Abstract

This is a short introduction to the ideas of the AdS/CFT correspondence. In order to be self-contained, the chapter includes an introduction to the study of strings as geometric objects moving in spacetime and in particular their solvability in flat space. I also mention why strings give rise to a theory of gravity. D-branes are introduced as a collection of geometric objects where strings can end. The low-energy dynamics of a collection of D-branes is explored in two different ways, and this serves as a basis for a formulation of the AdS/CFT correspondence: an equivalence between a gravitational formulation of the dynamics and a gauge theory description. The problem of how to compare observables between the two formulations is presented, and some basic aspects of the representation theory of the superconformal group are explored, so that one can have tests of the AdS/CFT proposal.

Introduction

Roughly ten years ago, the AdS/CFT correspondence was formulated by Maldacena [20]. In its simplest example, the AdS/CFT correspondence states that a certain four-dimensional quantum field theory that is made from gauge fields and some matter content – a theory similar to the theory of strong, weak or electromagnetic interactions – is equivalent as quantum theory to type IIB string theory (as a theory of quantum gravity) on spacetimes that are asymptotic to a particular classical solution of type IIB string theory, namely AdS5 × S5.

This correspondence has not been proved. This is in great part because we do not know what quantum gravity is.