Um estudo da Correspondência AdS/CFT: Do campo escalar à termodinâmica de buracos negros

Abstract

In this dissertation, the objective is to carry out an initial study of the AdS/CFT Correspondence. We present the concept of dualities and their importance in physics. Then, we state a particular example of duality known as the AdS/CFT correspondence. We construct the metric of spaces with constant curvature, starting with the sphere, moving on to the two-sheeted hyperboloid, and concluding with the de Sitter (dS) and Anti-de Sitter (AdS) spacetimes in (d+1) dimensions. We study the scalar field in an AdS spacetime, showing how holography can be applied to compute relevant quantities. We investigate the thermodynamics of a Schwarzschild black hole in AdS spacetime (SAdS), since, according to the holographic dictionary, it is the gravitational dual of a finite-temperature field theory. By calculating the entropy and specific heat of this system, we conclude with a discussion of the Hawking–Page transition. Finally, the thermodynamics of a charged Reissner–Nordström–AdS (RN–AdS) black hole is analyzed. This black hole corresponds, through the holographic dictionary, to a field theory at finite temperature and density on the boundary. In particular, we compute its thermodynamic potential.