d, given in terms of a Calabi-Yau four-fold in M-theory. We study the unitarity of noncommutative nonrelativistic field theories, we construct the sugra dual of noncommutative pure SYM theories with N=1 in 4d and N=2 in 3d, and we study holographically properties like UV/IR mixing, confinement, chiral symmetry breaking and moduli spaces.