Correlation functions in the CFT(d)/AdS(d+1) correpondence
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.
Cite
@article{arxiv.hep-th/9804058,
title = {Correlation functions in the CFT(d)/AdS(d+1) correpondence},
author = {Daniel Z. Freedman and Samir D. Mathur and Alec Matusis and Leonardo Rastelli},
journal= {arXiv preprint arXiv:hep-th/9804058},
year = {2009}
}
Comments
27 pages, LaTex, 1 eps figure, few misprints corrected, references added