On gravitational Phase Transitions, T-duality and Symmetry Breaking in AdS/CFT

In this thesis we study several problems in the context of AdS/CFT. The first is that of gravitational phase transitions between AdS and dS geometries in the Gauss-Bonnet theory of gravity. Such transitions are mediated by thermalons and do not require matter fields. The phenomenon is strongly expected to be generic in higher curvatures theories of gravity. The second problem is the generation of new Supergravity backgrounds and the study of their holographic duals. We generate new examples of supersymmetric flows from $AdS_5$ in the UV to $AdS_3$ in the IR. The new solutions are found to be holographically related to long linear quiver gauge theories. Finally we derive the Ward identities of 1+1 QFT using AdS/CFT. This is achieved by holographic renormalization with special boundary terms. The resulting Ward identities are the same as in higher dimensions and they show the expected symmetry breaking for large N.