Correlation functions in the CFT(d)/AdS(d+1) correpondence

TL;DR

This paper uses conformal techniques to compute correlation functions in AdS/CFT, explicitly calculating 3-point amplitudes for scalar and gauge fields, and comparing results with known conformal structures and non-renormalization theorems.

Contribution

It provides explicit calculations of 3-point correlators in AdS supergravity and compares them with boundary conformal field theory results, highlighting subtleties in normalization from supergravity.

Findings

3-point amplitudes for scalar and gauge fields are explicitly calculated.

Results for gauge fields match the conformal structure of N=4 SYM correlators.

Identifies a subtlety in normalizing scalar correlators from supergravity.

Abstract

Conformal techniques are applied to the calculation of integrals on AdS(d+1) space which define correlators of composite operators in the superconformal field theory on the d-dimensional boundary. The 3-point amplitudes for scalar fields of arbitrary mass and gauge fields in the AdS supergravity are calculated explicitly. For 3 gauge fields we compare in detail with the known conformal structure of the SU(4) flavor current correlator <J_i^a J_j^b J_k^c> of the N=4, d=4 SU(N) SYM theory. Results agree with the free field approximation as would be expected from superconformal non-renormalization theorems. In studying the Ward identity relating <J_i^a O^I O^J> to <O^I O^J> for (non-marginal) scalar composite operators O^I, we find that there is a subtlety in obtaining the normalization of <O^I O^J> from the supergravity action integral.