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

Resumo

In the present thesis we have the objective of testing and extending the domain of applicability of the holographic correspondence, a.k.a. AdS/CFT. This long term motivation has been made concrete in three different problem; there are also some additional specific goals for each them. The first is the role of higher curvature gravity corrections on thermal phase transitions between AdS and dS geometries. Apart from the purely gravitational interest, this research may eventually be helpful to clarify the correspondence in the case of dS geometries. Our main result is a phase transition from AdS boundary leading to the formation of dS cosmological horizon in Lanczos-Gauss-Bonnet gravity. In the presence of the higher curvature corrections no matter fields are required to match both sides of the bubble due to the Lanczos-Gauss-Bonnet term in the action. In the second we have made use of Non-Abelian T-duality (NATD) to generate new Supergravity solutions as well as to understand the inter- play of NATD with AdS/CFT. We are interested in deformations of Klebanov-Witten (KW) background AdS 5 xT 1,1 flowing to an AdS 3 factor in the IR. We generate new examples of them applying Non-Abelian T-duality on previously found solutions. After it, we compare the holographic observables of the generated solutions with those of the known deformations. The new geometries are smooth, supersymmetric and seem to be dual to long linear quiver gauge theories. Finally, we have carried the extension of the AdS/CFT correspondence, in particular the holographic renormalization procedure, to reproduce the Ward identities of symmetry breaking in a 1+1 holographic superconductor. It is established that alternative quantization is necessary in the three-dimensional bulk case, and after properly performed, the field theoretic higher dimensional Ward identities are recovered. This extension may be find application in AdS/CMT.