Holographic Methods for Condensed Matter Physics

Abstract

The physics of certain condensed matter systems is not well understood due to strong coupling preventing perturbative descriptions and in certain cases also numerical simulations. The AdS/CFT correspondence might allow a non-perturbative description of these systems in terms of a dual weakly coupled system. In this thesis the AdS/CFT correspondence is used to model a high-Tc superconductor by a gravity theory outside a black hole in AdS space. The frequency dependent conductivity is calculated using this model and a superconducting phase is shown to appear below a critical temperature. These computations are described in detail in the first part of the thesis. In the spirit of effective field theory, the second part of the thesis includes a higher curvature correction on the gravity side. The correction is shown to give a Drude peak and its properties are examined. Another way to introduce a Drude peak is by introducing a periodic lattice [1], as was recently done by Horowitz et al. Our way of obtaining the Drude peak is computationally much simpler than the periodic lattice and might be a useful effective description.