Applied Gauge/Gravity Duality from Supergravity to Superconductivity

Resumo

The sequence of chapters can be divided into three blocks. - The first block contains the introductory chapters. In chapter 1 we illustrate the problem of the high-Tc superconductors making a parallelism between the Fermi Liquid theory, the BCS theory of superconductivity and the theory which is currently supposed to describe electron doped high-Tc superconductors at weak coupling. In chapter 2 we describe the aspects of the AdS/CFT correspondence that will be relevant throughout the reading of the thesis. - The second block coincides with chapter 3. In this chapter we define the concept of holographic superconductivity and we study phenomenological models of holographic superconductors. These are bottom-up models in the sense that they do not come from any particular string theory. This chapter has several important results, among them we mention, the classification of the holographic phase transitions and the characterization of the optical conductivity. - The third block contains the chapters from 4 to 7. The mainstream is the study of top-down models of holographic superconductors that naturally arise as smaller sectors of consistent truncations of type IIB supergravity. In chapter 4 we consider N = 8 supergravity and we describe the building blocks of N = 2 supergravity looking for such holographic superconductors. In this setup, the AdS/CFT dictionary is very well understood and we identify the analog of a Cooper pair state. In chapter 5, we discuss holographic superconductivity in the type IIB theory on AdS5 x S5 whereas in chapter 6, we consider the more general setting of type IIB theory compactified on Sasaki-Einstein manifolds. Among several examples, we will consider the interesting case of AdS5 x T1;1. In chapter 7, we study a four dimensional N = 2 supergravity which is related to M-theory, we find a novel family of holographic superconductor and we describe in detail the properties of gravitational background providing its interpretation in the dual field theory. We close the discussion about phenomenological models of holographic superconductivity and supergravity with conclusions and outlook. Finally, the thesis is equipped with two appendices in which we set up the the notation that will be adopted in the various chapters. Both these appendices are also thought as a quick and practical reminder of known results in the literature about field theory and supergravity.