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 $\tilde{\Phi}\tilde{\Phi}$, $\tilde{C}\tilde{C}$ and $\tilde{\Phi}\tilde{C}$, the conformal fields which are symmetric traceless tensors of rank $l$ and have dimensions $\delta=2+l$ or $8+l+\eta(l)$ and $\eta(l)=\mathcal{O}(N^{-2})$ are identified. The unidentified fields have dimension $\delta=\lambda+l+\eta(l)$ with $\lambda\geq 10$. The anomalous dimensions $\eta(l)$ are calculated at order $\mathcal{O}(N^{-2})$ for both $2^{-{1/2}}(-\tilde{\Phi}\tilde{\Phi} + \tilde{C}\tilde{C})$ and $2^{-{1/2}}(\tilde{\Phi}\tilde{C} + \tilde{C}\tilde{\Phi})$ and are found to be the same, proving $U(1)_Y$ symmetry. The relevant coupling constants are given at order $\mathcal{O}(1)$.