##
**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.

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 |

### Keywords:

large \(N\) limit of conformal field theories; supergravity; low energy limit; near horizon geometry; supersymmetry generators; superconformal group
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\textit{J. Maldacena}, Adv. Theor. Math. Phys. 2, No. 2, 231--252 (1998; Zbl 0914.53047)

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### Online Encyclopedia of Integer Sequences:

Decimal expansion of (2*Pi)^3.Decimal expansion of (2*Pi)^4.

Decimal expansion of (2*Pi)^6.

a(n) = (2n^2 - n + 2) * (2n)! / ((n + 1) * (n + 2) * n!^2).