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The large-$$N$$ limit of superconformal field theories and supergravity. (English) Zbl 0969.81047
Summary: We show that the large-$$N$$ limits of certain conformal field theories in various dimensions include in their Hilbert space a sector describing supergravity on the product of anti-de Sitter spacetimes, spheres, and other compact manifolds. This is shown by taking some branes in the full M/string theory and then taking a low-energy limit where the field theory on the brane decouples from the bulk. We observe that, in this limit, we can still trust the near-horizon geometry for large $$N$$. The enhanced supersymmetries of the near-horizon geometry correspond to the extra supersymmetry generators present in the superconformal group (as opposed to just the super-Poincaré group). The ’t Hooft limit of $$3+1$$ $${\mathcal N}=4$$ super-Yang-Mills at the conformal point is shown to contain strings: they are IIB strings. We conjecture that compactifications of M/string theory on various anti-de Sitter spacetimes is dual to various conformal field theories. This leads to a new proposal for a definition of M-theory which could be extended to include five noncompact dimensions.

##### MSC:
 81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory 81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics 83E50 Supergravity 81T60 Supersymmetric field theories in quantum mechanics 83E30 String and superstring theories in gravitational theory 81V17 Gravitational interaction in quantum theory
##### Keywords:
anti-de Sitter spacetimes; spheres; near-horizon geometry
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