OPEs and 4-point Functions in AdS/CFT Correspondence

TL;DR

This paper compares 4-point functions in AdS/CFT at strong and weak coupling, identifying an operator that changes its contribution and suggesting it is not a chiral primary with a large anomalous dimension.

Contribution

It reproduces known supergravity 4-point functions from a CFT perspective and identifies a non-chiral operator with large anomalous dimension at strong coupling.

Findings

Reproduced supergravity 4-point functions from CFT.

Discovered a non-chiral operator contributing at weak but not strong coupling.

Indicated large anomalous dimension for this operator at strong coupling.

Abstract

Recently D'Hoker et al. (1999) computed 4-point correlation functions of axion and dilaton fields in type IIB SUGRA on AdS_5 x S^5. We reproduce from a CFT point of view all power law singular terms in these AdS 4-point amplitudes. We also calculate a corresponding 4-point function in the weak coupling limit, g_{YM}^2 N -> 0. Comparison reveals the existence of a primary operator that contributes to these same singular terms in the weak coupling limit but which does not contribute to the power law singular terms of the type IIB SUGRA 4-point function. We conclude that this new operator is not a chiral primary and hence acquires a large anomalous dimension in the strong coupling regime.