## The large $$N$$ limit of superconformal field theories and supergravity.(English)Zbl 0914.53047

Summary: We show that the large $$N$$ limit of certain conformal field theories in various dimensions include in their Hilbert space of 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 resp. 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 resp. 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:

 81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics 81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory 81T60 Supersymmetric field theories in quantum mechanics 83E50 Supergravity
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