The paper by Edward Witten explores the holographic principle in the context of Anti-de Sitter (AdS) space and supergravity. Witten proposes a precise correspondence between conformal field theory (CFT) observables and those of supergravity, suggesting that correlation functions in CFT are given by the dependence of the supergravity action on the asymptotic behavior at infinity. Specifically, the dimensions of operators in CFT are related to the masses of particles in supergravity. This correspondence is illustrated through the example of Type IIB supergravity on \(AdS_5 \times S^5\), where Kaluza-Klein modes match with chiral operators in \(\mathcal{N} = 4\) super Yang-Mills theory in four dimensions. The paper also discusses the Hamiltonian formulation of the correspondence and the large \(N\) phase transition in \(\mathcal{N} = 4\) theory related to the thermodynamics of AdS black holes. The discussion covers the boundary behavior of fields, the massless field equations, and sample calculations in classical supergravity, providing a detailed framework for understanding the holographic relation between AdS space and CFT.The paper by Edward Witten explores the holographic principle in the context of Anti-de Sitter (AdS) space and supergravity. Witten proposes a precise correspondence between conformal field theory (CFT) observables and those of supergravity, suggesting that correlation functions in CFT are given by the dependence of the supergravity action on the asymptotic behavior at infinity. Specifically, the dimensions of operators in CFT are related to the masses of particles in supergravity. This correspondence is illustrated through the example of Type IIB supergravity on \(AdS_5 \times S^5\), where Kaluza-Klein modes match with chiral operators in \(\mathcal{N} = 4\) super Yang-Mills theory in four dimensions. The paper also discusses the Hamiltonian formulation of the correspondence and the large \(N\) phase transition in \(\mathcal{N} = 4\) theory related to the thermodynamics of AdS black holes. The discussion covers the boundary behavior of fields, the massless field equations, and sample calculations in classical supergravity, providing a detailed framework for understanding the holographic relation between AdS space and CFT.