Conformal Field Theory Correlators from Classical Scalar Field Theory on $AdS_{d+1}$

TL;DR

The paper investigates the AdS/CFT correspondence by computing boundary CFT correlators from a classical scalar field on AdS_{d+1} at tree level. Starting with the free theory, it derives the Dirichlet Green's function and reproduces the boundary two-point function, establishing the standard conformal scaling. It then evaluates the bulk-interaction contributions, obtaining explicit expressions for the 3-point function and a conformally invariant representation of the 4-point function via Feynman parametrization and cross-ratio variables. The results demonstrate that classical bulk computations yield nontrivial CFT data and outline the extension to more complex fields such as fermions and gauge fields.

Abstract

We use the correspondence between scalar field theory on $AdS_{d+1}$ and a conformal field theory on $R^d$ to calculate the 3- and 4-point functions of the latter. The classical scalar field theory action is evaluated at tree level.