What Do CFTs Tell Us About Anti-de Sitter Spacetimes?

TL;DR

This paper explores how conformal field theories relate to Anti-de Sitter spacetimes, proposing methods to interpret the bulk S-matrix, address scattering issues, and connect to supergravity through a large N collective field theory.

Contribution

It introduces a novel interpretation of the bulk S-matrix via CFT correlators and proposes a large N collective field theory for local supergravity within the AdS/CFT framework.

Findings

Bulk S-matrix as a limit of scattering in AdS bubbles

Partitioning AdS to reconstruct transition amplitudes

Large N collective field theory for supergravity

Abstract

The AdS/CFT conjecture relates quantum gravity on Anti-de Sitter (AdS) space to a conformal field theory (CFT) defined on the spacetime boundary. We interpret the CFT in terms of natural analogues of the bulk S-matrix. Our first approach finds the bulk S-matrix as a limit of scattering from an AdS bubble immersed in a space admitting asymptotic states. Next, we show how the periodicity of geodesics obstructs a standard LSZ prescription for scattering within global AdS. To avoid this subtlety we partition global AdS into patches within which CFT correlators reconstruct transition amplitudes of AdS states. Finally, we use the AdS/CFT duality to propose a large N collective field theory that describes local, perturbative supergravity. Failure of locality in quantum gravity should be related to the difference between the collective 1/N expansion and genuine finite N dynamics.