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