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

Operator product expansions are applied to dilaton-axion four-point functions. In the expansions of the bilocal fields $\tilde{\mathrm{\Phi }}\tilde{\mathrm{\Phi }}$, $\tilde{C}\tilde{C}$ and $\tilde{\mathrm{\Phi }}\tilde{C}$, 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 $\lambda\geq 10$\mathrm{.}Theanomalousdimensions$\eta(l)$arecalculatedatorder$$\mathcal{O}$(N^{-2})$forboth$2^{-{1/2}}(-\tilde{\Phi}\tilde{\Phi} + \tilde{C}\tilde{C})$and$2^{-{1/2}}(\tilde{\Phi}\tilde{C} + \tilde{C}\tilde{\Phi})$andarefoundtobethesame,proving$U(1)_Y$symmetry\mathrm{.}Therelevantcouplingconstantsaregivenatorder$$\mathcal{O}$(1)$.