Ads/CFT correspondence in condensed matter

TL;DR

This paper introduces the AdS/CFT correspondence to condensed matter physicists, explaining how it relates gravity theories in higher-dimensional spacetimes to strongly-coupled quantum field theories on the boundary, enabling analysis of complex quantum phenomena.

Contribution

It provides an elementary introduction to AdS/CFT for condensed matter researchers, highlighting its application to studying real-time dynamics and response functions in quantum critical systems.

Findings

AdS/CFT relates gravity in (d+1)-dimensional spacetime to d-dimensional quantum field theories.

The correspondence simplifies computation of response functions at finite temperature.

Classical gravitational equations can be used to analyze quantum critical dynamics.

Abstract

The goal of these notes is to introduce, in a very 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 spacetime 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.