Study of the Ads/CFT correspondence in low dimensions

Abstract

This thesis is focused on the construction of supergravity backgrounds with AdS factors and their putative field theory descriptions via the AdS/CFT correspondence. We put emphasis on lower-dimensional theories, specifically on geometries with AdS3 and AdS2 subspaces with four Poincaré supersymmetries. Diverse techniques concerning the construction of supergravity solutions are discussed, from string theory dualities, such as T-duality (ATD) or its generalization to non-Abelian groups (NATD), as well as double analytical continuations and G-structure techniques. Regarding the field theory interpretation of the obtained solutions, geometrical aspects of the backgrounds are studied, leading us to propose dual field theories involving products of gauge groups and matter fields, namely, quiver field theories whose content is determined by Dp- and NS- branes. We test such dualities through different observables using holography. The thesis consists of nine chapters. The first chapter constitutes an introduction where the present work is set in context. We review in detail the construction of solutions in supergravity in Chapter 2. Chapter 3 contains the study of the D4-NS5-D6 brane system as an example of the field theoretical constructions used in the present work. A brief summary of the main results obtained in this work is given in Chapter 4. Chapters 5, 6, 7 and 8 contain the complete results of the thesis. Finally, the conclusions are provided in Chapter 9.