Edward Witten discusses the AdS/CFT correspondence, which relates conformal field theories (CFTs) in d dimensions to supergravity (and string theory) on the product of (d+1)-dimensional AdS space with a compact manifold. He proposes that correlation functions in CFTs correspond to the dependence of the supergravity action on the asymptotic behavior at infinity. For example, the dimensions of operators in CFTs correspond to the masses of particles in supergravity. He notes that Kaluza-Klein modes of Type IIB supergravity on AdS₅ × S⁵ match with chiral operators of N=4 super Yang-Mills theory in four dimensions. He also discusses the Hamiltonian version of the correspondence and the large N phase transition related to the thermodynamics of AdS black holes. The paper introduces the concept of AdS space and its boundary, which is a conformal compactification of Minkowski space. It describes the boundary behavior of massless fields and how they relate to conformal field theories. The paper also discusses the effective action for the conformal field theory on the boundary of AdS space, relating it to the supergravity action in the bulk. It includes examples of calculations for scalar and gauge fields, showing how their correlation functions can be derived from supergravity. The paper also addresses anomalies and the role of the Chern-Simons term in the effective action. It concludes with a discussion of the massive case and the implications for the AdS/CFT correspondence.Edward Witten discusses the AdS/CFT correspondence, which relates conformal field theories (CFTs) in d dimensions to supergravity (and string theory) on the product of (d+1)-dimensional AdS space with a compact manifold. He proposes that correlation functions in CFTs correspond to the dependence of the supergravity action on the asymptotic behavior at infinity. For example, the dimensions of operators in CFTs correspond to the masses of particles in supergravity. He notes that Kaluza-Klein modes of Type IIB supergravity on AdS₅ × S⁵ match with chiral operators of N=4 super Yang-Mills theory in four dimensions. He also discusses the Hamiltonian version of the correspondence and the large N phase transition related to the thermodynamics of AdS black holes. The paper introduces the concept of AdS space and its boundary, which is a conformal compactification of Minkowski space. It describes the boundary behavior of massless fields and how they relate to conformal field theories. The paper also discusses the effective action for the conformal field theory on the boundary of AdS space, relating it to the supergravity action in the bulk. It includes examples of calculations for scalar and gauge fields, showing how their correlation functions can be derived from supergravity. The paper also addresses anomalies and the role of the Chern-Simons term in the effective action. It concludes with a discussion of the massive case and the implications for the AdS/CFT correspondence.