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AdS/CFT and its Applications

In this thesis we study some applications of the gauge/gravity correspondence. In chapter 1 we introduce the gauge/gravity conjecture focusing on the aspects that will be relevant in the rest of the work, in chapter 2 we extend the Gubser-Klebanov-Polyakov-Witten (GKPW) prescription generalizing it to gravity backgrounds with two boundaries. In chapter 3 we discuss the Maldacena-Rey prescription to compute the quark-antiquark (and monopole-antimonopole) potential in some gravity backgrounds duals to conformal and non-conformal field theories. In particular, we analyze the stability of the classical solutions under small fluctuations. In chapter 4 we study the thermodynamic properties and the entanglement entropy of the 2+1 dimensional $p$ and $p+ip$ superconductors through their dual gravity backgrounds. We analyze the limit where the number of charged degrees of freedom is comparable with the total number of degrees of freedom, which means that the backreaction on the geometry due to the non-Abelian gauge field is relevant.