Aspects of the AdS/CFT correspondence in less supersymmetric backgrounds

Abstract

In this thesis we study the AdS/CFT correspondence in backgrounds with less supersymmetry. We consider AdS_5 x T {1,1} whose correspondence to N=1 gauge theory is known as the Klebanov-Witten model. We also consider real [beta]-deformations, often called [gamma]-deformations which are exactly marginal deformations of the gauge theory. Their supergravity duals can be found by a solution generating technique of Lunin and Maldacena.<br />We use (semi)classical approach and consider solutions of particular shape, the circular and folded spinning string, giant magnon and single spike. We focus on dispersion relations which are supposed to give the anomalous dimensions and three-point correlation functions at strong coupling. In a sector of [gamma]-deformed conifold we find giant magnon and single spike string solutions. We examine the dispersion relations and find a behavior analogous to the undeformed case. The transcendental functional relations between the conserved charges are shifted by certain [gamma]-dependent term. The latter is proportional to the total momentum and thus qualitatively different from known cases. In the analysis of the finite size corrections we find a leading and a subleading contribution in the first order approximation. This behavior is different from the known case of AdS_5 x S 5.<br />In the study of the correlation functions at strong coupling we used a recent method, that allows to consider three-point functions of operators corresponding to two heavy string states and a light supergravity state. We used several string solutions with one and two spins in the T {1,1} part of the geometry. The three-point functions we obtained for both, the single spin and the two spin case, are given implicitly, due to transcendental relations between conserved charges.<br />We also check the consistency of the structure constants of the correlators with those obtained from 2\pi {2}a_{\mathcal{L}AA}=\lambda\partial E/\partial\lambda and find complete agreement.