Conformal partial wave analysis of AdS amplitudes for dilaton-axion four-point functions

Abstract

Operator product expansions are applied to dilaton-axion four-point functions. In the expansions of the bilocal fields $\tilde{\hat{I}}¦\tilde{\hat{I}}¦$, $\tilde{C}\tilde{C}$ and $\tilde{\hat{I}}¦\tilde{C}$, the conformal fields which are symmetric traceless tensors of rank $l$ and have dimensions $\hat{I}´=2+l$ or $8+l+\hat{I}\cdot (l)$ and $\hat{I}\cdot (l)=\mathcal{O}(N^{-2})$ are identified. The unidentified fields have dimension $\hat{I}´=\hat{I}»+l+\hat{I}\cdot (l)$ with $\hat{I}»\ge 10$. The anomalous dimensions $\hat{I}\cdot (l)$ are calculated at order $\mathcal{O}(N^{-2})$ for both $2^{-1/2}(-\tilde{\hat{I}}¦\tilde{\hat{I}}¦+\tilde{C}\tilde{C})$ and $2^{-1/2}(\tilde{\hat{I}}¦\tilde{C}+\tilde{C}\tilde{\hat{I}}¦)$ and are found to be the same, proving $U(1{)}_Y$ symmetry. The relevant coupling constants are given at order $\mathcal{O}(1)$.

27 pages, 1 graph, 12 figures, Corrections in eqns. (1.10), (1.11)