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. |

81T30 | String and superstring theories |

81T60 | Supersymmetric field theories |

83E50 | Supergravity |