Anti de sitter space and holography

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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 AdS5×S5 match with the chiral operators of 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 N = 4 theory has a large N phase transition related to the thermodynamics of AdS black holes.

Original languageEnglish (US)
Pages (from-to)253-290
Number of pages38
JournalAdvances in Theoretical and Mathematical Physics
Issue number2
StatePublished - Mar 1998
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General Mathematics
  • General Physics and Astronomy


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