D-branes, gauge/string duality and noncommutative theories

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.