# The Large N Limit of Superconformal Field Theories and Supergravity

**Authors:** Juan M. Maldacena  
**arXiv:** [hep-th/9711200](https://arxiv.org/abs/hep-th/9711200)  
**Date:** 1997-11-27  
**Summary page:** https://www.summarizepaper.com/en/paper/hep-th--9711200v3/

## Key points

- Juan M. Maldacena's paper explores the relationship between conformal field theories and supergravity on different manifolds.
- The large $N$ limit of conformal field theories includes a sector describing supergravity on these spaces.
- The near horizon geometry for large $N$ can still be trusted even in low energy limits.
- This leads to a new proposal for a definition of M-theory which could include five non-compact dimensions.
- 't Hooft limit of 4-d ${\cal N} =4$ super-Yang-Mills at the conformal point contains IIB strings.
- Compactifications of M/string theory on various Anti-deSitter spacetimes are dual to various conformal field theories.

## Summary

In the paper "The Large N Limit of Superconformal Field Theories and Supergravity," Juan M. Maldacena explores the relationship between certain conformal field theories and supergravity on Anti-deSitter spacetimes, spheres, and other compact manifolds. 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, Maldacena shows that the large $N$ limit of these conformal field theories includes a sector describing supergravity on these spaces. He also observes that even in this low energy limit, we can still trust the near horizon geometry for large $N$. This enhanced supersymmetry of this near horizon geometry corresponds to extra supersymmetry generators present in the superconformal group (as opposed to just the super-Poincare group). This leads to a new proposal for a definition of M-theory which could be extended to include five non-compact dimensions. Furthermore, Maldacena demonstrates that 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. Based on this observation, he conjectures that compactifications of M/string theory on various Anti-deSitter spacetimes are dual to various conformal field theories. Overall, this paper provides important insights into the relationship between string theory and quantum gravity. It also offers a new perspective on how we might define M-theory in higher dimensions.