Correlation functions in the CFTd/AdSd+1 correspondence Original Research Article

Conformal techniques are applied to the calculation of integrals on AdSd+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 three gauge fields we compare in detail with the known conformal structure of the SU(4) flavor current correlator 〈JiaJjbJkc〉 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 〈JiaOIOJ〉 to 〈OIOJ〉 for (non-marginal) scalar composite operators OI, we find that there is a subtlety in obtaining the normalization of 〈OIOJ〉 from the supergravity action integral.