The Large N Limit of Superconformal Field Theories and Supergravity

TL;DR

This paper demonstrates that the large N limit of certain superconformal field theories includes a sector describing supergravity on AdS spaces, supporting the AdS/CFT correspondence and proposing a new M-theory definition.

Contribution

It establishes a connection between large N superconformal field theories and supergravity on AdS spaces, extending the AdS/CFT correspondence and proposing a new M-theory framework.

Findings

Large N limit includes supergravity sectors in the Hilbert space.

The near horizon geometry's supersymmetries match superconformal group symmetries.

The 4D N=4 super-Yang-Mills contains IIB strings in the 't Hooft limit.

Abstract

We show that the large $N$ limit of certain conformal field theories in various dimensions 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 superconformal group (as opposed to just the super-Poincare group). The 't Hooft limit of 4-d ${\cal N} =4$ 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 are 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.