Juan Martín Maldacena (フアン・マルダセナ): The Large N Limit of Superconformal field theories and supergravity

Juan Martín Maldacena

We show that the large N limit of certain conformal field theories in various dimen- sions include in their Hilbert space a sector describing supergravity on the product of Anti-deSitter 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 super- conformal group (as opposed to just the super-Poincare group). The ’t Hooft limit of 3+1 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-deSitter 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 non-compact dimensions.

• Conformal field theory
• Hilbert space
• Supergravity
• Anti-deSitter spacetime
• Brane
• IIB string
• M theory
• String theory
• Super-conformal group
• Super-Poincare group
• t Hooft limit
• Super-Yang-Mills