AdS/CFT Correspondence in Condensed Matter

This book introduces, in an elementary way, the idea of the anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence to condensed matter physicists. This theory relates a gravity theory in a (d+1)-dimensional anti-de Sitter space time to a strongly coupled d-dimensional quantum field theory living on its boundary. The AdS/CFT correspondence can be used to study finite temperature real time processes, such as response functions and dynamics far from equilibrium in quantum critical points in condensed matter systems. Computation of these quantities is reduced to solving classical gravitational equations in one higher dimension than the original theory.

This book is a concise introduction, presenting the general foundations for condensed matter physicists, to the AdS/CFT correspondence. The author has presented and focused on a review and explanation of relevant materials. The interested reader can consult the references to get more detailed explanations and information. There are many papers and good reviews about the subject, but most use a language that demands some knowledge about the subject. In this presentation the author has utilized more accessible language for a non-specialized reader.