Anti De Sitter Space And Holography

Abstract

Recently, it has been proposed by Maldacena that large $N$ limits of certain conformal field theories in $d$ dimensions can be described in terms of supergravity (and string theory) on the product of $d+1$-dimensional $AdS$ space with a compact manifold. Here we elaborate on this idea and propose a precise correspondence between conformal field theory observables and those of supergravity: correlation functions in conformal field theory are given by the dependence of the supergravity action on the asymptotic behavior at infinity. In particular, dimensions of operators in conformal field theory are given by masses of particles in supergravity. As quantitative confirmation of this correspondence, we note that the Kaluza-Klein modes of Type IIB supergravity on $Ad{S}_5\times {\mathbf{S}}^5$ match with the chiral operators of $\mathbb{N}=4$ super Yang-Mills theory in four dimensions. With some further assumptions, one can deduce a Hamiltonian version of the correspondence and show that the $\mathbb{N}=4$ theory has a large $N$ phase transition related to the thermodynamics of $AdS$ black holes.

40 pp.; additional references and assorted corrections

References in corpus (10)

• Supergravity and The Large N Limit of Theories With Sixteen Supercharges
• String Theory and Classical Absorption by Threebranes
• Microscopic derivation of the Bekenstein-Hawking entropy formula for non-extremal black holes
• M 5-brane and superconformal (0,2) tensor multiplet in 6 dimensions
• Conformal Theory of M2, D3, M5 and `D1+D5' Branes
• Conformal Maxwell theory as a singleton field theory on AdS_5, IIB three-branes and duality
• Spectrum of Large N Gauge Theory from Supergravity
• Singletons, Doubletons and M-theory
• Branes and anti-de Sitter spacetimes
• Infinite Lorentz boost along the M-theory circle and non-asymptotically flat solutions in supergravities

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