On Large N Conformal Theories, Field Theories in Anti-De Sitter Space and Singletons

TL;DR

This paper explores the correspondence between large N conformal field theories and supergravity on AdS spaces, analyzing correlation functions, Wilson loops, and the role of singletons in the AdS/CFT framework.

Contribution

It extends the AdS/CFT correspondence to interacting theories, compares higher-point functions, and proposes a novel statistical behavior for singletons.

Findings

Matching spectra of states in both theories

Comparison of three- and four-point correlation functions

Proposal that singletons obey quantum Boltzmann statistics

Abstract

It was proposed by Maldacena that the large $N$ limit of certain conformal field theories can be described in terms of supergravity on anti-De Sitter spaces (AdS). Recently, Gubser, Klebanov and Polyakov and Witten have conjectured that the generating functional for certain correlation functions in conformal field theory is given by the classical supergravity action on AdS. It was shown that the spectra of states of the two theories are matched and the two-point correlation function was studied. We discuss the interacting case and compare the three- and four-point correlation functions computed from a classical action on AdS with the large N limit of conformal theory. We discuss also the large N limit for the Wilson loop and suggest that singletons which according to Flato and Fronsdal are constituents of composite fields in spacetime should obey the quantum Boltzmann statistics.