Introduction to the AdS/CFT correspondence

This is an introductory review of the AdS/CFT correspondence and of the ideas that led to its formulation. We show how comparison of stacks of D3-branes with corresponding supergravity solutions leads to dualities between conformal large N gauge theories in 4 dimensions and string backgrounds of the form AdS5 × X₅ where X₅ is an Einstein manifold. The gauge invariant chiral operators of the field theory are in one-to-one correspondence with the supergravity modes, and their correlation functions at strong coupling are determined by the dependence of the supergravity action on AdS boundary conditions. The simplest case is when X₅ is a 5-sphere and the dual gauge theory is the N = 4 supersymmetric SU(N) Yang-Mills theory. We also discuss D3-branes on the conifold corresponding to X₅ being a coset space T 1;1 = (SU(2) ×SU(2))=U(1). This background is dual to a certain N = 1 superconformal field theory with gauge group SU(N) × SU(N).