Holography and Imbalanced Systems. The doubly charged electron star model.

Abstract

In this thesis we study applications of the so-called AdS/CFT correspondence to condensed matter systems. More precisely, we have constructed a model to describe strongly correlated imbalanced systems, which are characterized by a U(1)xU(1) global symmetry. This gravitational dual corresponds to an extension of the Electron Star model devised by Hartnoll and Tavanfar. In this system, we have incorporated an extra charged fermionic species, thus leading to a doubly charged electron star. We obtained the full background of the theory and introduced the imbalance by perturbing the IR of the gauge fields differently. Furthermore, we also made an attempt to model an imbalanced holographic superconductor by introducing a scalar field in the probe limit. However, this framework turned out not to be enough to describe superconductivity and thus a fully backreacted scheme is required to study this system in more detail. Further studies of this model involve calculating transport properties of the system, adding Dirac fields and obtaining spectral functions or introduce finite temperature into the model.